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The Hanning window and interpolation algorithm is used to the frequency estimation for voltage and current signals acquired in transformer terminal unit (TTU), and the algorithm is validated by the frequency estimation for actual voltage signals. On this basis, the influence of signal frequency, harmonic, signal-to-noise ratio (SNR), sampling duration, sampling frequency and quantization of analog digital converter (ADC) on the accuracy of frequency estimation is investigated based on the numerically generated voltage signal. The results reveal that the error is proportional to the difference between the actual signal frequency and the rated value (50 Hz). When the total harmonic distortion (THD) varies in the range of 0~10%, the error is almost independent of THD. The error decreases with SNR, and the rate of decrease reduces with SNR. The sampling frequency has little effect on the error when the sampling duration is kept constant. When the quantization bit varies from 4 to 16, it has little effect on the error. Suggestions on the selection of sampling parameters for TTU frequency analysis using the Hanning window and interpolation algorithm are also given.

Quantum control provides a pathway to extract more - and more useful - information from quantum sensors. In this presentation we will highlight a series of experimental and numerical studies demonstrating how quantum control can augment the performance of atomic and solid-state devices for gravimetry, precision navigation, and magnetometry. We begin with demonstrations that a class of cloud-compute-enabled AI agents can be used to autonomously optimize cold-atom loading and BEC production without user intervention. Next, we focus on the application of robust control to mitigate platform noise in fielded atom interferometers. We show 10X improvements interferometer visibility under realistic noise conditions, and also demonstrate up to 1000X improvements in sensitivity under transverse acceleration. Finally, we present novel operating techniques for magnetometry in cluttered environments, in which Slepian window functions are employed to suppress out-of-band sensitivity.

Objective: We aimed to develop a linear-systems model to evaluate the impact of mathematical assumptions related to multi-compartment 129Xe MRI methods. We employed a linear-systems approach to fill a knowledge gap associated with a single-point Dixon approach currently used for magnetization calculations and physiologic estimates. Methods: We generated a linear-systems model for magnetization calculations needed to generate multi-compartment 129Xe MRI data. 1Lung tissue and red-blood-cell compartments were isolated by acquiring data 90° out of phase and aligned with perpendicular quadrature channels. Results: In our linear-systems model, a single-lobe sinc-pulse in the time domain was used to excite 129Xe atoms in the tissue and red blood-cell compartments. We assumed that T2* exponential decay in the time domain was equivalent to convolution with a complex Lorentzian function in the frequency domain, and the gradient echo envelope was equivalent to convolution with a rectangular pulse with phase shifting. A rectangular window function and Dirac comb sampling in the time domain modeled analog-to-digital recording. Fast Fourier transforms were modelled by Dirac combs in both time and frequency domains. To account for non-uniform sampling, k-space was re-sampled using a unique sampling function convolution followed by Cartesian sampling. Phase inhomogeneities were corrected using reference gas and spectroscopy data. Conclusion: The proposed linear-system analysis provides a framework for modelling decay constants, peak overlap, and magnetization evolution common in multi-compartment 129Xe MRI. Understanding the spectral properties of 129Xe MRI will provide a way to identify novel compartments and their abnormalities in diverse pulmonary diseases.

An optimized depth-resolved dispersion compensation method for achieving better dispersion compensation effect is presented in optical coherence tomography signal processing. When performing depth-resolved dispersion compensation, it is necessary to use a rectangular window function to intercept the interference signals at different depths of the sample from the A-line signal before FFT. Windowed FFT will cause errors in phase extraction, which will lead to inaccurate dispersion coefficient. Herein, the rectangular window function needs to be optimized. The phase is extracted after FFT of the interference signal obtained by the primary rectangular window. According to the functional relationship between the phase and the wave number in the presence of dispersion, the obtained phase is fitted to the quadratic polynomial by the least square method, and the standard error of the fitted quadratic polynomial is used as the criterion. Constantly changed the width and center position of the rectangular window to obtain the smallest standard error. The smallest standard error corresponds to the optimized rectangular window, which is used to intercept the signal and perform FFT to obtain a phase close to the true value. Therefore, the dispersion compensation coefficients of the OCT system at different depths are accurately extracted. It is verified by simulation and experiment that this method can achieve better dispersion compensation effect.

An improved Blackman Harris apodization function is studied for rectify the shortcomings of large main lobe width of Blackman Harris apodization function in apodization processing of Fourier transform spectrometer. The basic principle of apodized interferogram is analyzed. The Chebyshev function with tunable parameters is introduced to improve Blackman Harris function. Compared with the original function through Matlab simulation, the improved apodization function shows not only the characteristics of main lobe width is enhanced, but also the side lobe attenuation can be adjusted, so the function is more flexible in engineering application.

In this work, we introduce the windowed generalized phase-shifting algorithms (WG-PSAs) using static and dynamic weighting functions/widows. These algorithms are derived from a weighted least square fitted to the monochromatic temporal fringe, thereby, the selection of the window plays an important role due to the fact that it shall reduce the influence of those intensities jeopardizing the phase estimation. In order to make the best selection, we propose to employ an adaptive/dynamic window which has the ability to detect the fringe patterns that jeopardize the phase retrieval. This window is computed iteratively by analyzing the error between the measured and fitted intensities. Furthermore, we provide the analysis of our scheme using the frequency transfer function (FTF) formalism for phaseshifting algorithms. Finally, we executed numerical experiments with synthetic data in which we compare the performance of the dynamic window versus several static ones from the state-of-the-art; although our scheme is more computationally expensive due to the iterative procedure, it works better than the traditional generalized PSAs with a window included or not.

Optimum sparse arrays and sensor placement is an effective tool for improving target detection and estimation capabilities, which is specifically true in the case of the limited system resources. In this paper, we propose a novel approach for maximizing the Signal-to-Interference plus noise ratio (MaxSINR) for receive beamforming applications in a computationally efficient manner. The proposed approach blends the concept of sparse array windowing function and the DFT approach, where the sparse array design is primarily conceived in the transformed domain. We show that the proposed objective function in the transform domain sorts the favorable sparse array configurations w.r.t. the average SINR performance. The proposed approach, therefore, facilitates the implementation of greedy sensor placement approach that permits sequential sensor selection. The transformed domain design is coupled with the sequential sensor placement allowing an efficient implementation.

Side lobe artifacts on point spread functions can be traced back to (1) fringe visibility variation across the spectrum, (2) errors in sampling instances, and (3) window functions. We demonstrate signal processing methods for correcting for all three of these issues. These methods require a system calibration step. If the systems slowly age, the recalibration step could be performed in the field with a fixtured target.

The inevitable noises and oscillation of generated terahertz (THz) signal subject to mechanism of hardware could distort and affect optical properties of the measured materials. Several well-known techniques used to attenuate oscillation and noises could achieve expectation. In this work, a piece of fractal artwork was chosen as the sample. Double Gaussian filtered inverse filtering (DGIF) and Hanning window inverse filtering (HIF) deconvolution techniques were employed to remove the oscillation of raw signal and ripples of THz B-scan image. A technique of composite multiscale entropy (CMSE) on complexity assessment of time series was introduced to compare the entropy profiles of the raw signal and two deconvovled signals.

The laser diode (LD) is modulated by the injection current of triangular waveform and a photo diode (PD) is packaged in the rear of the LD. The laser reflected by the target re-enters the cavity of LD and contains the target’s displacement information. The information is carried within the laser intensity and can be pickup by the PD. We call this laser intensity as self-mixing interferometry (SMI) signal. While processing the sensing SMI signals, we should carefully determine the windowing function and reduce the effect of windowing in the FFT and IFFT process while applying the mathematical model. Simulation results show that the proposed design is able to accomplish the measurement of micro-displacement with high resolution and great accuracy.

Resting heart rate (RHR) is considered an important biomedical indicator to evaluate cardiovascular function. High RHR is an important prognostic factor for sudden cardiac death and heart failure in the general population, and especially among patients with known cardiac disease. The imaging photoplethysmography (IPPG) technology is used to achieve the accurate detection of RHR signal, which has the advantages of low cost, simple operation, fast acquisition speed etc. In this paper, we propose a new simple, inexpensive and easy-to-use method to measure the RHR in vivo. The result shows that Fast Fourier Transform with Hamming window filters, band-pass filter gives more accurate results. The color change of the fingertip is enlarged by using the mobile phone camera. From the distribution of color change of the fingertip, the RHR is estimated with the primary calibration result of the relationship between color variation and the blood volume change.

In recent years, the synchrosqueezing transform (SST) has gained popularity as a method for the analysis of signals that can be broken down into multiple components determined by instantaneous amplitudes and phases. One such version of SST, based on the short-time Fourier transform (STFT), enables the sharpening of instantaneous frequency (IF) information derived from the STFT, as well as the separation of amplitude-phase components corresponding to distinct IF curves. However, this SST is limited by the time-frequency resolution of the underlying window function, and may not resolve signals exhibiting diverse time-frequency behaviors with sufficient accuracy. In this work, we develop a framework for an SST based on a "quilted" short-time Fourier transform (SST-QSTFT), which allows adaptation to signal behavior in separate time-frequency regions through the use of multiple windows. This motivates us to introduce a discrete reassignment frequency formula based on a finite difference of the phase spectrum, ensuring computational accuracy for a wider variety of windows. We develop a theoretical framework for the SST-QSTFT in both the continuous and the discrete settings, and describe an algorithm for the automatic selection of optimal windows depending on the region of interest. Using synthetic data, we demonstrate the superior numerical performance of SST-QSTFT relative to other SST methods in a noisy context. Finally, we apply SST-QSTFT to audio recordings of animal calls to demonstrate the potential of our method for the analysis of real bioacoustic signals., Comment: 20 pages, 6 figures, submitted to Proceedings of the SPIE Conference on Wavelets and Sparsity XVII (2017)

Computer-generated hologram(CGH) can encode the picture. The image, which equals the original object of traditional optics, can be divided into two parts. A portion of it encoding into Fourier computer generated hologram(CGH), while the remaining are coded into Fresnel computer generated hologram. So in the processing of information transmission, the possibility of being stolen details can be greatly reduced. When the image is coded into the Fourier CGH and Fresnel CGH and reached the receiving end, the original image should be obtained by the reconstruction of the two computer generated holograms. This article presents three important things. Firstly, it provides the recording and reconstruction - both of them consist of the holographic technique - of the source program of Fresnel CGH and Fourier CGH in MATLAB. MATLAB(Matrix Laboratory) is the abbreviation of Laboratory Matrix and commercial mathematical software produced by the United States company. Secondly, it isolates the original image and the conjugate image in regeneration of Fourier CGH by using all zero matrix. Even though the original image and the conjugate image can be separated, the two of them also prevent us to acquire the original message. For reserving the most important image, we should apply the window function to filter one of them. Finally, in the coding of Fourier CGH and Fresnel CGH, this passage describes several functions to decrease the noise of the original image which is encoded into program. The function can be available in Fourier CGH and Fresnel CGH.

The main lobe and the side lobes of strong scatterers are sometimes clearly visible in SAR images. Sidelobe reduction is of particular importance when imaging scenes contain objects such as ships and buildings having very large radar cross sections. Amplitude weighting is usually used to suppress sidelobes of the images at the expense of broadening of mainlobe, loss of resolution and degradation of SAR images. The Spatial Variant Apodization (SVA) is an Adaptive SideLobe Reduction (ASLR) technique that provides high effective suppression of sidelobes without broadening mainlobe. In this paper, we apply SVA to process COSMO-SkyMed (CSK) StripMap and Spotlight X-band data and compare the images with the standard products obtained via Hamming window processing. Different test sites have been selected in Italy, Argentina, California and Germany where corner reflectors are installed. Experimental results show clearly the resolution improvement (20%) while sidelobe kept to a low level when SVA processing is applied compared with Hamming windowing one. Then SVA technique is applied to Interferometric SAR image processing (INSAR) using a CSK StripMap interferometric tandem-like data pair acquired on East-California. The interferometric coherence of image pair obtained without sidelobe reduction (SCS_U) and with sidelobe reduction performed via Hamming window and via SVA are compared. High resolution interferometric products have been obtained with small variation of mean coherence when using ASLR products with respect to hamming windowed and no windowed one.

This article presents implementation of the Simulated Annealing (SA) algorithm for tapered fiber Bragg gratings (TFBGs) design. Particularly, together with well-known Coupled Mode Theory (CMT) and Transfer Matrix Method (TMM) the algorithm optimizes the group delay response of TFBG, by simultaneous shaping of both apodization function and tapered fiber transition profile. Prior to the optimization process, numerical model for TFBG design has been validated. Preliminary results reveal great potential of the SA-based approach and with proper definition of the design criteria may be even applied for optimization of the spectral properties of TFBGs.

In phase-shifting Fizeau interferometers, phase-shift errors and multiple-beam interference are the most common sources of systematic error affecting high-precision phase measurements. Nonsinusoidal waveforms can be minimized by applying synchronous detection with more than four samples. However, when phase-shift calibration is inaccurate, these algorithms cannot eliminate the effects of nonsinusoidal characteristics. Moreover, when measuring the surface profile of highly reflective samples, the calculated phase is critically determined not only by the decrease in the fringe contrast, but also by the coupling error between the harmonics and phase-shift errors. In this study, we calculate phase errors using phase-shifting algorithms that take into account the coupling error. We show that the 4 N – 3 algorithm, which consists of a polynomial window function and a discrete Fourier transform term, results in the smallest phase error. As a demonstration, the surface profile of a highly reflective silicon wafer is measured using a wavelength-tuning Fizeau interferometer and the 4 N – 3 algorithm.

Discrete Fourier transform (DFT) is one of the most wildly used tools for signal processing. In this paper, a novel sliding window algorithm is presented for fast computing 2D DFT when sliding window shifts more than one-point. The propose algorithm computing the DFT of the current window using that of the previous window. For fast computation, we take advantage of the recursive process of 2D SDFT and butterfly-based algorithm. So it can be directly applied to 2D signal processing. The theoretical analysis shows that the computational complexity is equal to 2D SDFT when one sample comes into current window. As well, the number of additions and multiplications of our proposed algorithm are less than those of 2D vector radix FFT when sliding window shifts mutiple-point.

Near real-time stereo based on effective cost aggregation is a local matching algorithm, it can achieve good accuracy and meet near real-time requirements. However, addition of supplementary window cost function in this method makes the edges of objects lose some precision. This paper proposes a novel stereo matching algorithm, whose aggregation strategies rely on segmentation. It can improve the matching accuracy and computational efficiency. First, dividing the left image into segments of homogeneous color with assume that disparity inside segments varies smoothly, then using the segmented image block as the matching window to search similar region in the right image. Second, the existing matching cost function includes segmentation window function and supplementary window cost function, former one tends to assign the same disparity value to all points belonging to the same segment, the latter reduces the dependence of the center pixel point on segmentation block in the high texture area and more dependent on pixels in neighborhood. However, this function makes the edges of objects lose some precision. Therefore, this paper proposes an adaptive supplementary window cost function using the image segmentation block size as adaptive parameter for added window, this function can not only solve mismatching in the high texture regions but also improve the precision at the edges of the objects. The experimental results demonstrate that our method shows the capabilities to improve the accuracy of fast local methods and can be regarded as an interesting trade-off between accuracy and speed, especially in regions of high texture and close to boundaries.

In breast X-ray imaging, breast texture has been characterized by a radial noise power spectrum (NPS) that has an inverse power-law shape with exponent β. The technique to estimate the radial power-law coefficient β is typically based on averaging 2-dimensional noise power spectra (NPS), calculated from partly overlapping image regions each weighted by a suitable window function. The linear regression applied over a selected frequency range to the logarithm of the 1- dimensional NPS as a function of the logarithm of the radial frequencies, gives β. For each step in this process, several alternative techniques have been proposed. This paper investigates the effect of image region of interest (ROI) size, image data windowing and alternative ways to determine radial frequency in terms of bias, variance and root mean square error (RMSE) in the estimated β. The effects of these three factors were analytically derived and evaluated using synthetic images with known β varying from 1 to 4 to cover the range of textures encountered in 2D and 3D breast X-ray imaging. Our results indicate that the RMSE in estimated β is smallest when the ROIs are multiplied with an appropriate window function and either no radial averaging or radial averaging with small frequency bins is applied. The ROI size yielding the smallest RMSE depends on several factors and needs to be validated with numerical simulations. In clinical practice however, there might be a need to compromise in the choice of the ROI size to balance between the RMSE magnitudes inherent to the applied β estimation technique and encompass the breast texture range so as to obtain an accurate shape of the NPS. When using 2.56 cm x 2.56 cm ROI sizes, applying a 2D Hann window and no radial frequency averaging, the RMSE in the estimated β ranges from 0.04 to 0.1 for true β values equal to 1 and 4. While many subtleties in real images were not modeled to simplify the mathematics in deriving our results, this work is illustrative in demonstrating the limits of commonly used algorithm steps to estimate accurate β values.

Digital holography (DH) is a 3D imaging technique with a theoretical axial accuracy of better than 1-2 nanome-ters. However, practically, the axial error has been quoted to be tens of nanometers which is much larger than the theoretical value. Previous studies of the axial error mainly focused on the phase error introduced by lens. However, it is found that CCD aperture size is also an important contributors to axial error by our group. It is necessary to investigate the reduction approach of such axial error. The most possible connection between the limited CCD aperture size and the axial error is the diffraction effect. Window functions once have been applied to digital holograms for diffraction suppression and improve the lateral resolution of the intensity image. How-ever, their impacts on phase image and the associated axial dimension measurement are still unknown. In this paper, window functions are applied to digital holograms for phase/axial error reduction. Both simulation and experiment are performed. Moreover, the relation between axial error and window functions is also illustrated by the mathematical formulas derived in the theory. And all the results validate that the window functions can reduce the axial error of digital holography. Published version

When observing unchanging targets or slow-changing targets, a rotating array can be used instead of a stationary array in an interferometric radiometer to reduce the complexity and the cost. The configuration of a stationary array determines its coverage in spatial frequency domain. But for a rotating array, the baselines were distributing on a series of concentric circles with radiuses of the baseline lengths, no matter what its configuration was. According to the characteristics of the distribution of the baselines, the expressions of system sensitivity and spatial resolution of a rotating interferometric radiometer were deduced in thwas paper. For a rotating interferometric radiometer with big synthetic aperture, like the Geostationary Interferometric Microwave Sounding (GIMS) prototype, it was very difficult to find a suitable calibration source to measure the system sensitivity. Therefore, the system sensitivity of the GIMS prototype was estimated based on the sensitivity of all channels by the sensitivity formula. Since the array factor of an interferometric radiometer was the pulse response of a point target, the spatial resolution of the GIMS prototype obtained by imaging an artificial quasi point target was used to demonstrate the formula in this paper, and the results were nearly identical. In addition, some different window functions were used to weight visibility samples of the prototype, and their effects on the sensitivity and the spatial resolution were analyzed. The principle of selecting the weighted window was described at the end.

In this paper, the authors have investigated whether the noise whitening procedure developed as a preprocessing step before despeckling of detected images may be useful also in contexts where phase information is exploited. In a preliminary test set, an interferometric pair of COSMO-SkyMed StripMap images, featuring industrial buildings and vegetated areas, has been: 1) focused without Hamming window (aimed at improving the focusing of targets at the cost of introducing a spatial correlation of background noise), starting from raw data. 2) focused with Hamming window, starting from raw data; 3) preprocessed for complex noise whitening, starting from data at point 2). From the complex interferograms, coherence and interferometric phase maps have been calculated for the three cases by means of boxcar filtering. In case 1) coherence is low on vegetation and also suffers from spreading of areas characterized by strong backscattering because of the presence of high sidelobes. In case 2) points targets and buildings in general are much more defined, thanks to the sidelobe suppression achieved by Hamming filtering, but the background coherence is abnormally increased, due to the introduction of a spatial correlation. Case 3) is the most favorable because whitening operation carries out low coherence on vegetation and high coherence on buildings, where the effects of Hamming filtering are retained. An analysis of the phase field reveals that case 3) should be expedited also in terms of phase unwrapping. Thus, the whitening procedure, devised as a blind preprocessing patch of SLC data, with the goal of a better despeckling, is useful also for SAR interferometry, in which the tradeoff, dictated by the coefficient of the Hamming window, between the ideal situations of focused targets and uncorrelated speckle may be relaxed.

A recently developed technique for phase imaging using table top sources is to use multiple fine-pitch gratings. However, the strict manufacturing tolerences and precise alignment required have limited the widespread adoption of grating-based techniques. In this work, we employ a technique recently demonstrated by Bennett et al.1 that ultilizes a single grid of much coarser pitch. Phase is extracted using Fourier processing on a single raw image taken using a focused mammography grid. The effects on the final image of varying grid, object, and detector distances, window widths, and of a variety of windowing functions, used to separate the harmonics, were investigated.

Surface profilers and optical interferometers produce 2D maps of surface and wavefront topography. Traditional standards and methods for characterizing the properties of these surfaces use coordinate space representations of the surface topography. The computing power available today in modest personal computers makes it easy to transform into frequency space and apply well-known signal processing techniques to analyze the data. The Power Spectral Density (PSD) function of the surface height distribution is a powerful tool to assess the quality and characteristics of the surface in question. In order to extract useful information about the spectral distribution of surface roughness or mid-spatial frequency error over a particular spatial frequency band, it is necessary to pre-process the data by first detrending the surface figure terms and then applying a window function before computing the PSD. This process eliminates discontinuities at the borders of the profile that would otherwise produce large amounts of spurious power that would mask the true nature of the surface texture. This procedure is now part of a new draft standard that is being adopted by the US OEOSC for analysis of the statistics of optical surface, OP1.005. 1 Illustrations of the usefulness of these procedures will be presented.

For the surface shape measurement of a semiconductor with a highly reflective index, it is im portant to effectively suppress the harmonic signal s from multi ple reflection s. In application, the phase extraction algorithm should have a maximum value when there is no phase -shift miscalibration. In this presentation, a new 4N - 3 phase extraction algorithm , which has the ability to suppress harmonic signal s and exhibits a fringe contrast maximum value when there is no phase -shift error , was derived. This n ew 4N - 3 algorithm consists of a new polynomial window function and a discrete Fourier transform term and has the ability to compensate for 2 nd -order nonlineari ty in the phase shift. The suppression ability of the new polynomial window function is compared with other conventional window functions. The sampling functions of the new 4N - 3 algorithm have much smaller amplitudes in the vicinity of the detection freq uency than does synchronous detection or other phase extraction algorithm s with conventional window functions . Keywords: H ighly reflective index, p hase measurement, nonlinearity, window function

We demonstrate a task-based assessment of image quality in dedicated breast CT in order to optimize the number of projection views acquired. The methodology we employ is based on the Hotelling Observer (HO) and its associated metrics. We consider two tasks: the Rayleigh task of discerning between two resolvable objects and a single larger object, and the signal detection task of classifying an image as belonging to either a signalpresent or signal-absent hypothesis. HO SNR values are computed for 50, 100, 200, 500, and 1000 projection view images, with the total imaging radiation dose held constant. We use the conventional fan-beam FBP algorithm and investigate the effect of varying the width of a Hanning window used in the reconstruction, since this affects both the noise properties of the image and the under-sampling artifacts which can arise in the case of sparse-view acquisitions. Our results demonstrate that fewer projection views should be used in order to increase HO performance, which in this case constitutes an upper-bound on human observer performance. However, the impact on HO SNR of using fewer projection views, each with a higher dose, is not as significant as the impact of employing regularization in the FBP reconstruction through a Hanning filter.

Among structural health mon itoring techniques, nonlinear ultrasonic spectroscopy methods are found to be effective diagnostic approach to detecting nonlinear damage such as fatigue crack, due to their sensitivity to incipient structural changes. In this paper, a nonlinear ultrasonic modulation method was developed to detect and locate a fatigue crack on an aluminum plate. The method is different with nonlinear wave modulation method which recognizes the modulation of low -frequency vibration and high -frequency ultrasonic wave; it reco gnizes the modulation of tone burst and high -frequency ultrasonic wave. In the experiment , a Hanning window modulated sinusoid al tone burst and a continuous sinusoidal excitation were simultaneously imposed on the PZT array which was bonded on the surface of an aluminum plate. The modulation s of tone burst and continuous sinusoidal excitation was observed in different a ctuator -sensor path s, indicating the presence and location of fatigue crack . The results of experiments show that the proposed method is cap able of detecting and locating the fatigue crack successfully. Keywords: SHM , Damage detection , Fatigue crack , N onlinear ultrasonic modul ation, STFT, PZT array, Damage I ndex, Imaging

Due to the finite size of the hologram aperture in digital holography, high frequency intensity and phase fluctuations along the edges of the images, which reduce the precision of phase measurement. In this paper, the apodization filters are applied to improve the phase measurement in the digital holography. Firstly, the experimental setup of the lensless Fourier transform digital holography is built, where the sample is a standard phase grating with the grating constant of 300μm and the depth of 150nm. Then, apodization filters are applied to phase measurement of the sample with three kinds of the window functions: Tukey window, Hanning window and Blackman window, respectively. Finally, the results were compared to the detection data given by the commercial white-light interferometer. It is shown that aperture diffraction effects can be reduced by the digital apodization, and the phase measurement with the apodization is more accurate than in the unapodized case. Meanwhile, the Blackman window function produces better effect than the other two window functions in the measurement of the standard phase grating.

A procedure is proposed to reconstruct the radar cross section (RCS) of interested targets from synthetic aperture radar (SAR) images. Key factors in imaging are considered for exact RCS reconstruction, including image defocusing from target motion, system over-sampling, window function, zero-padding and image calibration. Experimental results for both numerically calculated inverse SAR (ISAR) and spaceborne SAR image demonstrate the effectiveness and accuracy of the proposed technique.

Accurate propagation models are required for predicting the propagation of electromagnetic waves within complex environments. This paper proposes the use of a new method to accurately compute the divergence and curl of electromagnetic fields. The computation of the derivatives of vector fields is normally approximated using numerical methods such as the Finite-Dierence Time-Domain Method (FDTD), the Finite Integration Technique and the Multi-Resolution Time-Domain Method. These methods are all limited in terms of their accuracy, resolution, computational efficiency and numerical stability. This paper introduces a new method for computing derivatives based on Two-Dimensional (2D) Digital Signal Processing (DSP) techniques. The method involves computing a numerical approximation of the derivative of a function by considering the frequency domain definition of the derivative and designing a 2Dfinite impulse response (FIR) filter that implements the differentiation. Appropriate windowing functions are used to ensure that the FIR response is as close to the ideal 2D differentiator response as possible. This paper provides an example where the curl of a vectorfield is determined using this method and accuracy within a few percent is achieved. The proposed innovative method can be extended to three dimensions and used to find numerical solutions of Maxwells Equations, thus allowing it to be applied to the design of accurate propagation models.© (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Synthetic aperture (SA) imaging techniques can enhance spatial resolution in medical ultrasound imaging. However, it suffers from the degradation of image quality close to a virtual source (e.g., transmit focal point) since there is no enough transmit acoustic field energy. In this paper, a new SA imaging technique (i.e., dynamic synthetic aperture, DSA) where the number of synthetic scanlines for acoustic field superposition is dynamically adjusted based on the transmit acoustic field analysis. For the DSA technique, the dynamic apodization window function was generated from the Field II simulation and applied in the phantom and in vivo experiments. The raw radio-frequency (RF) data for phantom and in vivo experiments were captured by an Ultrasonix's SonixTouch research platform connected with a SonixDAQ parallel acquisition system. From the phantom experiment, the proposed DSA method shows the enhanced spatial resolution over the depth compared to the conventional receive dynamic focusing (CRDF). In addition, it doesn't yield any artifacts associated with the lack of enough transmit acoustic energy shown in the conventional SA imaging technique. The consistent results were obtained with the in vivo breast data. This result indicates that the proposed DSA method could be used for enhancing image quality of medical ultrasound imaging.

Orthogonal Frequency Division Multiplexing (OFDM) is the primary modulation technique used for Integrated Services for Digital Broadcasting for Terrestrial (ISDB-T). However, the performance of OFDM systems is often affected by impulsive noise significantly. In this paper, we propose an adaptive scheme of impulsive noise suppression for ISDB-T receivers. We detect the position and burst duration of impulsive noise by using guard band in frequency-domain, and use an adaptive window function to suppress the impulsive interference in time-domain. Simulation results confirm the validity of the proposed scheme for ISDB-T receivers in AWGN channel and Rayleigh fading channel.

We propose a new phase retrieval technique using a windowed Fourier transform (WFT) method for fringe pattern analysis to obtain a high-resolution phase map. The WFT method has been studied to improve the noise robustness of FT methods. In our proposed technique, an extra step is added to isolate the WFT spectrum containing phase information from other spectra, which is effective when a narrow window function is used for the high-resolution phase map. We demonstrate phase retrieval along both x- and y-axes from a two-dimensional fringe pattern obtained by X-ray Talbot imaging. Differential phase maps in high resolution with effective noise reduction are retrieved by the proposed method.

The calculation for the spectrum of beams passing through a multi-apertured ABCD optical system has not been finished in any personal computer when the aperture number is more than a certain value. By means of the expansion of the window function of the hard-edge aperture into a finite sum of complex Gaussian functions, an approximate analytical expression for the spectrum of polychromatic Gaussian beams passing through a multi-apertured ABCD optical system is derived and illustrated with numerical examples. The numerical results find an agreement with those by straightforward integral of the cross-spectral density function, but the computing time is strongly reduced. Key words: Laser optics; fast algorithm; multi-apertured ABCD optical system ; spectrum 1.Introduction In the past twenty years, much interest was focused on the spectral behavior of spatially fully and partially coherent polychromatic beams during propagation e and extensive theoretical and experimental studies of the spectral changes includi ng spectral shifts and spect ral switches have been made

Noise excitation sources in radar systems have become increasingly useful in applications requiring wideband spectral responses and covertness. However, in applications requiring spectral controllability, traditional analog noise sources prove troublesome and require additional hardware such as sets of digital filters whose own spectral characteristics must also be accounted for. In an effort to reduce these issues and increase the applications of noise waveforms, a technique for generating a fully controllable pseudo-noise waveform is presented. This pseudo-noise waveform will be generated through the use of a multi-tone waveform. By randomizing the phase angles and setting the appropriate amplitudes to the individual tones, the result is a waveform whose temporal pattern resembles noise and frequency response is broadband. The capabilities of this digitally produced pseudo-noise multi-tone waveform is presented by optimization via a water-filling technique, thereby producing a flat spectral response for a user defined amplitude, effectively removing the spectral effects of the radar components. This optimized waveform is used to present methods for increasing signal to noise ratio (SNR) of cross-correlated responses of the waveform through the application of window functions to the waveform. As a whole, this paper showcases the ability to use this pseudo-noise multi-tone waveform for complete ultra-wideband (UWB) spectral control through water-filling and a method for increasing SNR of the cross correlated response of the transmitted and received radar waveform for a bandwidth of 2.5 GHz ranging from 2 to 4.5 GHz.

A method for obtaining windowing functions for focused range-doppler imaging of rotation objects is given. Focused range-doppler imaging of rotation objects involves the evaluation of a non-standard transform rather than the discrete Fourier transform. As such, familiar windowing functions such as Hamming are inappropriate for sidelobe control. Previous methods of evaluation involve resampling and interpolation to emulate the discrete Fourier transform. In this paper, a correction factor applied to any standard window function is derived and results shown.

Focusing and apodization are an essential part of signal processing in ultrasound imaging. Although the fundamental principles are simple, the dramatic increase in computational power of CPUs, GPUs, and FPGAs motivates the development of software based beamformers, which further improves image quality (and the accuracy of velocity estimation). For developing new imaging methods, it is important to establish proof-of-concept before using resources on real-time implementations. With this in mind, an effective and versatile Matlab toolbox written in C++ has been developed to assist in developing new beam formation strategies. It is a general 3D implementation capable of handling a multitude of focusing methods, interpolation schemes, and parametric and dynamic apodization. Despite being flexible, it is capable of exploiting parallelization on a single computer, on a cluster, or on both. On a single computer, it mimics the parallization in a scanner containing multiple beam formers. The focusing is determined using the positions of the transducer elements, presence of virtual sources, and the focus points. For interpolation, a number of interpolation schemes can be chosen, e.g. linear, polynomial, or cubic splines. Apodization can be specified by a number of window functions of fixed size applied on the individual elements as a function of distance to a reference point, or it can be dynamic with an expanding or contracting aperture to obtain a constant F-number, or both. On a standard PC with an Intel Quad-Core Xeon E5520 processor running at 2.26 GHz, the toolbox can beamform 300.000 points using 700.000 data samples in 3 seconds using a transducer with 192 elements, dynamic apodization in transmit and receive, and cubic splines for interpolation. This is 19 times faster than our previous toolbox.

Beam characterization is of critical importance when analyzing and interpreting data from Cosmic Microwave Background (CMB) experiments. In this paper we present scanning strategies, data analysis methods and results of the 44 GHz (Q-Band) beam characterization for the Q/U Imaging ExperimenT (QUIET) Phase- I, using the Crab nebula (Tau A) and Jupiter as polarized and unpolarized point sources, respectively. The beams are modeled as a sum of gaussian terms multiplied by orthogonal polynomials after symmetrization using observations taken at different rotation angles about the optical axis. The l-space window function calculation procedure is explained and applied, along with the corresponding propagation of parameter uncertainty. These window functions encode the effect of the finite resolution of the instrument on its ability to measure the angular power spectrum, as a function of multipole . Additionally, the instrumental polarization is characterized in terms of two-dimensional Mueller fields which describe the coupling of the Stokes parameters. The data presented in this work were collected during the first season of QUIET observations that started in October 2008.

In this paper we develop spectral models for windowed speckle-modulated continuous coherent ladar signals with arbitrary coherence time as a function of the window duration and shape. This processing chain (compute the spectrum of the window random signal) is typical for many coherent ladar applications where the target is distributed in range, such as wind lidar. We link the peak of the spectrum to the signal's carrier-to-noise ratio (CNR) and the number of integrated signal photoelectrons. We also develop theoretical models for the SNR of the integrator output and the resultant coherent integration efficiency. In addition, we generalize Goodman's rectangular integrator diversity model to arbitrary window functions and show that the product of diversity and efficiency is close to one for arbitrary integration times and window functions. These general models are then applied to various signal autocorrelation functions and window functions. The analysis demonstrates that the shape of the window function has little impact on the output SNR, efficiency and speckle diversity. We show that if the coherence time is long compared to the integration time then the conventional CNR expression is valid, and the signal has unit diversity and the coherent integration efficiency is 100%. However, when the coherence time is short compared to the integration time, the CNR is reduced by roughly the ratio of these times and the diversity is increased by roughly the same factor. Finally, we also show how signal detectivity is related to SNR and diversity.

Most contemporary still and video cameras employ various optically birefringent materials as optical low-pass filters (OLPF) in order to minimize alias artifacts in the image. Due to the slope characteristics of these filters, camera designers are faced with the choice of either under correcting to maintain image resolution, allowing some aliasing, or eliminating aliases with a more aggressive design that will also compromise the image modulation transfer function (MTF). Furthermore, most OLPFs are designed as optical elements with a frequency response that does not change even if the frequency responses of other elements of the capturing systems are altered. In this paper, we demonstrate the use of a parallel optical window or, alternatively, a rigid mirror positioned between a lens and an imager as an OLPF. Controlled x- and y-axis rotations of the window and the mirror result in a manipulation of the point spread function (PSF) of the system and frequency content of imaged continuous scenes. We evaluate the system MTF when various window functions are used to shape PSF, such as rectangle, triangle, Blackman-Harris etc. We also present results of our experiments when the dynamic OLPF's support and shape are altered to accommodate the optical performance of lenses and imager characteristics.

Multi-temporal remote sensing image registration is the key step of change detection, and because of the remarkable difference and the probably unknown of sensor parameters, the automatic registration of different temporal remote sensing images is very difficult. Image registration based on Fourier-Mellin transform(FMT) is a global and phase correlation method, which is based on Fourier and Log-polar transform. This method finds the transformation parameters for registration of the images while working in the frequency-domain and it is resilient to noise, occlusions and so on. In this paper, an improved approach based on Fourier-Mellin algorithm is proposed for the registration. Spectrum aliasing and resampling interpolation will bring errors during Fourier-Mellin transform. To get a better registration result, we have improved it by adding window function and filtering to reduce spectrum aliasing and increase the robustness.

A new processing technique called Non-Harmonic Analysis (NHA) is proposed for OCT imaging. Conventional Fourier-Domain OCT relies on the FFT calculation which depends on the window function and length. Axial resolution is counter proportional to the frame length of FFT that is limited by the swept range of the swept source in SS-OCT, or the pixel counts of CCD in SD-OCT degraded in FD-OCT. However, NHA process is intrinsically free from this trade-offs; NHA can resolve high frequency without being influenced by window function or frame length of sampled data. In this study, NHA process is explained and applied to OCT imaging and compared with OCT images based on FFT. In order to validate the benefit of NHA in OCT, we carried out OCT imaging based on NHA with the three different sample of onion-skin,human-skin and pig-eye. The results show that NHA process can realize practical image resolution that is equivalent to 100nm swept range only with less than half-reduced wavelength range.

Support vector machines (SVMs) have become useful and universal learning machines. SVMs construct a decision function by support vectors (SVs) and their corresponding weights. The training phase of SVMs definitely uses all training samples, which leads to a large computational complexity for a large scale sample set. Moreover support vectors could not be found until a quadratic programming (QP) problem is solved. Actually we know only SVs play a role in the decision function. Hence, pseudo density estimation (PDE) is presented to extract a set of boundary vectors (BVs) which may contain SVs. The PDE method is a variant of Parzen window method. Hyperspheres are considered as the window functions. In our method, for each sample we construct a hypersphere with an unfixed radius. The ratio of the number of samples contained in the hypersphere of a sample to the total training samples can be taken as the pseudo density of the corresponding sample. The set of BVs is taken as the training input to SVMs. In doing so, it speeds the training procedure of SVMs. It is convenient for PDE to determine its parameter. The experiments show that SVMs using PDE have the similar generalization performance to SVMs.

Work is devoted to important topic of acoustic signals processing in a pilot's cabin of aircraft in which the high noise level is observed. We have investigated heuristic approach of acoustic signal nonlinear filtration. First of all the kernel estimate of the cumulative distribution function was done. The signal was transformed using the estimate of the cumulative distribution function as a functional transform. Then measurements of acoustic signals' parameters and an estimation of their spectral density were done. The estimation was measured by means of fast Fourier transform procedure with use of window functions. At the second stage the new procedure of the adaptive filtration based on the Wiener frequency approach has been offered. The estimations of spectra received at the first stage have been thus used. Results are confirmed by experimental processing of spoken language signals.

In this paper, we simulate sensor behavior by synthesizing different features of a sensor output under normal mode of operation. Any deviation from the normal behavior indicates a change. The synthesized features indicate behavior of different physical processes that a sensor is monitoring. The shapes of these features must be extracted from sensor output for sensor health management. The extracted features are compared to features of healthy sensor to monitor its performance. In this paper, we compare Fourier and Wavelet Transform methods for extraction of the sensor output features. The wavelet Transform Analysis is performed on the simulated data described above with Poisson distributed noise. The simulated data with Poisson distributed noise of SNRs ranging from 10 to 500 are generated. The data are analyzed using Discrete as well as Discretized Continuous Wavelet Transforms. The Short-Time Fourier Transform of the Signal is taken using the Hamming window. Three window widths are used. The DC value is removed from the windowed data prior to taking the FFT. The resulting three dimensional spectral plots provide good time frequency resolution. The results indicate distinct shapes corresponding to each process.

A new deflection tomography system was put forward and named Auto-adapted Iterative Deflection Tomography (AIDT). It was tested to approach accurate reconstruction of a high frequency field containing shock waves with sufficient projections. A high frequency field was constructed with Gauss and rectangle window functions. It was simulated to project in all directions with angle resolving rate per degree. Two cross projections was selected to simulate reconstructing the model field by AIDT. Then, the number of projections was increased step by step in order to approach the accurate values of the model. All reconstructed results were studied. As a result, all high frequency sections are distorted much. With a few projections, such as two projections, the reconstructed results lost the basic characteristics of the model. With projections increasing, the distortions get lighter and lighter. Near the critical projections, such as twenty-four projections, the reconstructed field becomes similar to the model except some high frequency sections. When eighty-four projections are employed, the reconstructed result is in accord with the model. In this case, the Mean Square Error(MSE) is 0.00003609. But up to one hundred and eighty projections, the reconstructed result almost stopped improving. In this case, the MSE is 0.00003231. As we know, these are most accurate reconstructions to now. AIDT can accurately reconstruct high frequency fields with shock waves.

A new deflection tomography algorithm was suggested and tested with a simulated flow field. The programs calculating deflection projection and inverse projection were worked out based on optical refraction principle and mathematical, physical significance of tomography. With our home-made Simple Self-correlative Algebraic Reconstruction Technique (SSART), a new deflection tomography algorithm was programmed and named auto-adapted deflection tomography system . A section of a complex flow field was simulated with Gauss and rectangle window functions. One positive and one negative Gauss peaks were constructed on the section in order to make the model contain double-polar components. One square tower was constructed on the section in order to make the model contain much more high-frequency waves. The deflection projections were figured out according to the tomography algorithm with direction interval one degree. So, we got 180 direction projections in total. 12 projections were selected out by direction step 15 degree, and 84 projections were picked out by direction interval 2 or 3 degree. The section was reconstructed with the projections by SSART. The reconstructed results were compared with the model. The reconstructive effect was estimated with Mean-square error(MSE) and Peak error(PE). As the result, the system could reconstruct the simulated field accurately. With twelve projections, MSE was about from 0.0001 to 0.0006 at the end of 300 cycle iterations, and PE was about from 0.007 to 0.020. With selected 84 projections, the MSE was 0.00000999, and PE was 0.00013142. So, the auto-adapted deflection tomography system can accurately reconstruct complex flow fields.

FIR filter has some advantages, such as system stability, simple implement, and linear phase. It has been widely used in digital signal processing and other relative fields. Clonal selection algorithm has been applied successfully in solving problems like memory acquisition, multi-modal optimization and traveling salesman problem. This paper proposes a novel FIR filter design method. It combines clonal selection algorithm and window function method to achieve optimization. In the design process, float coding is adopted to increase the convergence precision. Some simulation experiments are carried out to verify the performance of the presented algorithm. The results show that the introduced method is able to design some FIR filter which is difficult for other methods. The filter design approach discussed in this paper is universal and easy to implement.

In such applications as fast 3D imaging with 2D arrays and point-of-care imaging with an ultra portable devices, periodic sparse arrays(PSA) can be efficiently used to increase the effective aperture size with less number of active elements than the conventional method. Generally, PSA can be represented as sub-arrays distributed uniformly in P -element intervals, each with L consecutive elements, where L < P. Since the continuous wave beam pattern in the far-field is given by Fourier transform of aperture function, the beam pattern of PSA is a multiplication of beam patterns of the upsampled dense array by the ratio of P and L -elements sub-array. A recent method to design a PSA pair provides analytically the values of P and L for transmit and receive arrays to eliminate the dominant grating lobes, which occur at the same position on both transmit and receive. In this work, we present a method to design a PSA pair with improved performance by further suppressing the residual grating lobes of PSA. It can be accomplished by properly shading amplitude of the transmit and receive sparse arrays. This shading window function is also obtained by signal analysis of aperture functions. The beam patterns of various PSA pairs based on the proposed design method are evaluated through computer simulations. The simulation results show that the residual grating lobes are reduced by about 10dB more in all cases. Consequently, our method can be used to improve the performance of beam pattern or enhance the periodicity of sparse array.

We propose another window function used in production process of A-line by Fourier transform in optical frequency domain imaging. It is shown that cosine tapered window has an advantage over Gaussian window employed conventionally.