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Context. The integrals of highly oscillating functions of many variables are one of the central concepts of digital signal and image processing. The object of research is a digital processing of signals and images using new information operators. Objective. The work aims to construct a cubature formula for the approximate calculation of the triple integral of a rapidly oscillating function of a general form.Method. Modern methods of digital signal processing are characterized by new approaches to obtaining, processing and analyzing information. There is a need to build mathematical models in which information can be given not only by the values of the function at points, but also as a set of traces of the function on the planes and as a set of traces of the function on the lines. There are algorithms which are optimal by accuracy for calculating the integrals of highly oscillating functions of many variables (regular case), which involve different types of information in their construction. As a solution of a broader problem for the irregular case, the work presents the cubature formula for the approximate calculation of the triple integral of the highly oscillating function in a general case. The presented algorithm for approximate calculation of the integral is based on the application of operators that restore the function of three variables using a set of traces of functions on the mutually perpendicular planes. Operators use piece-wise splines as auxiliary functions. The cubature formula correlates with a formula of the Filon type. An error estimation of the approximation of the integral from the highly oscillating function by the cubature formula on the class of differential functions is obtained.Results. The cubature formula of the approximate calculation of the triple integral from the highly oscillating function of a general form is researched.Conclusions. The experiments confirm the obtained theoretical results on the error estimation of the approximation triple integral from the highly oscillating function in a general form by the cubature formula. The prospect of further research is to obtain an estimation of the approximation error on wider classes of functions and to prove that the proposed cubature formula is optimal by the order of accuracy.

This study investigates the effect of some radio climatic factors on the Received Signal Strength (RSS) of a Digital Terrestrial Television Broadcast Station (DTTBS) in Katsina City, Nigeria. The RSS was measured at intervals along selected routes around the station using a digital signal strength meter. GPS receiver was used to log the line of sight, geographic coordinates and heights of data points from the station. The atmospheric pressure, temperature and humidity corresponding to data points were concurrently measured using a compact weather station whereas the corresponding surface radio refractivity (Ns) values were computed. Data were collected during dry and wet season months’ in the year 2017. Results shown that, Ns is inversely proportional to RSS irrespective of routes and seasons with correlation coefficients of -0.51 and -0.57 during dry and wet season months respectively. Higher mean value of, 358.50 (N-units) was deduced during wet compared to the dry season months of 301.20 (N-units). Average atmospheric pressure of 951.92 and 949.61 (hPa) and as well as humidity values of 32.25 and 77.93 %RH were deduced during dry and wet season months’ respectively. Findings also show that pressure is inversely proportional to RSS. The overall effects of pressure, temperature and humidity on RSS is better understood using the effect of Ns since the latter is derived from those parameters. This study concludes that the specified radio climatic factors have attenuation effect on UHF signal and should be put into consideration when planning link’s design and power budgets on the UHF band.

The problem of automatic parasitic chirp components detection and suppression in a digital signal is considered. The detection is based on the calculation of the discrete Wigner distribution accompanied by the Hough transform. The filtration is achieved by a series of discrete fractional Fourier transforms converting the signal to special coordinates, where the entire energy of the parasitic signals is accumulated at a few samples and then reset. The main novelty is the utilization of new construction of discrete fractional Fourier transform coordinated with the discrete Wigner distribution. The advantages of the proposed approach are illustrated by the simulations.

In the field of digital signal analysis and processing, the ubiquitous domain transformation is the discrete Fourier transform (DFT), which converts the signal of interest within a limited time window from discrete time to the discrete frequency domain. The active use in real-time or quasi-real-time applications has been made possible by a family of fast implementations of the DFT, called fast Fourier transform (FFT) algorithms.

One of the first things analysts will begin to do as data is transcribed from an ET signal or artifact is to examine its information entropy or Shannon entropy. This is a measure of how many bits of information are represented by each symbol or state within a message or information density. The areas of the message that contain lots of repetition, white space, and obvious structure will have a low information density relative to parts of the message that are efficiently encoded. Efficiently encoded regions will look more like random noise. Lowdensity regions are interesting because this is where we are most likely to find more easily decoded information, such as uncompressed images, diagrams, etc. This form of analysis will work for any series of digits or symbols and can be used to map the information density of any digital signal, whether its code is binary or any other numeric base system.

Texture analysis and classification of image components belong to common problems of the interdisciplinary area of digital signal and image processing. The paper is devoted to the pattern matrix construction using features evaluated by the discrete Fourier transform (DFT) or the discrete wavelet transform (DWT) using the relative power in selected frequency bands or scale levels, respectively. Image features are then used to recognize groups of similar pattern vectors by self-organizing neural networks forming a mathematical tool for cluster analysis. Further classification methods including the decision tree, support vector machine, nearest neighbour method and neural networks are then applied for construction of specific models and evaluation of their accuracy and cross validation errors. The proposed algorithm is applied for analysis of given microscopic images representing wax structures covering breathing openings on leaves affected by environmental pollution in different locations. The classification accuracy depends upon the method used and it is higher than 92% for all experiments.

The elevation detection accuracy of the laser receiver in the laser levelling control system directly affects land-levelling operations. To effectively improve the effect of levelling operations and meet the requirements for the accuracy of elevation detection in different industries, this study optimization designed a multilevel adjustable laser receiver. First, we examined the laser signal detection technology and processing circuit, designed the photoelectric conversion array for the detection of the rotating laser, and converted it into a photocurrent signal. We also designed the filter, amplifier, and shaping and stretching circuits for analogue-to-digital conversion of the photocurrent signal. The digital signal was calculated based on the deviation of the elevation by using a microprocessor and was output by a controller area network (CAN) bus. The laser beam spot diameter transmission and diffusion were then studied, and with the detectable spot diameters were compared and analyzed. Accordingly, an algorithm was proposed to calculate the deviation of laser receiver elevation. The resolution of the elevation deviation was set to &plusmn, 3 mm, however, this value could be adjusted to &plusmn, 6 mm, &plusmn, 9 mm, &plusmn, 12 mm, and &plusmn, 15 mm, according to the requirements. Finally, the laser receiver was tested and analyzed, and the test results of the elevation detection accuracy showed that when the laser receiver was within a radius of 90 m, the elevation detection accuracy was within the &plusmn, 3 mm range. The outcomes of the farmland-levelling test showed that the standard deviation S d of the field surface decreased from 9.54 cm before levelling to 2.42 cm after levelling, and the percentage of sampling points associated with absolute errors of &le, 3 cm was 84.06%. These outcomes meet the requirements of high-standard farmland construction. The test results of concrete levelling showed that within a radius of 30 m, the standard deviation S d of the elevation adjustment of the left laser receiver was 1.389 mm, and the standard deviation S d of the elevation adjustment of the right laser receiver was 1.316 mm. Furthermore, the percentage of the sampling points associated with absolute elevation adjustment errors of &le, 3 mm in the cases of the two laser receivers was 100% after levelling, whereas the standard deviation S d of the sand bed surface was 0.881 mm. Additionally, the percentage of the sampling points associated with absolute errors of &le, 3 mm was 100%. This met the construction standards of the concrete industry.

Targeting the hybrid analog-digital private communication field, this paper aims to estimate the parameters of an analog circuit model. An oscilloscope stores the samples of a voltage in a.csv file. The data series is processed using a digital signal technique the singular value decomposition. Singular values and corresponding right-eigenvectors are used to estimated the values of the parameters of the model characterizing the circuit that produced the measured output. The decomposition is performed using small windows of samples of the output of a jerk-type circuit from the literature and an averaging operation improves the estimation.

Background: In contrast to many neuroimaging modalities, clinical interpretation of EEG does not take advantage of post-processing and digital signal analysis. In most centers, EEG is still interpreted at sensor level, exactly as half a century ago. A major task in clinical EEG interpretation is the identification of interictal epileptiform discharges (IEDs). However, due to overlap with the background activity, IEDs can be hard to detect in the scalp EEG. Since traditional montages, like bipolar and average reference, are linear transformations of the recorded channels, the question is, whether we can provide linear transformations of the digital EEG to take it back into the brain, at least on a macroscopic level. The goal is to make focal epileptiform activities better visible and separate most of the overlap. Methods: Multiple discrete sources provide a stable linear inverse to transform the EEG into source space with little cross-talk between source regions. The model can be based on a few dipoles or regional sources adapted to the individual EEG and MRI data or on few standard sources evenly distributed throughout the brain, e.g. below the 25 EEG standard electrodes. Results: Auditory and somatosensory evoked potentials serve as teaching examples to show how various source spaces can reveal the underlying source components including their loss or alteration due to lesions. Source spaces were able to reveal the propagation of source activities in frontal IEDs and the sequential activation of the major nodes of the underlying epileptic network in myoclonic epilepsy. The power of multiple discrete sources in separating the activities of different brain regions could also be demonstrated for the ongoing EEG in cases with frontal cortical dysplasia and bitemporal lobe epilepsy as the new source space 25 made IEDs more clearly visible over the EEG background signals. The more focal nature of source versus scalp space was quantitatively confirmed using a new measurement of focality. Conclusion: Multiple discrete sources have the power to transform the EEG back into the brain by defining new EEG traces in source space. Using standard source space 25, these can serve for improved clinical interpretation of EEG.

The purpose of this project was to develop a system that could estimate impact force in tennis forehand stroke. Such estimation is critical feedback during training. Method: A tennis racket was used for this study. A strain gauge was embedded into the body of the racket. Changes in strain measurement (analogue signal) was converted to digital signal using the AD converter and was synced with the motion capture system. Calibration of the strain gauge was conducted by hanging fixed weights of equal increment on the racket and expressed as a relation of fixed weight mass and strain data (captured on motion capture) using linear regression equation. The equations summation of forces was used to determine the impact force. Results and Discussions: The peak impact resultant force estimates were similar to those reported in the literature. Despite the sampling frequency of 200Hz, data estimated from this study may give a representation of peak resultant impact force as the data were not filtered. Conclusion: The system developed in this study may be suitable to estimate peak resultant impact forces. Coaches could simply use the data gathered and in future, synchronise with an app on mobile devices to establish impact force directly and instantaneously with acceptable accuracy.

The standard method of calculating the spectrum of a digital signal is based on the Fourier transform, which gives the amplitude and phase spectra at a set of equidistant frequencies from signal samples taken at equal intervals. In this paper a different method based on stochastic inversion is introduced. It does not imply a fixed sampling rate, and therefore it is useful in analysing geophysical signals which may be unequally sampled or may have missing data points. This could not be done by means of Fourier transform without preliminary interpolation. Another feature of the inversion method is that it allows unequal frequency steps in the spectrum, although this property is not needed in practice. The method has a close relation to methods based on least-squares fitting of sinusoidal functions to the signal. However, the number of frequency bins is not limited by the number of signal samples. In Fourier transform this can be achieved by means of additional zero-valued samples, but no such extra samples are used in this method. Finally, if the standard deviation of the samples is known, the method is also able to give error limits to the spectrum. This helps in recognising signal peaks in noisy spectra.

Usually, the transport of information requires either an electromagnetic field or matter as a carrier. It turns out that the Dirac vacuum modes could be exploited as a potentially loss-free carrier of information between two distant locations in space. At the first location, a spatially localized electric field is placed, whose temporal shape is modulated, for example, as a binary sequence of distinguishable high and low values of the amplitude. The resulting distortion of the vacuum state reflecting this information propagates then to a second location, where this digital signal can be read off sequentially by a static electric field pulse. If this second field is supercritical, it can create electron-positron pairs from the manipulated vacuum state. The original information transported by the vacuum mode is then imprinted on the temporal behavior of the created particle yield for a selected energy.

Nowadays, methods for digital signal and image processing are widely used in scientific and technical areas. Current stage of research in astronomy, radiology, computed tomography, holography, and radar is characterized by broad use of digital technologies, algorithms, and methods. Correspondingly, an issue of development of new or improvement of known mathematical models arose, especially for new types of input information. There are the cases when input information about function is given on the set of traces of the function on planes, the set of traces of the function on lines, and the set of values of the function in the points. The paper is dedicated to the improvement of mathematical models of digital signal processing and imaging by the example of constructing formulas of approximate calculation of integrals of highly oscillating functions of two variables (irregular case). The feature of the proposed methods is using the input information about function as a set of traces of function on lines. The estimation of proposed method has been done for the Lipschitz class and class of differentiable functions. The proposed formula is based on the algorithm, which is also effective for a class of discontinuous functions.

Because of their nonlinearity, vibrational modes of resonantly driven nanomechanical systems have coexisting stable states of forced vibrations in a certain range of the amplitude of the driving force. Depending on its phase, which encodes binary information, a signal at the same frequency increases or decreases the force amplitude. The resulting force amplitude can be outside the range of bistability. The values of the mode amplitude differ significantly on the opposite sides of the bistability region. Therefore the mode amplitude is very sensitive to the signal phase. This suggests using a driven mode as a bi-directional bifurcation amplifier, which switches in the opposite directions depending on the signal phase and provides an essentially digital output. We study the operation of the amplifier near the critical point where the width of the bistability region goes to zero and thus the threshold of the signal amplitude is low. We also develop an analytical technique and study the error rate near the threshold. The results apply to a broad range of currently studied systems and extend to micromechanical systems and nonlinear electromagnetic cavities., The originally submitted manuscript

Continuous monitoring of health state is important in elder and chronically ill (but otherwise not critical) patients. Ideally, the patient should not be aware of being continuously monitored. This study describes an automatic and non-conscious heart rate monitoring system based on the ballistocardiogram (BCG). The bi-axial BCG can be recorded by two piezoelectric force sensors and high-gain amplifiers. Digital signal pre-processing has been implemented to increase the SNR and an algorithm to automatically detect the heart rate has been evaluated. The high gain required makes the system susceptible to forces other than those related to the cardiovascular system, such as those due to body movements. The sensitivity and positive predictive values obtained are 97.8 % and 98.4 % but if the records where the BCG is masked are discarded, the respective values increase to 99.2 % and 99.5 %. These values are comparable to those typically obtained for the ECG.

The aliasing error resulted from truncating signals incoherently is one of main spectrum errors. The investigation on the error remains quite limited. This restricted the development of high accuracy spectrum analysis. This work discussed the truncation effect and the corresponding aliasing error in quantity, and revealed its dependence upon the truncation conditions. Then a concise technique was proposed to suppress the truncation aliasing error of DFT spectrum by modifying the first datum of the digital signal in time domain. Under general truncation conditions, the simulations show that the error correction of the 5 spectral lines near the main lobe is effective and the maximum absolute error of the main spectral line is decreased from ±2.4‰ to ±0.5‰.

In asynchronous sampling, discrete Fourier transform (DFT) spectrum involves errors. Scholars have done great investigations on the correction techniques of DFT spectrum, but the errors have not been completely eliminated all along. In this paper, spectrums were examined from the principle of conservation of energy. It is unnoticed before that the energy of the digital signal, which is the analysis object of DFT, isn't equal to that of the finite continuous signal truncated by rectangular window. Thus the energy of their spectrums are different according to the Parseval's theorem. The Energy Loss-Gain (ELG) error was introduced to express the energy difference between these two spectrums. The ELG error is zero if the observed continuous signal is truncated in integral multiple of half cycle and it is related to the cycle number and sampling number in one cycle. Analysis show that the ELG error decreases with the increment of these two parameters, which are helpful to the engineering.

To prove the famous Riemann hypothesis, that the real part of the root is always exactly equal to 1/2, a series of 500 and the other prime numbers has been converted from decimal to binary number system. At the same time was a clear non-trivial zeros. Any prime number can be represented as quantized into binary digital signal. Quantization step to not dilute a number of prime numbers is 1. Number of levels (binary digits) depends on the power of the quantized number of primes. As a result, we get two types of zeros - the trivial and nontrivial. Capacity of a finite number of primes must be taken based on the completeness of block incidence matrix. Average statistical indicator is a binary number, and influencing variable - itself a prime number. The binary representation allows to visualize and geometric patterns in the full range of prime numbers.

Oxygen content controller in the closed environment contains two parts, master machine and slave machine, of which the master one in the control room can monitor and control the slave ones hanged on it. The master one can not only read the current value of the salve but also control the parameter values and set the upper and lower limits, and the slave one can set its own limits meanwhile. The slave machines monitor the current oxygen content by 4OX2 oxygen sensor, and convert the content signal into digital signal which is conventional to process by the microcontroller.And then the digital signal will be compared with the limit, if less than the lower limit, the relay will open the valve to release oxygen into the air. On the contrary, if more than the upper threshold, the valve will be closed. In addition, the slave machine also has the calibration function and set its own communication address using DIPswitches. The communication between the master and slave is accomplished by the full duplex RS485 through max489 chip.

Autocorrelation function and cross-correlation function can be used to illustrate the dependency relation of random processes. The degree of mini-transmutation is often too small to detect. A new approach via utilization of correlation coefficient between two different signals in time domain was proposed to measure the tiny distortion of three dimensional objects. The correlation analysis and deduction on transformation from 3-D surface distribution to 1-D time series signal were made rationally. Numeric simulation experiments of discrete digital signal generated from triangular function composite generator were done and six groups of correlation coefficient curves were given deliberately with different signal length. The correlation and similarity degree among different similar waveforms were analyzed in detail. It shows that the approach is valid to detect the degree of distortion between the original standard one and the practical one.

Dam safety monitoring data can be viewed as a digital signal sequence which consists of different frequency components. Identifying outliers to ensure the reliability of observational data becomes a foundation work of dam monitoring data analysis. Outliers of time signal series can be detected by wavelet transform. Lipschitz index can be used to measure the local singularity of a function, and the original abnormal signal can be found in the position of wavelet transform modulus maxima. Take horizontal displacement values observed by Lijiaxia concrete dam as example, an assumed error are added to the time series signal deliberately. A 4-level decomposition of the observation data was done by using wavelet db1, the results show that the modulus maxima occur at the given time. Therefore, outliers can be detected and located accurately by wavelet transform, which is important to analyze the safety monitoring data of dam.

Work on single tone frequency estimation has focused on uniformly sampled data. However, it has been shown that, for a given number of samples, more information on the frequency of a signal can be gained by non-uniform sampling schemes [M. Wieler, S. Trittler, F.A. Hamprecht, Optimal design for single tone frequency estimation, Digital Signal Process., in press]. Unfortunately, an optimum sampling pattern (that, for example, minimizes the Cramer-Rao bound) does not automatically have a fast and simple algorithm for frequency estimation associated with it. For application in an interferometric measurement system, an algorithm is needed that gathers as much information as possible from a low number of samples, while at the same time keeping the computational effort sufficiently low to process millions of time series in a few seconds. This paper proposes a simple approximation to the optimum sampling pattern by using uniformly sampled blocks of data and further proposes to estimate phase and frequency in each of these blocks and to exploit these intermediate results in the final estimation. An approach to do so is investigated in detail. Results are compared to the Cramer-Rao bound (CRB), and it is shown that this algorithm almost reaches this limit on the variance of unbiased estimators, at a computational complexity lower than that of a typical FFT-based approach. For M=32 samples and a signal-to-noise ratio of 10, the standard deviation of the frequency estimate is lower by more than 50% compared to uniform sampling. In addition, the algorithm can easily be applied to poorly characterized systems, e.g. systems for which the noise is not known exactly. Finally, we demonstrate that the proposed strategy yields results that are within 3% of the theoretically achievable accuracy for the theoretically optimum sampling pattern.

This correspondence presents a novel method for the construction of translation-invariant discrete wavelet packet (TIDWP) transforms for any decomposition level k, starting from any phase of a critically sampled discrete wavelet-packet representation of level k. The process is performed by phase shifting, i.e., the direct recovering of the wavelet coefficients omitted by the downsampling operations of each decomposition level without reconstructing the input signal. The proposed method enables tradeoffs between memory utilization and computational efficiency for the construction of translation-invariant representations. Hence, it is useful in resource-constrained TIDWP-based applications of digital signal compression, image segmentation and detection of transients

This paper presents a new method by which sets of discrete 1D projections can be used to construct large families of 2D discrete arrays. These compact arrays have targeted, specific periodic correlation values that span the full range between perfect auto-correlation to zero cross-correlation. The array size is variable and the array elements can be binary or contain grey integer values. Arrays with these properties are useful for digital signal synchronisation, communications and watermarking. We show that multiple copies of zero cross-correlation arrays can be co-located without interference and that the presence of individual arrays is able to be determined independently. The arrays with perfect periodic auto-correlation also have high aperiodic auto-correlation and optimally low cross-correlation, making them well-suited for use as digital watermarks.

Sometimes the accelerated life testing (ALT) of some products still take time and it is hard to implement real-time monitoring on samples to check whether the samples fail or not. Under this condition, periodic inspection is always conducted to monitor the sample performance, obtaining the failure time data in ALT. But periodic inspection may cause problems in some cases. When the failure is detected during the inspection, its timing point is recorded by estimation. So the failure time is not accurate since it may happen at any time in the adjacent inspection interval and cannot be detected immediately after the failure happen. The extreme case is that the sample fails immediately when the inspection is accomplished. Thus, there exists big uncertainty in failure time data if the interval is quite long which will affect the accuracy of evaluation results. However, there are some methods which may help to detect the failure happen indirectly. For example, the fluctuation or excursion of the output digital signal of samples may indicate the failure to some degree. Even so, the failure time cannot be recognized directly because the judging criteria of failure of different inspectors may slightly vary. This leads to the estimation of the exact failure time is not precise. Therefore, the failure time data of ALT is not precise and should be fuzzy data. The life estimation of ALT should be a fuzzy interval value rather than just a single number. Hence, in this paper, a statistical method for constant-stress ALT with Type II censored samples based on fuzzy theory is proposed which assumes that the life time of the product follows Weibull distribution.

The theory of multidimensional continuous and discrete systems is applied to derive a parametric description of musical sounds from a physical model of real or virtual string instruments. The mathematical representation of this model is given by a partial differential equation for a vibrating string. Suitable functional transformations with respect to time and space turn this partial differential equation into a multidimensional transfer function. It is the starting point for the derivation of a discrete-time system by classical analog to discrete transformations. The coefficients of this discrete model depend explicitly on the geometric properties and material constants of the underlying physical model. This ensures a meaningful behaviour of the discrete system under varying conditions and allows for an intuitive control by the user. Furthermore, the performance of real-time implementations is discussed. Finally, several extensions of this synthesis method for computer music applications are presented.

In certain digital signal processing applications, residues \(\) of an input integer signal x are measured with respect to integer moduli \(\). The signal x is then recovered by solving the system of simultaneous linear congruences \(\). Since the residues ri are measured quantities, they are subject to noise contamination. To provide noise protection, the moduli mi may be chosen to possess common factors. Accurate approximations for x may then be determined by solving approximate or ``relaxed" simultaneous congruences. This paper presents a coherent mathematical theory for the approximate solution of simultaneous congruences with inaccurate residues when no exact solution exists. After precisely formulating the notion of relaxed congruences, it is found that, under nonrestrictive technical assumptions, unique solutions to these congruences always exist. A variety of examples illustrating characteristics of solutions of relaxed congruences are provided, and a fast, efficient algorithm for solving them numerically is presented. The problem of finding an optimal approximate solution is then discussed. Several optimality criteria are proposed and procedures for finding optimal approximate solutions are outlined. Error bounds are derived which specify the maximum amount that an approximate solution based upon inaccurate residues may differ from the corresponding true solution based upon the exact residues.

A system for automated traffic accident detection in intersections was designed. The input to the system is a 3-s segment of audio signal. The system can be operated in two modes: the two-class and multiclass modes. The output of the two-class mode is a label of “crash” or “noncrash.” In the multiclass mode of operation, the system identifies crashes as well as several types of noncrash incidents, including normal traffic and construction sounds. The system is composed of three main signal processing stages: feature extraction, feature reduction, and classification. Five methods of feature extraction were investigated and compared; these are based on the discrete wavelet transform, fast Fourier transform, discrete cosine transform, real cepstral transform, and mel frequency cepstral transform. Statistical methods are used for feature optimization and classification. Three types of classifiers are investigated and compared; these are the nearest-mean, maximum-likelihood, and nearest-neighbor methods. The results of the study show that the optimum design uses wavelet-based features in combination with the maximum-likelihood classifier. The system is computationally inexpensive relative to the other methods investigated, and the system consistently results in accident detection accuracies of 95% to 100% when the audio signal has a signal-to-noise-ratio of at least 0 decibels.

Sherman, P., On the Statistical Nature of Real Sinusoids Associated with Rotating Machinery, Digital Signal Processing12 (2002) 471–483 This paper represents the first phase of an ongoing investigation into the nature of sinusoidal types of random processes associated with real world phenomena. While perfect sinusoids exist only in the mathematical sense, their use as an approximation model in relation to real world phenomena has been and continues to be widespread, often with much value. The motivation for this work is the belief that knowledge of their deviation from such a model can provide additional useful information. The focus of this paper is on sinusoids in relation to random processes associated with rotating machinery. The tools used include mathematical limit theorem results, standard signal processing tools including spectral estimation and Kalman filtering, and basic statistics. Some noteworthy results include the normality of amplitude and frequency probability distributions, the characterization of the same as stationary random processes, and the potential to improve condition monitoring of rotating machinery.

The problem of synchronous fractional sample rate conversion (FSRC) of a digital signal by L / M , where L and M are coprime integers [6,10], is revisited. Based on a novel approach two different efficient causal block implementations of FSRC are concurrently derived and compared with each other. While the computational load of both structures, being performed in an LTI MIMO subsystem at the subnyquist rate F o / L = F i / M , is identical, their group delay is always different. By column and row shifts of the matrix representation of the MIMO subsystem it is possible to transform each structure into any arbitrary implementation with changed group delay. Moreover it is shown that, by structural manipulation of the signal flow graph of the MIMO subsystem, both implementations ultimately require the same amount of computation and storage in spite of different group delay. Finally, by using Nyquist( L )filters, the maximum number of input samples to FSRC is retained at its output.

We describe a method for the calculation of photoionization cross-sections using square-integrable amplitudes obtained from the diagonalization of finite-basis set representations of the electronic Hamiltonian. Three examples are considered: a model example in which the final state is a free particle, the hydrogen atom and neutral atomic sodium. The method exploits the Whittaker-Shannon-Kotel'nikov sampling theorem, which is widely used in digital signal sampling and reconstruction. The approach reproduces known data with very good accuracy and converges to the exact solution with increase of the basis set size.

In digital signal and image processing one can only process discrete signals of finite length, and the space [Formula: see text] is the preferred setting. Recently, Kutyniok and Strohmer constructed orthonormal Wilson bases for [Formula: see text] with general lattices of volume [Formula: see text] ([Formula: see text] even). In this paper, we extend this construction to Wilson frames for [Formula: see text] with general lattices of volume [Formula: see text], where [Formula: see text] and [Formula: see text]. We obtain a necessary and sufficient condition for two sequences having Wilson structure to be dual frames for [Formula: see text]. When the window function satisfies some symmetry property, we obtain a characterization of a Wilson system to be a tight frame for [Formula: see text], show that a Wilson frame for [Formula: see text] can be derived from the underlying Gabor frame, and that the dual frame having Wilson structure can also be derived from the canonical Gabor dual of the underlying Gabor frame.

The discrete Hartley transform (DHT) has proved to be a valuable tool in digital signal/image processing and communications and has also attracted research interests in many multidimensional applications. Although many fast algorithms have been developed for the calculation of one- and two-dimensional (1-D and 2-D) DHT, the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention; hence, the multidimensional Hartley transform is usually calculated through the row-column approach. However, proper multidimensional algorithms can be more efficient than the row-column method and need to be developed. Therefore, it is the aim of this paper to introduce the concept and derivation of the three-dimensional (3-D) radix-2 /spl times/ 2 /spl times/ 2 algorithm for fast calculation of the 3-D discrete Hartley transform. The proposed algorithm is based on the principles of the divide-and-conquer approach applied directly in 3-D. It has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row-column approach based on similar algorithms.

In this paper, the designs of digital fractional order differentiator (DFOD) using discrete sine transforms (DST) are presented. First, the definition of fractional differentiation is reviewed briefly. Then, the DST-based interpolation method is applied to compute the fractional differentiation of a given digital signal. Next, the transfer functions of DFOD are obtained from the DST computational results by using index mapping method. Finally, some numerical and application examples are demonstrated to show the effectiveness of the proposed DST-based design method.

We study the dynamics of non-ergodic piecewise linear maps under perturbations. We show that for the class of maps that can be conjugated to piecewise rotations, sets following the same codings change Hausdorff continuously under perturbations of the map. It follows that the size f of the set of points that iterate arbitrarily close to discontinuities changes semi-continuously under perturbations. This implies f changes continuously on a dense Gδ set and this supports a stronger numerical result by Ashwin, Chambers and Petkov, that the measure of such a set changes continuously. The main tools used in the paper include properties of convexity and symbolic dynamics. The scope of our work includes maps that appear in digital filters. A digital filter is a type of signal processing algorithm (software) used for filtering a digital signal.

This article presents new fast algorithms for the type-II, -III, and -IV discrete W transform (DWT). The type-II and -III DWT is decomposed into two length-N/2 type-I DWTs, and the type-IV is converted into two length-N/2, type-II or type-III DWTs. The proposed algorithms achieve a simple computational structure and naturally support a wide range of sequence lengths. Savings on the number of arithmetic operations are achieved for the type-II to -IV DWT when N=15*2/sup r/.

SUMMARY A formula for recovering the original signal from itsirregularly sampled values using wavelets, which extendsthe Walter sampling theorem to the irregular sampling caseand generalizes the PaleyŒWiener 1/4-Theorem by remov-ing the symmetricity constraint for sampling, is pre-sented.a 1999 Scripta Technica, Electron Comm Jpn Pt 3,82(5): 65Œ71, 1999Key words: Wavelet; sampling theorem; scalingfunction; orthogonality; biorthogonality. 1. Introduction In digital signal and image processing, digital com-munications, and so forth, a continuous signal is usuallyrepresented and processed by using its discrete samples.How, then, are we to reconstruct the original signal from itsdiscrete samples? The classical Shannon sampling theoremgives the following formula for band-limited finite energysignals.For a finite energy s-band continuous signalf( t), 2t ˛ R , that is, supp f^(w) I [- s , s] and f ˛ L (R), it canbe recovered by the formulawhere f^ is the Fourier transform of f(t) defined byIf we let s =

Soil micromorphological studies have used various techniques for pore analysis, including optical measurements, electron microscopy and computed tomography. This study examined a method based on X-ray photon mapping, in which a scanner obtains the sample's X-ray spectrum, selects those portions which have been specified as the elements to map and then only separates that part of the spectrum to be analysed by the software. With this new technique, the resulting chemical maps are composed of the distribution of selected elements within the sample and the only digitising is to convert the analogue X-ray signal into a digital signal that can be computer processed. The approach provided two-dimensional chemical maps of soil blocks, clearly showing macropore sizes and distributions and enabling calculation of macroporosity values. The results showed mean macroporosity values of 17–18%. The main benefits of the technique are the precision of data and image processing and the elimination of laborious thin section preparation, as hardened soil blocks can be scanned automatically.

Starting with a real-valued N-point discrete-time signal, frequency-domain algorithms are provided for computing (1) the complex-valued standard N-point discrete-time "analytic" signal of the same sample rate; (2) the complex-valued decimated N/2-point discrete-time "analytic" signal of half the original sample rate; and (3) the complex-valued interpolated NM-point discrete-time "analytic" signal of M times the original sample rate. Special adjustment of the transform end points are shown to be necessary in order to generate proper discrete-time "analytic" signals.

A bandlimited signal sampled at a sampling rate higher than the Nyquiste rate can be reconstructed uniquely from its samples even when a finite number of samples is being lost. This pape a solution to this problem which partially originates from MARKS [1]. The solution described here is available in a parallel and a sequential (iterative) form. The parallel implementation requires the solution of a single s ystem of linear equations. Some investigation of the numerical properties of this system is done and a numerical example is given.

The purposes of this work are to establish a high-resolution measurement of the leaky Rayleigh wave velocity with an acoustic microscope for polycrystalline metals and to measure local stresses with the acoustoelasticity of the Rayleigh wave. The V(z) signal acquisition system of conventional acoustic microscopes has been updated to enhance the velocity resolution. A new procedure of digital signal processings has been proposed for finding the accurate oscillation interval of the V(z) to measure precisely the leaky Rayleigh wave velocity. The relative velocity variation of the leaky Rayleigh wave has been reduced to 0.01% for 2017 aluminum alloy by using this signal acquisition and processing. The biaxial stress field around a small hole under tension has been measured by the proposed method and the results are compared with stresses estimated by finite element analysis.

This paper presents two matrix factorizations for recursive pruned discrete cosine transforms. Both factorizations have lower computational complexity when compared to the method of El-Sharkawy and Eshmawy (1995).

In this work, an approximated sampling theorem for any arbitrary continuous time waveform is established. The approximation error bounds for some typical classes of signals are computed. This theorem is essential for performing wavelet analysis if the signal concerned is time limited rather than band limited. An efficient reconstruction method making use of wavelet denoising is proposed to restore a source signal that is contaminated by white Gaussian noise. Under certain conditions, it is proved theoretically that the method is able to bound the estimation mean square error in the order of log/sup 2/(n)/n, where n is the number of discrete samples in the reconstruction.

Fixed-point optimization utility software is developed that can aid scaling and wordlength determination of digital signal processing algorithms written in C or C++. This utility consists of two programs: the range estimator and the fixed-point simulator. The former estimates the ranges of floating-point variables for purposes of automatic scaling, and the latter translates floating-point programs into fixed-point equivalents to evaluate the fixed-point performance by simulation. By exploiting the operator overloading characteristics of C++, the range estimation and the fixed-point simulation can be conducted by simply modifying the variable declaration of the original program. This utility is easily applicable to nearly all types of digital signal processing programs including nonlinear, time-varying, multirate, and multidimensional signal processing algorithms. In addition, this software can be used to compare the fixed-point characteristics of different implementation architectures. An optimization example for an 8/spl times/8 inverse discrete cosine transform (IDCT) architecture that conforms to the IEEE standard specifications is presented. The optimized results require 8% fewer gates when compared with the previous best implementation.

The mth order B-spline N m (x) with integer knots generates a multiresolution analysis, ... ⊂ V -1 ⊂ V 0 ⊂... with the mth order of approximation in wavelet transformation (WT). We have compared the WT method with Fourier transformation processing analytical chemistry signals in detail and have found that the WT method has many advantages. This method can directly provide the frequency domain distribution of a signal in a time domain. The algorithms are simpler and take less time in operation, and one needs only to decompose the digital signal rather than to undertake many transformations. Moreover, it is not necessary to preprocess the original signal to analyze the pattern of data and to know the statistical character of the noise. When the signal-to-noise ratio is 0.2, the processed results of theoretical and experimental data can still be satisfactory.

Approximation techniques are an important aspect of digital signal and image processing. Many lossy signal compression procedures such as the Fourier transform and discrete cosine transform are based on the idea that a signal can be represented by a small number of transformed coefficients which are an approximation of the original. Existing approximation techniques approach this problem in either a time/spatial domain or transform domain, but not both. This paper briefly reviews various existing approximation techniques. Subsequently, we present a new strategy to obtain an approximation f/spl circ/(x) of f(x) in such a way that it is reasonably close to the original function in the domain of the variable x, and exactly preserves some properties of the transformed domain. In this particular case, the properties of the transformed values that are preserved are geometric moments of the original function. The proposed technique has been applied to single-variable functions, two-dimensional planar curves, and two-dimensional images, and the results obtained are demonstrative.

In this paper, the closed-form design of fractional order differentiator (FOD) using discrete cosine transform (DCT) is presented. First, the definition of fractional derivative is reviewed briefly. Then, the DCT-based interpolation method is applied to compute the fractional derivative of a given digital signal. Next, the transfer function of FOD is obtained from the DCT computational results by using suitable index mapping. Finally, several numerical examples are demonstrated to show the effectiveness of the proposed design method.

Although most of existing anisotropic diffusion (AD) methods are supported by prefect mathematical theories, they still lead to smoothed edges and anatomy details (EADs). They are caused by not considering the discrete nature of digital signal. In order to improve the performance of AD in sinogram restoration of low-dosed computed tomography (LDCT), we propose a new AD method, named regularized multidirections and multiscales anisotropic diffusion (RMDMS-AD), by extending AD to regularized AD (RAD) in multidirections and multiscales. Since the multidirections can reduce the discrete errors to the maximum extent, meanwhile multiscales and RAD make searching neighborhood of solution be as large as possible which can get more optimal solution to AD, the new proposed method can improve the performance of AD both in denoising and in stability of solution. Moreover, the discrete errors and ill-posed solutions occur mostly near the EADs; the RMDMS-AD will also preserve EADs well. Comparing the proposed new method to existing AD methods using real sinogram, the new method shows good performance in EADs preserving while denoising and suppressing artifacts.

The differential non-linearity arising from digital signal operations has been examined. Serious degradation of the differential linearity is observed when a series of discrete integer data is processed by a digital system. Two practical correction methods have been proposed: one is to utilize random numbers for converting the discrete integer data into floating point data. The other method is to consider each integer number with its width in order to cover the number line until the neighboring discrete value. Experimental results show great improvements of the differential linearity for both of the two methods, however, the latter method gives a better result.

An all-optical converter which translates binary time-coded words of a 1550 nm communication signal into equivalent space-coded ones has been realized in free-propagation. The conversion is performed by means of optical gates realized using CdTe:In crystals. The device constitutes an input stage for free-space optical signal processing. Architecture, components and experimental results are reported.