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The short-time Fourier transform (STFT) is extensively used to convert signals from the time-domain into the time–frequency domain. However, the standard STFT has the drawback of having a fixed window size. Recently, we proposed a variant of that transform which fixes the window size in the frequency domain (STFT-FD). In this paper, we revisit that formulation, showing its similarity to existing techniques. Firstly, the formulation is revisited from the point of view of the STFT and some improvements are proposed. Secondly, the continuous wavelet transform (CWT) equation is used to formulate the transform in the continuous time using wavelet theory and to discretize it. Thirdly, the constant-Q transform (CQT) is analyzed showing the similarities in the equations of both transforms, and the differences in terms of how the sweep is carried out are discussed. Fourthly, the analogies with multi-resolution STFT are analyzed. Finally, the representations of a period chirp and an electrocardiogram signal in the time–frequency domain and the time-scale domain are obtained and used to compare the different techniques. The analysis in this paper shows that the proposed transform can be expressed as a variant of STFT, and as an alternative discretization of the CWT. It could also be considered a variant of the CQT and a special case of multi-resolution STFT.

Separating individual source signals is a challenging task in musical and multitalker source separation. This work studies unsupervised monaural (co-channel) speech separation (UCSS) in reverberant environment. UCSS is the problem of separating the individual speakers from multispeaker speech without using any training data and with minimum information regarding mixing condition and sources. In this paper, state-of-art UCSS algorithms based on auditory and statistical approaches are evaluated for reverberant speech mixtures and results are discussed. This work also proposes to use multiresolution cochleagram and Constant Q Transform (CQT) spectrogram feature with two-dimensional Non-negative matrix factorization. Results show that proposed algorithm with CQT spectrogram feature gave an improvement of 1.986 and 1.262 in terms of speech intelligibility and 0.296 db and 0.561 db in terms of signal to interference ratio compared to state-of-art statistical and auditory approach respectively at T60 of 0.610s.

Most speech authentication algorithms are over-optimized for robustness and efficiency, resulting in poor discrimination. Hashing shorter sequence is likely to cause the same hashing sequence to come from different speech segments, which will cause serious deviations in authentication. Few people pay attention to the research on the discrimination of hashing sequence length, so this paper proposes a long sequence speech authentication algorithm based on constant Q transform (CQT) and tensor decomposition (TD). In this paper, hashing long sequence is used to solve the problem of poor collision resistance of existing algorithms, fast and accurate authentication can be achieved for important speech fragments with large data volumes. The sub-band in the frequency domain are first divided into different matrix, then the variance set of sub-band in the frequency domain is obtained, and finally the feature values are obtained by CQT and TD transformation. The obtained feature values have strong robustness and can cope with the interference of complex channel environment. In this paper, Texas Instruments and Massachusetts Institute of Technology (TIMIT) speech database and the Text to Speech (TTS) are used to establish a database of 51600 speeches to verify the performance of the algorithm. Experimental results show that compared with the existing speech authentication algorithms, the proposed algorithm has the characteristics of high discrimination, strong robustness and high efficiency.

Acoustic scene recognition (ASR), recognizing acoustic environments given an audio recording of the scene, has a wide range of applications, e.g. robotic navigation and audio forensic. However, ASR remains challenging mainly due to the difficulty of representing audio data. In this article, we focus on traffic acoustic data. Traffic acoustic sense recognition provides complementary information to visual information of the scene; for example, it can be used to verify the visual perception result. The acoustic analysis and recognition, in consideration of its simple and convenient, can effectively enhance the perception ability which only applies visual information. We propose an audio data representation method to improve the traffic acoustic scene recognition accuracy. The proposed method employs the constant Q transform (CQT) and histogram of gradient (HOG) to transfer the one-dimensional audio signals into a time-frequency representation. We also propose two data representation mechanisms, called global and local feature selections, in order to select features that are able to describe the shape of time-frequency structures. We finally exploit the least absolute shrinkage and selection operator (LASSO) technique to further improve the recognition accuracy, by further selecting the most representative information for the recognition. We implemented extensive experiments, and the results show that the proposed method is effective, significantly outperforming the state-of-the-art methods.

V diplomski nalogi obravnavamo problem avtomatske transkripcije glasbe z uporabo globokih nevronskih mrež, natančneje s konvolucijskimi nevronskimi mrežami. Avtomatska transkripcija glasbe je postopek zapisa not iz poslušanja glasbenega posnetka. Preučili smo dosedanje pristope in ugotovili pomanjkanje raziskav o velikosti in o obliki posameznih arhitektur globokih modelov. Raziskali smo uspešnost štirih različnih arhitektur konvolucijskih nevronskih mrež na zbirki klavirskih posnetkov MAPS, ki je pogosta izbira za učenje avtomatske transkripcije glasbe. Preučili smo tudi dva različna pristopa normalizacije spektrogramov: standardizacijo in logaritemsko kompresijo. Izkazalo se je, da na uspešnost transkripcije pozitivno vpliva večje število konvolucijskih plasti v nevronski mreži. Prav tako je bila transkripcija na logaritemsko kompresiranih spektrogramih za 10 % uspešnejša od transkripcije na standardiziranih spektrogramih. In this thesis we explore the problem of automatic music transcription using deep neural networks, more specific convolutional neural networks. Automatic music transcription is a task of writing the sheet music from musical recordings. We analysed previous studies and found that there was a lack of research about the size and the shape of architecture of deep models. We explored the performance of four different architectures of convolutional neural networks on the piano recordings dataset MAPS, which is a common benchmark for learning automatic music transcription. We also compared two different normalization techniques for spectrograms: standardization and the logarithmic compression. We found out that the performance of transcription is highly correlated with the higher number of convolutional layers. Transcription is also 10% more successful with logarithmic compression instead of standardization.

Classification of bird sounds can be done in various methods and ways. One method that can be used is CNN (Convolutional Neural Network). CNN is an algorithm used for image classification. For bird sounds to be classified by CNN, conversion from analogue sound to digital images is required objectively and accurately. This study will discuss the conversion of analogue sound from birds into spectrogram images using one of Constant-Q Transform (CQT) and Mel Spectrogram. Bird voices are recorded using a voice recorder. The recorded voice will represent the audio signal digitally. Constant-Q Transform will map the audio signal from a time domain to a frequency domain. The frequency will be converted into a log scale and the colour dimensions (amplitude) into decibels to form a spectrogram. The spectrogram will be mapped on a mel scale to form a mel spectrogram. This research is the change of bird’s voice analogously to mel spectrogram, classified in CNN. The resulting images from this study can be classified using CNN to help classify bird sounds.

The playback speech contains information from the environment, playback and recorder used. This work focuses on proposal of a novel normalization scheme, namely, low frequency frame-wise normalization (LFFN) as one of the modules in feature extraction process that is hypothesized to help in capturing the artifacts from the playback speech. It is based on low frequency bin processing that is performed frame-wise and hence its name. The constant-Q transform (CQT) based features are found to provide the benchmark results for detection of spoofing attacks. In this work, LFFN is combined with CQT to extract two new features from octave and linear power spectra, respectively. The first one is obtained by CQT, LFFN and octave segmentation that is referred to as constant-Q normalization segmentation coefficients (CQNSC). The latter uses conventional constant-Q cepstral coefficient (CQCC) and LFFN to obtain constant-Q normalization cepstral coefficients (CQNCC). The studies are performed on ASVspoof 2017 version 2.0 corpus that is designed for studying playback speech detection. The experimental results show the effectiveness of proposed LFFN with CQT based features. We obtain equal error rate of 10.63% and 10.31% for CQNSC and CQNCC features on the evaluation set of ASVspoof 2017 version 2.0 corpus, respectively.

Recent studies have reported the success of linear prediction analysis (LPA)-related features, which are extracted as a short-term spectral feature for replay attack detection due to the advantage of the imperfection in the LPA-based signal produced by recording and playback devices. However, exploiting LPA-based signals is focused on only magnitude-based features and ignores phase-based features. In this paper, we propose two novel LPA-based relative phase features, namely, linear prediction residual-based relative phase (LPR-RP) and linear prediction analysis estimated speech-based relative phase (LPAES-RP). The key idea of both LPR-RP and LPAES-RP is to extract the phase information based on LPA-based signals. In the LPR-RP feature, we modify the relative phase (RP) feature extraction using a linear prediction residual (LPR) derived from the difference between the original/raw speech and LPA estimated speech signal (LPAES) instead of the original/raw speech signal. LPES-RP feature exploits the LPAES signal to replace the original/raw speech signal. Because the trace of the recording and playback device artifacts is the primary evidence for detecting the replayed signal, the advantages of the imperfection of LPR and LPAES are expected to provide efficient phase information for the replay attack detection task. In addition, using the individual LPR-RP/LPAES-RP feature, our proposed features are combined with two standard features, mel-frequency cepstral coefficients (MFCC), constant Q transform cepstral coefficients (CQCC) and the original RP feature, at score level to further improve the detection decision. The performance of the proposed LPR-RP/LPAES-RP feature and combination are evaluated using the ASVspoof 2017 version 2 database. On the evaluation subset, our proposed LPR-RP and LPAES-RP feature achieves a promising improvement over baseline features (MFCC/CQCC). Moreover, the combined systems of LPR-RP, RP, and CQCC obtains an equal error rate of 9.26%.

Deep clustering technique is a state-of-the-art deep learning-based method for multi-talker speaker-independent speech separation. It solves the label ambiguity problem by mapping time-frequency (TF) bins of the mixed spectrogram to an embedding space, and assigning contrastive embedding vectors to different TF regions in order to predict the mask of the target spectrogram of each speaker. The original deep clustering transforms the speech into the TF domain through a short-time Fourier transform (STFT). Since the frequency component of STFT is linear, while the frequency distribution of human auditory system is nonlinear. Therefore, we propose to use constant Q transform (CQT) instead of STFT to achieve a better simulation of the frequency resolving power of the human auditory system. The ideal upper bound of signal-to-distortion (SDR) of CQT based deep clustering is higher than that based on STFT. In the same experimental setting on WSJ0-2mix corpus, we gave a detail description in selecting meta-parameters of CQT for speech separation, and finally the SDR improvements of this method achieved about 1dB better performance than the original deep clustering.

Automatic Music Transcription (AMT) is an important task in Music Information Retrieval (MIR). Many researchers have focused on the structure of Convolutional Neural Network (CNN) for transcription. In this paper, we construct a CNN-based (EB) piano music transcription model using the energy-balanced constant Q transform spectrogram, which is called EB-enhanced CNN model. Unlike standard CNN-based methods, the proposed model makes the energy of the input features more balanced, so that many previously missed pitches due to weak energy can be successfully detected. Training and evaluation are performed on the MAPS dataset, a public dataset for piano transcription. As a result, our technique achieves a 3.53% f1 score improvement compared with the state-of-the-art method on the MAPS ENSTDkCl subset.

The “2019 Automatic Speaker Verification Spoofing And Countermeasures Challenge” (ASVspoof) competition aimed to facilitate the design of highly accurate voice spoofing attack detection systems. the competition did not emphasize model complexity and latency requirements; such constraints are strict and integral in real-world deployment. Hence, most of the top performing solutions from the competition all used an ensemble approach, and combined multiple complex deep learning models to maximize detection accuracy - this kind of approach would sit uneasily with real-world deployment constraints. To design a lightweight system, we combined the notions of skip connection (from ResNet) and max feature map (from Light CNN), and evaluated the accuracy of the system using the ASVspoof 2019 dataset. With an optimized constant Q transform (CQT) feature, our single model achieved a replay attack detection equal error rate (EER) of 0.37% on the evaluation set, surpassing the top ensemble system from the competition that achieved an EER of 0.39%.

The constant Q transform (CQT) has been shown to be one of the most effective speech signal pre-transforms to facilitate synthetic speech detection, followed by either hand-crafted (subband) constant Q cepstral coefficient (CQCC) feature extraction and a back-end binary classifier, or a deep neural network (DNN) directly for further feature extraction and classification. Despite the rich literature on such a pipeline, we show in this paper that the pre-transform and hand-crafted features could simply be replaced by end-to-end DNNs. Specifically, we experimentally verify that by only using standard components, a light-weight neural network could outperform the state-of-the-art methods for the ASVspoof2019 challenge. The proposed model is termed Time-domain Synthetic Speech Detection Net (TSSDNet), having ResNet- or Inception-style structures. We further demonstrate that the proposed models also have attractive generalization capability. Trained on ASVspoof2019, they could achieve promising detection performance when tested on disjoint ASVspoof2015, significantly better than the existing cross-dataset results. This paper reveals the great potential of end-to-end DNNs for synthetic speech detection, without hand-crafted features., Comment: Accepted in IEEE Signal Processing Letters 2021

This paper proposes a deep learning framework applied for Acoustic Scene Classification (ASC), which identifies recording location. In general, we apply three types of spectrograms: Gammatone (GAM), log-Mel and Constant Q Transform (CQT) for front-end feature extraction. For back-end classification, we present a re-trained model with a multi-kernel CDNN-based architecture for the pre-trained process and a DNN-based network for the post-trained process. Our obtained results over DCASE 2016 dataset show a significant improvement, increasing by nearly 8% compared to DCASE baseline of 77.2%.

This chapter demonstrates the use of different data distributions in different phases of a parallel fast Fourier transform (FFT), which is a regular computation with a predictable but challenging data access pattern. Both the block and cyclic distributions are used and also intermediates between them. Each required data redistribution is a permutation that involves communication. By making careful choices, the number of such redistributions can be kept to a minimum. FFT algorithms can be concisely expressed using matrix/vector notation and Kronecker matrix products. This notation is also used here. The chapter then shows how permutations with a regular pattern can be implemented more efficiently by packing the data. The parallelization techniques discussed for the specific case of the FFT are also applicable to other related computations, for instance in signal processing and weather forecasting.

Speech and audio signal processing frequently requires to recover a time-domain signal from the magnitude of a spectrogram. Conventional methods inversely transform the magnitude spectrogram with a phase spectrogram recovered by the Griffin–Lim algorithm or its accelerated versions. The short-time Fourier transform (STFT) perfectly matches this framework, while other useful spectrogram transforms, such as the constant-Q transform (CQT), do not, because their inverses cannot be computed easily. To make the best of such useful spectrogram transforms, we propose an algorithm which recovers the time-domain signal without the inverse spectrogram transforms. We formulate the signal recovery as a nonconvex optimization problem, which is difficult to solve exactly. To approximately solve the problem, we exploit a stochastic convex optimization technique. A well-organized block selection enables us both to avoid local minimums and to achieve fast convergence. Numerical experiments show the effectiveness of the proposed method for both STFT and CQT cases.

For certain applications, keyword spotting (KWS) requires some degree of personalization. This is the case for KWS for hearing assistive devices, e.g., hearing aids, where only the device user should be allowed to trigger the KWS system. In this paper, we first develop a new realistic hearing aid experimental framework. Next, using this framework we show that the performance of a state-of-the-art multi-task deep learning architecture exploiting cepstral features for joint KWS and users' own-voice/external speaker detection drops significantly. To overcome this problem, we use phase difference information through GCC-PHAT (Generalized Cross-Correlation with PHAse Transform)-based coefficients along with log-spectral magnitude features. In addition, we demonstrate that working in the perceptually-motivated constant-Q transform (CQT) domain instead of in the short-time Fourier transform (STFT) domain allows for the generation of compact and coherent features which provide superior KWS performance. Our experimental results show that our CQT-based proposal achieves a relative KWS accuracy improvement of around 18% compared to using cepstral features while dramatically decreasing the number of multiplications in the multi-task architecture, which is key in the context of low-resource devices like hearing assistive devices.

This chapter takes a small detour and discusses some numerical approximations that will be necessary to theoretically compute electron microscopy images. Specifically, digital sampling (pixels and levels) and the all important fast Fourier transform are introduced. The FFT will be the principle tool to speed up later calculation. If you are familiar with these topics, this chapter may be skipped.

The work addresses the need of fast and accurate F0 detection method for faithful transcription of Indian classical music. Three prominent F0 detection methods, viz. discrete Fourier transform (DFT), constant Q transform (CQT), and YIN algorithm are described and compared on the basis of accuracy and frame size against simulated signals of standard MIDI note frequencies. The same analysis is repeated on recorded data containing vocal recitals of eight notes from an octave in the equal tempered musical scale. That YIN method is most accurate and applicable for small frame size and is concluded.

Acoustic scene classification (ASC) has attracted much attention in recent years. In previous studies, the most common architecture is convolutional neural network (CNN) fed by three main features, i.e. log-mel energies, harmonic-percussive source separation (HPSS) and constant-Q transform (CQT). In this paper, we present a hybrid constant-Q transform (HCQT) based CNN system for ASC. Specifically, we first extract CQT and HCQT from each audio clip as the acoustic features, as well as other several features such as Mel-frequency cepstral coefficients, log-mel energies and its HPSS. Then, we feed those features into 5-layer or 9-layer CNNs with average pooling separately. Considering different features that have complementary information with each other, we further develop several methods to integrate the outputs of the CNNs, including averaging, weighted averaging, random forests and extremely randomized trees. To the best of our knowledge, this is the first time HCQT based method is being used for ASC. Essentially, the method combines two CQTs with different resolutions for remedying the high-frequency bins of the traditional CQT. In addition, we investigate different ensemble strategies of the CNN models thoroughly. We evaluated the proposed system in the DCASE 2019 challenge. Experimental results show that HCQT is more effective than the conventional CQT. Furthermore, the accuracies of our system on the validation and leaderboard datasets are 77.5% and 79.3% respectively, which outperforms the two comparison baselines significantly.

This paper proposes an effective algorithm for polyphonic audio-to-score alignment that aligns a polyphonic music performance to its corresponding score. The proposed framework consists of three steps: onset detection, note matching, and dynamic programming. In the first step, onsets are detected and then onset features are extracted by applying the constant Q transform around each onset. A similarity matrix is computed using a note-matching function to evaluate the similarity between concurrent notes in the music score and onsets in the audio recording. Finally, dynamic programming is used to extract the optimal alignment path in the similarity matrix. We compared five onset detectors and three spectrum difference vectors at selected audio onsets. The experimental results revealed that our method achieved higher precision than did the other algorithms included for comparison. This paper also proposes an online approach based on onset detection that can detect most notes within only 10 ms. Based on our experimental results, this online approach outperforms all methods included for comparison when the tolerance window is 50 ms.

The gyrator transform is a linear canonical transform, which generates the rotation of an optical signal in position-spatial frequency planes. Gyrator wavelet transform is a relatively newer optical information processing tool obtained by combining the gyrator transform with the wavelet transform. This combination provides multi-resolution analysis of an image which is twisted in spatial frequency planes. The proposed tool satisfies basic algebraic properties, such as the linearity property and Parseval's theorem. Considering the usefulness of this tool, here a study of features, applications, and implementation of the gyrator wavelet transform is presented. This work studies the features of the gyrator wavelet transform, which can find a role in different applications such as edge enhancement, image encryption, image hiding, and watermarking.

The seislet transform uses a prediction operator that is connected to the local slope or frequency of seismic events. We have combined the 1D nonstationary seislet transform with empirical-mode decomposition (EMD) in the [Formula: see text]-[Formula: see text] domain. We used EMD to decompose data into smoothly variable frequency components for the following 1D seislet transform. The resultant representation showed remarkable sparsity. We developed a detailed algorithm and used a field example to demonstrate the application of the new seislet transform for sparsity-promoting seismic data processing.

The Sparse Fourier Transform (SFT), designed for signals that contain a small number of frequencies, enjoys low complexity, and thus is ideally suited for big data applications. In this paper, we propose Robust Sparse Fourier Transform, (RSFT), which is a modification of SFT that extends the SFT advantages to real world, noisy settings. RSFT can accommodate off-grid frequencies in the data. Furthermore, by incorporating Neyman–Pearson detection in the SFT stages, frequency detection does not require knowledge of the exact sparsity of the signal, and is robust to noise. We analyze the asymptotic performance of RSFT, and study the computational complexity versus detection performance tradeoff. We show that, by appropriately choosing the detection thresholds, the optimal tradeoff can be achieved. We discuss the application of RSFT on short-range ubiquitous radar signal processing and demonstrate its feasibility via simulations.

The Python-code empymod computes the 3D electromagnetic field in a layered earth with vertical transverse isotropy by combining and extending two earlier presented algorithms in this journal. The bottleneck in frequency- and time-domain calculations of electromagnetic responses derived in the wavenumber-frequency domain is the transformations from the wavenumber to the space domain and from the frequency to the time domain, the so-called Hankel and Fourier transforms. Three different Hankel transform methods (quadrature, quadrature-with-extrapolation [QWE], and filters) and four different Fourier transform methods (fast Fourier transform [FFT], FFTLog, QWE, and filters) are included in empymod, which allows us to compare these different methods in terms of speed and precision. The best transform in terms of speed and precision depends on the modeled frequencies. Published digital filters for the Hankel transform are very fast and precise for frequencies in the range of controlled-source electromagnetic data, but they fail in the frequency range of ground-penetrating radar. Conventional quadrature, on the other hand, is in comparison very slow but can model any frequency. Examples comparing empymod with analytical solutions and with existing electromagnetic modelers illustrate the capabilities of empymod.

Signal transforms are very important tools to extract useful information from scientific, engineering, or medical raw data. Unfortunately, traditional transform techniques impose unrealistic assumptions on the signal, often producing erroneous interpretation of results. Well-known integral transforms, such as short-time Fourier transform, though have fast implementation algorithms (e.g., FFT), are still computationally expensive. They have multiple parameters that should be tuned, and it is not readily clear how to tune them for long-duration non-stationary signals. To solve these problems, one needs a computationally inexpensive transform with no parameters that will highlight important data aspects. We propose a simple transform based on extrema points of the signal. The transform value at a given point is calculated based on the distance and magnitude difference of two extrema points it lies between, rather than considering every point around it. We discuss implementation of the developed algorithm and show examples of successfully applying the transform to noise-corrupted synthetic signals and to sleep studies detecting delta wave in brain EEG signal. Ideas for improvement and further research are discussed.

International audience; The frequency-scale domain decomposition technique has recently been proposed for operational modal analysis. The technique is based on the Cauchy mother wavelet. In this paper, the approach is extended to the Morlet mother wavelet, which is very popular in signal processing due to its superior time-frequency localization. Based on the regressive form and an appropriate norm of the Morlet mother wavelet, the continuous wavelet transform of the power spectral density of ambient responses enables modes in the frequency-scale domain to be highlighted. Analytical developments first demonstrate the link between modal parameters and the local maxima of the continuous wavelet transform modulus. The link formula is then used as the foundation of the proposed modal identification method. Its practical procedure, combined with the singular value decomposition algorithm, is presented step by step. The proposition is finally verified using numerical examples and a laboratory test.

Broad evaluation of constant Q cepstral coefficients for spoofing detection.Linearisation of geometric space enables constant Q cepstral processing.Variable spectro-temporal resolution key to detection performance.State-of-the-art performance across three standard databases.Cross-database results point towards new approach for generalisation. Recent evaluations such as ASVspoof 2015 and the similarly-named AVspoof have stimulated a great deal of progress to develop spoofing countermeasures for automatic speaker verification. This paper reports an approach which combines speech signal analysis using the constant Q transform with traditional cepstral processing. The resulting constant Q cepstral coefficients (CQCCs) were introduced recently and have proven to be an effective spoofing countermeasure. An extension of previous work, the paper reports an assessment of CQCCs generalisation across three different databases and shows that they deliver state-of-the-art performance in each case. The benefit of CQCC features stems from a variable spectro-temporal resolution which, while being fundamentally different to that used by most automatic speaker verification system front-ends, also captures reliably the tell-tale signs of manipulation artefacts which are indicative of spoofing attacks. The second contribution relates to a cross-database evaluation. Results show that CQCC configuration is sensitive to the general form of spoofing attack and use case scenario. This finding suggests that the past single-system pursuit of generalised spoofing detection may need rethinking.

The Clifford Fourier transform (CFT) can be applied to both vector and scalar fields. However, due to problems with big data, CFT is not efficient, because the algorithm is calculated in each semaphore. The sparse fast Fourier transform (sFFT) theory deals with the big data problem by using input data selectively. This has inspired us to create a new algorithm called sparse fast CFT (SFCFT), which can greatly improve the computing performance in scalar and vector fields. The experiments are implemented using the scalar field and grayscale and color images, and the results are compared with those using FFT, CFT, and sFFT. The results demonstrate that SFCFT can effectively improve the performance of multivector signal processing.

Fil: Medina, Juan Miguel. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Saavedra 15. Instituto Argentino de Matematica Alberto Calderon; Argentina

Fractional Fourier Transform are introduced as sparsifying transforms.Linear Canonical Transforms are introduced as sparsifying transforms.Various approaches for compressing three-dimensional images are suggested. Display Omitted Sparse recovery aims to reconstruct signals that are sparse in a linear transform domain from a heavily underdetermined set of measurements. The success of sparse recovery relies critically on the knowledge of transform domains that give compressible representations of the signal of interest. Here we consider two- and three-dimensional images, and investigate various multi-dimensional transforms in terms of the compressibility of the resultant coefficients. Specifically, we compare the fractional Fourier (FRT) and linear canonical transforms (LCT), which are generalized versions of the Fourier transform (FT), as well as Hartley and simplified fractional Hartley transforms, which differ from corresponding Fourier transforms in that they produce real outputs for real inputs. We also examine a cascade approach to improve transform-domain sparsity, where the Haar wavelet transform is applied following an initial Hartley transform. To compare the various methods, images are recovered from a subset of coefficients in the respective transform domains. The number of coefficients that are retained in the subset are varied systematically to examine the level of signal sparsity in each transform domain. Recovery performance is assessed via the structural similarity index (SSIM) and mean squared error (MSE) in reference to original images. Our analyses show that FRT and LCT transform yield the most sparse representations among the tested transforms as dictated by the improved quality of the recovered images. Furthermore, the cascade approach improves transform-domain sparsity among techniques applied on small image patches.

We propose an approach to the fast numerical evaluation of the continuous wavelet transform with the Morlet wavelet based on the replacement of the Gaussian factor in the latter by a hierarchical sequence of B-splines and their application to the image formed by the analyzed signal multiplied by a set of periodic functions. We show that the suggested approach results in a significant reduction of the resulting data storage (almost linear dependence on the sample length vs. the quadratic one required by conventional methods). In order to illustrate the workability of the proposed technique we applied it to the analysis of the data on the blood flow velocity data obtained in vivo from chorioallantoic membrane of chicken embryo, which exhibit non-stationarity, bi- or multirhythmicity.

The Fourier transform is widely used to diagnose induction motor faults through the monitoring of fault signatures from measured signals such as stator currents. For a good frequency resolution, Fourier transform needs a long signal acquisition time that increases the probability of speed fluctuations which, leads to fault signatures variations. In addition, limited acquisition time and acquired points generate unwanted sidelobes leakage phenomenon, caused by step frequency resolution. In signal processing, the use of window functions allows the avoidance of this phenomenon with the cost of losing a part of signal information. In this paper, the authors propose a new method for the diagnosis of induction motor broken bar fault based on sliding window discrete Fourier transform and the effect of sidelobes of sideband frequencies on the fundamental component amplitude of stator current. The main advantage of the proposed method is that one can detect the amplitude of the fault indicator frequency in vicinity of the fundamental one in shorter time and with good precision even if the motor turns at no-load when compared to used methods, as fast Fourier transform, zoom fast Fourier transform, multiple signal classification, and zoom multiple signal classification. The simulation and experimental results validate the effectiveness of the proposed method.

An ensemble lossless watermarking scheme is proposed in the present study by integrating different concepts like redistributed invariant wavelet transform, discrete fractional Fourier transform, singular value decomposition (SVD) and visual cryptography within the framework of a single algorithm. The invariant wavelet transform helps to obtain the transform domain, which is invariant to flipping and rotation of image, this is followed by discrete fractional Fourier transform to obtain the translation invariant domain. Finally, embedding positions are selected based on a key and reliable features are extracted by performing SVD on a window centered at these positions. Based on these reliable features a binary map is generated through which a master share is created. The corresponding ownership share is produced from the master share and the watermark. In verification process the same operations of the embedding process are applied to the test image to obtain the master share and the watermark is recovered by stacking it over the ownership share. There are two main features of the proposed scheme (1) The quality of the image to be watermarked do not degrade during the process and (2) the extracted watermark can still be identified even from a seriously distorted image. These findings are also demonstrated with the help of a comparative study with several related schemes.

This article proposes a new transceiver design for Single carrier frequency division multiple access (SCFDMA) system based on discrete wavelet transform (DWT). SCFDMA offers almost same structure as Orthogonal frequency division multiple access (OFDMA) with extra advantage of low Peak to Average Power Ratio (PAPR). Moreover, this article also suggests the application of Walsh Hadamard transform (WHT) for linear precoding (LP) to improve the PAPR performance of the system. Supremacy of the proposed transceiver over conventional Fast Fourier transform (FFT) based SCFDMA is shown through simulated results in terms of PAPR, spectral efficiency (SE) and bit error rate (BER).

In the process of estimating the thrust of an aircraft engine, there is a big problem that the differential pressure signal has large fluctuation. To deal with this problem, we develop an effective and robust adaptive de-noising algorithm based on domain transform combined with wavelet transform (D-WT). First, we do the domain transform for the signal, then sample the transformed signal, and finally the wavelet threshold transform is performed for the signal. Compared with the traditional wavelet transforms, the D-WT method filters the noise effectively and keeps more details.