Showing papers on "Time–frequency analysis published in 2001"
TL;DR: A criterion that can provide a measure of time–frequency distribution concentration is proposed that does not need normalization in order to behave properly when cross-terms are present and does not discriminate low concentrated components with respect to the highly concentrated ones within the same distribution.
366 citations
TL;DR: For phase-amplitude problems, the original Fourier transform is found to be more important than the amplitude for the FRFT/LCT, and the WDF is used to explain why fractional/canonical convolution can be used for space-variant pattern recognition.
Abstract: The fractional Fourier transform (FRFT) is a useful tool for signal processing. It is the generalization of the Fourier transform. Many fractional operations, such as fractional convolution, fractional correlation, and the fractional Hilbert transform, are defined from it. In fact, the FRFT can be further generalized into the linear canonical transform (LCT), and we can also use the LCT to define several canonical operations. In this paper, we discuss the relations between the operations described above and some important time-frequency distributions (TFDs), such as the Wigner distribution function (WDF), the ambiguity function (AF), the signal correlation function, and the spectrum correlation function. First, we systematically review the previous works in brief. Then, some new relations are derived and listed in tables. Then, we use these relations to analyze the applications of the FRPT/LCT to fractional/canonical filter design, fractional/canonical Hilbert transform, beam shaping, and then we analyze the phase-amplitude problems of the FRFT/LCT. For phase-amplitude problems, we find, as with the original Fourier transform, that in most cases, the phase is more important than the amplitude for the FRFT/LCT. We also use the WDF to explain why fractional/canonical convolution can be used for space-variant pattern recognition.
266 citations
TL;DR: A ridge theorem of the Gaussian chirp dictionary is proved, from which an estimate of the locally optimal scale and chirP is built and the efficiency and speed of the method is demonstrated on a sound signal.
Abstract: We introduce a modified matching pursuit algorithm, called fast ridge pursuit, to approximate N-dimensional signals with M Gaussian chirps at a computational cost O(MN) instead of the expected O(MN/sup 2/logN). At each iteration of the pursuit, the best Gabor atom is first selected, and then, its scale and chirp rate are locally optimized so as to get a "good" chirp atom, i.e., one for which the correlation with the residual is locally maximized. A ridge theorem of the Gaussian chirp dictionary is proved, from which an estimate of the locally optimal scale and chirp is built. The procedure is restricted to a sub-dictionary of local maxima of the Gaussian Gabor dictionary to accelerate the pursuit further. The efficiency and speed of the method is demonstrated on a sound signal.
204 citations
TL;DR: The idea disclosed in this work is that a nonstationary approach can be approximated using signal bases that are especially suited for the analysis/synthesis of non stationary signals using orthogonal signal bases of the chirp type that in practice correspond to the fractional Fourier transform signal basis.
Abstract: Traditional multicarrier techniques perform a frequency-domain decomposition of a channel characterized by frequency-selective distortion in a plurality of subchannels that are affected by frequency flat distortion. The distortion in each independent subchannel can then be easily compensated by simple gain and phase adjustments. Typically, digital Fourier transform schemes make the implementation of the multicarrier system feasible and attractive with respect to single-carrier systems. However, when the channel is time-frequency-selective, as it usually happens in the rapidly fading wireless channel, this traditional methodology fails. Since the channel frequency response is rapidly time-varying, the optimal transmission/reception methodology should be able to process nonstationary signals. In other words, the subchannel carrier frequencies should be time-varying and ideally decompose the frequency distortion of the channel perfectly at any instant in time. However, this ideally optimal approach presents significant challenges both in terms of conceptual and computational complexity. The idea disclosed in this work is that a nonstationary approach can be approximated using signal bases that are especially suited for the analysis/synthesis of nonstationary signals. We propose in fact the use of a multicarrier system that employs orthogonal signal bases of the chirp type that in practice correspond to the fractional Fourier transform signal basis. The significance of the methodology relies on the important practical consideration that analysis/synthesis methods of the fractional Fourier type can be implemented with a complexity that is equivalent to the traditional fast Fourier transform.
202 citations
TL;DR: A new kernel for the design of a high resolution time-frequency distribution (TFD) is introduced and it is shown that this distribution can solve problems that the Wigner-Ville distribution (WVD) or the spectrogram cannot.
Abstract: The paper introduces a new kernel for the design of a high resolution time-frequency distribution (TFD). We show that this distribution can solve problems that the Wigner-Ville distribution (WVD) or the spectrogram cannot. In particular, the proposed distribution can resolve two close signals in the time-frequency domain that the two other distributions cannot. Moreover, we show that the proposed distribution is more accurate than the WVD and the spectrogram in the estimation of the instantaneous frequency of a stepped FM signal embedded in additive Gaussian noise. Synthetic and real data collected from real-world applications are shown to validate the proposed distribution.
150 citations
TL;DR: A lower bound on the uncertainty product of signal representations in two FrFT domains for real signals is obtained, and it is shown that a Gaussian signal achieves the lower bound.
Abstract: The fractional Fourier transform (FrFT) can be thought of as a generalization of the Fourier transform to rotate a signal representation by an arbitrary angle /spl alpha/ in the time-frequency plane. A lower bound on the uncertainty product of signal representations in two FrFT domains for real signals is obtained, and it is shown that a Gaussian signal achieves the lower bound. The effect of shifting and scaling the signal on the uncertainty relation is discussed. An example is given in which the uncertainty relation for a real signal is obtained, and it is shown that this relation matches with that given by the uncertainty relation derived.
129 citations
TL;DR: It is shown that the proposed interference excision method permits both data-dependent windowing and time-varying filtering and leads to improved BER performance of the DS/SS system.
Abstract: A new adaptive excision approach for nonstationary interference excision in direct sequence spread spectrum (DS/SS) communications is introduced. The proposed excision approach is based on the attractive localization properties of the impulse responses of the multiple pole filters. These impulse responses have Gaussian-like shapes and decrease in bandwidth with higher pole multiplicities. When used as data windows, they field a large class of computationally efficient short-time Fourier transforms (STFTs). Localization measures can be applied to determine the optimum window that maximally concentrates the interference in the time-frequency (t.-f.) domain. Interference mitigation is then achieved by applying a binary excision mask to the corresponding STFT for each data bit. We show that the proposed interference excision method permits both data-dependent windowing and time-varying filtering and leads to improved BER performance of the DS/SS system. The paper also derives the general optimum receiver implementing the STFT-based interference excision system.
118 citations
TL;DR: The earlier known phenomena, connected with voluntary movements, were confirmed and a new evidence concerning focal ERD/surround ERS and beta activity post-movement synchronization was found.
89 citations
TL;DR: In this paper, the authors employed a suitable time-frequency representation (Wavelet Transform or Short Time Fourier Transform) to extract the envelope of reflected pulse echo, together with a suitable pulse detection algorithm (threshold or correlation) for time-of-flight estimation.
75 citations
TL;DR: Results show that bionic wavelet transform performs better than WT in these three aspects, and that BWT is appropriate for speech signal processing, especially for cochlear implants.
Abstract: A new adaptive wavelet transform, named bionic wavelet transform (BWT), is developed based on a model of the active auditory system. The most distinguishing characteristic of BWT is that its resolution in the time-frequency domain can be adaptively adjusted not only by the signal frequency but also by the signal instantaneous amplitude and its first-order differential. The automatically adjusted resolution, even in a fixed frequency along the time-axis, is achieved by introducing the active control of the auditory system into the wavelet transform (WT). Other properties of BWT include that: 1) BWT is a nonlinear transform that has high sensitivity and frequency selectivity; 2) BWT represents the signal with a concentrated energy distribution; and 3) the inverse BWT can reconstruct the original signal from its time-frequency representation. In order to compare these three properties between BWT and WT, experiments were conducted on both constructed signals and real speech signals. The results show that BWT performs better than WT in these three aspects, and that BWT is appropriate for speech signal processing, especially for cochlear implants.
72 citations
TL;DR: The present technique of determining MNF has the advantage that it is possible to determine the frequency content of the ME signal during short and nonstationary contractions, and confirmed earlier studies that MNF is independent of angular velocity.
Abstract: A time-frequency approach using wavelets to study movements at different angular velocities is considered. The authors summarized the application of the continuous wavelet transform (CWT) to the analysis of the surface myoelectric (ME) signal. The present technique of determining MNF has the advantage that it is possible to determine the frequency content of the ME signal during short and nonstationary contractions. In addition, the CWT method is very reliable for the analysis of nonstationary biological signals and does not require any smoothing function as do methods based on Wigner-Ville. However, using time-frequency methods involves two main tradeoffs: i.e., potential increases in performance for a given application versus computational complexity and storage requirements. Our results confirmed earlier studies that MNF is independent of angular velocity.
TL;DR: A new method is presented for the analysis of event-related EEG phenomena, in particular event related desynchronisation (ERD) and event related synchronisation (ERS) related to a voluntary movement, which offers high time-frequency resolution and increased ERD/ERS sensitivity.
Abstract: A new method is presented for the analysis of event-related EEG phenomena, in particular event related desynchronisation (ERD) and event related synchronisation (ERS) related to a voluntary movement; the method offers: high time-frequency resolution and, hence, increased ERD/ERS sensitivity (especially in the gamma band, where improvement can exceed an order of magnitude); the ability to analyse the whole picture of energy changes at once, without setting a priori the analysed frequency bands; and a parametric description of the signal's structures. The main idea is based upon averaging energy distributions of single EEG trials in the time-frequency plane. As the estimator for the signal's energy density, matching pursuit is chosen, with stochastic Gabor dictionaries. Other possible estimates are presented on a simulated signal and discussed briefly. The consistency of the results with previous findings is evaluated on the data from a classical voluntary finger movement experiment.
TL;DR: The robust short-time Fourier transform (STFT) and the robust Wigner distribution (WD), based on the simple median filter, are proposed and their efficiency in time-frequency analysis is demonstrated.
TL;DR: It is shown that similar problems arise with the Cohen-Lee (1988, 1989) instantaneous bandwidth of a signal and a new formulation for the instantaneous bandwidth is proposed that is consistent with its interpretation as the conditional standard deviation in frequency of a TFD.
Abstract: Cohen (1989, 1995) has introduced and extensively studied and developed the concept of the instantaneous bandwidth of a signal. Specifically, instantaneous bandwidth is interpreted as the spread in frequency about the instantaneous frequency, which is itself interpreted as the average frequency at each time. This view stems from a joint time-frequency distribution (TFD) analysis of the signal, where instantaneous frequency and instantaneous bandwidth are taken to be the first two conditional spectral moments, respectively, of the distribution. However, the traditional definition of instantaneous frequency, namely, as the derivative of the phase of the signal, is not consistent with this interpretation, and new definitions have therefore been proposed previously. We show that similar problems arise with the Cohen-Lee (1988, 1989) instantaneous bandwidth of a signal and propose a new formulation for the instantaneous bandwidth that is consistent with its interpretation as the conditional standard deviation in frequency of a TFD. We give the kernel constraints for a distribution to yield this new result, which is a modification of the kernel proposed by Cohen and Lee. These new kernel constraints yield a modified Cohen-Lee TFD whose first two conditional moments are interpretable as the average frequency and bandwidth at each time, respectively.
TL;DR: In this paper, a combination of Littlewood{Paley and Gabor theory was used to characterize L p in terms of Gabor expansions, and it was shown that partial sums of these expansions converge in L p -norm.
Abstract: It is known that Gabor expansions do not converge unconditionally in L p and that L p cannot be characterized in terms of the magnitudes of Gabor coecien ts. By using a combination of Littlewood{Paley and Gabor theory, we show that L p can nevertheless be characterized in terms of Gabor expansions, and that the partial sums of Gabor expansions converge in L p -norm.
TL;DR: This work builds on Cohen's work on instantaneous bandwidth and frequency by extending it to a multiwindow framework for polynomial phase signals, and develops a method utilizing this new multiwindow time-varying spectral technique for estimating the instantaneous frequency of a signal.
Abstract: We build on Cohen's work (Cohen and Lee 1988, 1989; Cohen 1990, 1995) on instantaneous bandwidth and frequency by extending it to a multiwindow framework for polynomial phase signals. Unlike the case with a single spectrogram, which Cohen considered, our multiwindow framework allows one to obtain a time-varying spectral estimate that simultaneously satisfies instantaneous bandwidth and frequency constraints. We then develop a method utilizing this new multiwindow time-varying spectral technique for estimating the instantaneous frequency of a signal. The method is computationally simple, asymptotically unbiased for noise-free signals, and provides a signal-to-noise ratio (SNR) improvement of more than 3 dB over other estimators, including the cross-polynomial Wigner distribution method, for quadratic and cubic FM signals.
TL;DR: Results show that Wavelet transform can well isolate weak sub-harmonics or higher-harmonic from the fundamental harmonic response and the random property of chaotic response in the time–frequency domain can easily be observed by the wavelet transform even for a set of short recorded response data.
Abstract: Wavelet transform (WT) is a method that converts a time response presentation in 1D-space into a time-frequency response in 2D-space The main advantages of this transformation are its amplified functional and its 2D analysis presentation The present study is focused on investigating the nonlinear and chaotic behaviors in the time–frequency domain presentation by using wavelet transform The dynamic information from the time–frequency domain is very useful and important for an understanding of the dynamic behavior and control of nonlinear and chaotic systems The present study results show that: (1) WT can well isolate weak sub-harmonics or higher-harmonics from the fundamental harmonic response; (2) the random property of chaotic response in the time–frequency domain can easily be observed by the wavelet transform even for a set of short recorded response data; (3) dynamic behavior of the response phase in the time and frequency domain can be observed by its WT The proposed method is illustrated by investigating the dynamic behavior of a five-degree-of-freedom Duffing's structural system, and the chaotic response is simulated by a single-degree-of-freedom Duffing's system
TL;DR: Results with synthetic signals and a real-world signal indicate the potential of the HRT method in identifying the components in noisy environments and could be extended to detect components generated by any FM law provided they can be modeled by parametric equations.
TL;DR: In this paper, a method based on time-frequency representations is presented for identifying the non-linear modal parameters of a multi-degree-of-freedom nonlinear lightly damped mechanical system.
21 Oct 2001
TL;DR: Qualitative results indicate the potential of the proposed reduced multi-Gabor systems to yield a salient representation of typical audio signals while at the same time reducing computational costs as compared to a full multiresolution decomposition.
Abstract: We consider the construction of multiresolution Gabor dictionaries appropriate for audio signal analysis. Motivated by a desire for parsimony and efficiency, we propose and formalise the idea of reduced multi-Gabor systems, showing that they constitute a frame for L/sup 2/(R) and other Hilbert spaces of interest. In order to demonstrate the practicality of such a scheme, we apply it to the atomic decomposition of music and speech signals observed in noise. Qualitative results indicate the potential of this method to yield a salient representation of typical audio signals while at the same time reducing computational costs as compared to a full multiresolution decomposition.
TL;DR: In this article, an adaptive phase energy (APE) approach for time-frequency representation of varying harmonic signals is presented. But the APE is not suitable for the case of non-stationary signals.
TL;DR: A chirp time–frequency representation for non-stationary signals is proposed, and—via a multi-window Gabor expansion—the corresponding evolutionary spectra is associated with it.
21 Oct 2001
TL;DR: The main benefits of the proposed reassignment stage are that it yields an improved time-frequency localisation estimate relative to standard methods, and that it produces a measure of the variance of these estimates to be used as an aid in later processing.
Abstract: The reassignment method for the short-time Fourier transform is proposed as a technique for improving the time and frequency estimates of musical audio data. Based on this representation, four classes of expected objects (sinusoid, unresolved sinusoid, transient and noise) are proposed and explained. Pattern classification methods are then used to extract objects conforming to these classes from individual frames of the reassigned spectrogram, with each frame being examined independently. Results for several simple real-world examples are presented, showing the capability of this method even without the aid of tracking from frame to frame. The main benefits of the proposed reassignment stage are that it yields an improved time-frequency localisation estimate relative to standard methods, and that it produces a measure of the variance of these estimates to be used as an aid in later processing.
TL;DR: A sensitivity analysis technique in the frequency domain is applied to point out the more important parameters of the model to validate the optimized model of a building thermal model.
TL;DR: The various applications in MRS of the wavelet transform and related time‐frequency methods are surveyed and the mathematical tools needed are reviewed.
Abstract: We survey the various applications in MRS of the wavelet transform and related time-frequency methods. For the sake of completeness, we first quickly review the mathematical tools needed.
TL;DR: A joint time-frequency (TF) resolution of the Gabor transform-based signal analysis is investigated, and an appropriate adaptation of the window length according to the rate of frequency modulation is discussed.
Abstract: A joint time-frequency (TF) resolution of the Gabor transform-based signal analysis is investigated. First, different window functions used in the Gabor transform are compared with regard to their time duration and frequency bandwidth. Next, optimal windows with small TF support are found. Finally, a practical choice of windows maximizing signal energy concentration in the TF domain is examined. In this case, the error of signal reconstruction from the Gabor coefficients and the mean square width of the short-time signal spectrum are computed for different time-varying test signals and minimized in the optimization process. An appropriate adaptation of the window length according to the rate of frequency modulation is discussed.
Journal Article•
TL;DR: Matching Pursuit with stochastic dictionaries is characterized by an unmatched resolution in time-frequency space; moreover it allows for parametric description of all signal features in the framework of the same formalism.
Abstract: Matching Pursuit (MP)--a method of high-resolution signal analysis--is described in the context of other methods operating in time-frequency space. The method relies on an adaptive approximation of a signal by means of waveforms chosen from a very large and redundant dictionary of functions. The MP performance is illustrated by simulations and examples of sleep spindles and slow wave activity analysis. An improvement of the original procedure, relying on the introduction of stochastic dictionaries, is proposed. A comparison of the performance of dyadic and stochastic dictionaries is presented. MP with stochastic dictionaries is characterized by an unmatched resolution in time-frequency space; moreover it allows for parametric description of all (periodic and transient) signal features in the framework of the same formalism. Matching pursuit is especially suitable for analysis of non-stationary signals and is a unique tool for the investigation of dynamic changes of brain activity.
01 Jan 2001
TL;DR: A new scheme based on the combination of spherical harmonic functions and wavelet networks on the sphere to model a surface efficiently in a coarse to fine hierarchy is presented.
Abstract: In this paper we present a new scheme for the representation of object surfaces. The purpose is to model a surface efficiently in a coarse to fine hierarchy. Our scheme is based on the combination of spherical harmonic functions and wavelet networks on the sphere. The coefficients can be estimated from scattered data sampled from a star-shaped object’s surface. Spherical harmonic functions are used to model the coarse structure of the surface, while spherical Gabor wavelets are used for the representation of fine scale detail. Theoretical background on wavelets on the sphere is provided as well as a discussion of implementation issues concerning convolutions on the sphere. Results are presented which show the efficiency of the proposed representation.
TL;DR: Wavelet transform is a new technique to analyze signals and images, and it can reveal the local and global features of signal and image from different aspects.
Abstract: Wavelet transform is a new technique to analyze signals and images, and it can reveal the local and global features of signal and image from different aspects. In this study, the electroch...
TL;DR: An efficient method for robustly calculating time-frequency attributes of a signal, including instantaneous mean frequency, bandwidth, kurtosis, and other moments is presented, which performs as well as the best techniques based on adaptive TFRs.
Abstract: We present an efficient method for robustly calculating time-frequency attributes of a signal, including instantaneous mean frequency, bandwidth, kurtosis, and other moments. Most current attribute estimation techniques involve a costly intermediate step of computing a (highly oversampled) two-dimensonal (2-D) quadratic time-frequency representation (TFR), which is then collapsed to the one-dimensonal (1-D) attribute. Using the principles of hybrid linear/quadratic time-frequency analysis (time-frequency distribution series), we propose computing attributes as nonlinear combinations of the (slightly oversampled) linear Gabor coefficients of the signal. The method is both computationally efficient and accurate; it performs as well as the best techniques based on adaptive TFRs. To illustrate, we calculate an attribute of a seismic cross section.