Topic
Time–frequency analysis
About: Time–frequency analysis is a research topic. Over the lifetime, 5407 publications have been published within this topic receiving 104346 citations.
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TL;DR: In this article, an improved method is developed to improve the Hilbert-Huang transform (HHT) and provide a more precise description of the signal being inspected, which is performed on a number of carefully selected "monocomponent" functions rather than on the IMFs possibly with multiple numbers of frequency components.
77 citations
TL;DR: The concept of cepstrum is applied to eliminate the wave-shape function influence on the TF analysis, and a new algorithm, named de-shape synchrosqueezing transform (de-shape SST), is proposed.
Abstract: We propose to combine cepstrum and nonlinear time–frequency (TF) analysis to study multiple component oscillatory signals with time-varying frequency and amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of cepstrum is applied to eliminate the wave-shape function influence on the TF analysis, and we propose a new algorithm, named de-shape synchrosqueezing transform (de-shape SST). The mathematical model, adaptive non-harmonic model, is introduced and the de-shape SST algorithm is theoretically analyzed. In addition to simulated signals, several different physiological, musical and biological signals are analyzed to illustrate the proposed algorithm.
76 citations
TL;DR: Application of the TVOPS-VFCDM to renal blood flow data indicates some promise of a quantitative approach to understanding the dynamics of renal autoregulatory mechanisms as well as a possible approach to quantitatively discriminating between different strains of rats.
Abstract: A high resolution approach to estimating time-frequency spectra (TFS) and associated amplitudes via the use of variable frequency complex demodulation (VFCDM) is presented. This is a two-step procedure in which the previously developed time-varying optimal parameter search (TVOPS) technique is used to obtain TFS, followed by using the VFCDM to obtain even greater TFS resolution and instantaneous amplitudes associated with only the specific frequencies of interest. This combinational use of the TVOPS and the VFCDM is termed the TVOPS-VFCDM. Simulation examples are provided to demonstrate the performance of the TVOPS-VFCDM for high resolution TFS as well as instantaneous amplitude estimation. The simulation results show that the TVOPS-VFCDM approach provides the highest resolution and most accurate amplitude estimates when compared to the smoothed pseudo Wigner–Ville, continuous wavelet transform and Hilbert–Huang transform methods. Application of the TVOPS-VFCDM to renal blood flow data indicates some promise of a quantitative approach to understanding the dynamics of renal autoregulatory mechanisms as well as a possible approach to quantitatively discriminating between different strains of rats.
76 citations
TL;DR: In this paper, it was shown that an S-sparse Gabor representation in finite dimension with sparse time-frequency representations with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that S≤Cn/log(n)
Abstract: We consider signals and operators in finite dimension which have sparse time-frequency representations As main result we show that an S-sparse Gabor representation in ℂ
n
with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that S≤Cn/log (n) Our results are applicable to the channel estimation problem in wireless communications and they establish the usefulness of a class of measurement matrices for compressive sensing
76 citations
TL;DR: A deconvolutive short-time Fourier transform (DSTFT) spectrogram method is proposed, which improves the time-frequency resolution and reduces the cross-terms simultaneously by applying a 2-D deconvolution operation on the STFT spectrogram.
Abstract: The short-time Fourier transform (STFT) spectrogram, which is the squared modulus of the STFT, is a smoothed version of the Wigner-Ville distribution (WVD). The STFT spectrogram is 2-D convolution of the the signal WVD and the window function WVD. In this letter, we propose a deconvolutive short-time Fourier transform (DSTFT) spectrogram method, which improves the time-frequency resolution and reduces the cross-terms simultaneously by applying a 2-D deconvolution operation on the STFT spectrogram. Compared to the STFT spectrogram, the spectrogram obtained by the proposed method shows a clear improvement in the time-frequency resolution. Computer simulations are provided to illustrate the good performance of the proposed method, compared with some traditional time-frequency representation (TFR) methods.
76 citations