Instantaneous frequency estimation based on synchrosqueezing wavelet transform

Jiang, Qingtang; Suter, Bruce W.

doi:10.1016/j.sigpro.2017.03.007

Cited by 95 publications

(54 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A continuous wavelet transform (CWT) for the time domain signal x ( t ) is defined as follows:

{CWT}_{a, b} = \frac{1}{\sqrt{a}} \int_{- \infty}^{+ \infty} x ((), t) ψ^{*} ((), \frac{t - b}{a}) italicdt,

where a and b are scaling and translation parameters, respectively, and ψ * ( t ) is the complex conjugate of wavelet function (mother wavelet). For each wavelet function, a specific condition known as admissibility condition should be held:

\int_{0}^{+ \infty} \frac{{(||, \overset{ψ}{true} ((), ω))}^{2}}{ω} italicdω < \infty,

where

\overset{ψ}{true} ((), ω)

is the Fourier transform of ψ ( t ). Inequality (2) is satisfied if we have

{\overset{false^}{ψ} (ω)|}_{ω = 0} = 0

that is equivalent to have:

\int_{- \infty}^{+ \infty} ψ ((), t) italicdt = 0

.…”

Section: Basic Of Wavelet Transformmentioning

confidence: 99%

See 1 more Smart Citation

A new discrete wavelet transform appropriate for hardware implementation

Meshkat

Dehghani

2020

Circuit Theory & Apps

View full text Add to dashboard Cite

Summary A new method for computation of discrete wavelet transform is introduced. The impulse response of the finite impulse response (FIR) filter, as the main block in filter bank method, is realized such that orthonormal wavelet transform is achieved without using any multiplier as the most challenging part of the FIR filters. It is proved that the calculated Sobolev regularity of the proposed wavelet is higher than that of Daubechies for the same support width. Compared with most popular known wavelets, simulation results of the newly introduced wavelet for signal denoising prove remarkable advantage of our wavelet especially in terms of complexity and power consumption. The proposed wavelet and well‐known Daubechies wavelet are separately implemented on the Spartan‐6 FPGA (Field Programmable Gate Array) to compare the performance of them. The occupied slices and LUTs (Lookup Table) in realization of the proposed wavelet in comparison with those of Daubechies wavelet are decreased by 50% and 56%, respectively. Its power consumption at 100 MHz is also reduced by 86% in comparison with the Daubechies wavelet, and maximum frequency is increased by 186%. Implementation with standard cells of a 0.18‐μm CMOS (Complementary Metal Oxide Semiconductor Field Effect Transistor) technology shows 75% and 85% reduction in the power and chip area, respectively.

show abstract

“…A continuous wavelet transform (CWT) for the time domain signal x ( t ) is defined as follows:

{CWT}_{a, b} = \frac{1}{\sqrt{a}} \int_{- \infty}^{+ \infty} x ((), t) ψ^{*} ((), \frac{t - b}{a}) italicdt,

\int_{0}^{+ \infty} \frac{{(||, \overset{ψ}{true} ((), ω))}^{2}}{ω} italicdω < \infty,

where

\overset{ψ}{true} ((), ω)

is the Fourier transform of ψ ( t ). Inequality (2) is satisfied if we have

{\overset{false^}{ψ} (ω)|}_{ω = 0} = 0

that is equivalent to have:

\int_{- \infty}^{+ \infty} ψ ((), t) italicdt = 0

.…”

Section: Basic Of Wavelet Transformmentioning

confidence: 99%

“…where a and b are scaling and translation parameters, respectively, and ψ * (t) is the complex conjugate of wavelet function (mother wavelet). For each wavelet function, a specific condition known as admissibility condition should be held 30 :…”

Section: Basic Of Wavelet Transformmentioning

confidence: 99%

A new discrete wavelet transform appropriate for hardware implementation

Meshkat

Dehghani

2020

Circuit Theory & Apps

View full text Add to dashboard Cite

show abstract

“…Let x(t) ∈ B ε,△ and g be a function in the Schwartz class with supp( g) ⊆ [−△, △]. Let Γ 0 (t), Γ 0 (t) be defined by (12). Then we have the following.…”

Section: Stft-based Synchrosqueezing Transformmentioning

confidence: 99%

“…The 2nd-order SST improves the concentration of the time-frequency representation. Other SST related methods include the generalized WSST [16], a hybrid EMT-SST computational scheme [7], the synchrosqueezed wave packet transform [28], WSST with vanishing moment wavelets [5], the multitapered WSST [9], the demodulation-transform based SST [25,12,26], higher-order FSST [21], signal separation operator [6] and empirical signal separation algorithm [14]. The statistical analysis of synchrosqueezed transforms has been studied in [29].…”

Section: Introductionmentioning

confidence: 99%

Analysis of adaptive short-time Fourier transform-based synchrosqueezing transform

Cai

Jiang

et al. 2020

Anal. Appl.

Self Cite

View full text Add to dashboard Cite

Recently the study of modeling a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes has been a very active research area. The synchrosqueezing transform (SST) is a powerful method for instantaneous frequency estimation and component separation of non-stationary multicomponent signals. The short-time Fourier transform-based SST (FSST for short) reassigns the frequency variable to sharpen the timefrequency representation and to separate the components of a multicomponent non-stationary signal. Very recently the FSST with a time-varying parameter, called the adaptive FSST, was introduced. The simulation experiments show that the adaptive FSST is very promising in instantaneous frequency estimation of the component of a multicomponent signal, and in accurate component recovery. However the theoretical analysis of the adaptive FSST has not been carried out. In this paper, we study the theoretical analysis of the adaptive FSST and obtain the error bounds for the instantaneous frequency estimation and component recovery with the adaptive FSST and the 2nd-order adaptive FSST.

show abstract

“…with vanishing moment wavelets [41], the multitapered SST [42] and the demodulation-transform based SST [43,44]. In addition, the synchrosqueezed curvelet transform for two-dimensional mode decomposition was introduced in [45], the signal separation operator which is related to FSST was proposed in [46] and the empirical signal separation algorithm was introduced in [47].…”

Section: Introductionmentioning

confidence: 99%

Adaptive short-time Fourier transform and synchrosqueezing transform for non-stationary signal separation

et al. 2020

Self Cite

View full text Add to dashboard Cite

The synchrosqueezing transform, a kind of reassignment method, aims to sharpen the timefrequency representation and to separate the components of a multicomponent non-stationary signal. In this paper, we consider the short-time Fourier transform (STFT) with a time-varying parameter, called the adaptive STFT. Based on the local approximation of linear frequency modulation mode, we analyze the well-separated condition of non-stationary multicomponent signals using the adaptive STFT with the Gaussian window function. We propose the STFT-based synchrosqueezing transform (FSST) with a time-varying parameter, named the adaptive FSST, to enhance the time-frequency concentration and resolution of a multicomponent signal, and to separate its components more accurately. In addition, we also propose the 2nd-order adaptive FSST to further improve the adaptive FSST for the non-stationary signals with fast-varying frequencies. Furthermore, we present a localized optimization algorithm based on our well-separated condition to estimate the time-varying parameter adaptively and automatically. Simulation results on synthetic signals and the bat echolocation signal are provided to demonstrate the effectiveness and robustness of the proposed method.where A k (t), φ k (t) > 0, has been a very active research area over the past few years. Note that the number of component K may change with time t, but it should be constant for long enough time intervals. The representation of x(t) in (1) with A k (t) and φ k (t) varying slowly or more slowly than φ k (t) is called an adaptive harmonic model (AHM) representation of x(t), where A k (t) are called the instantaneous amplitudes and φ k (t) the instantaneous frequencies (IFs). To decompose x(t) as an AHM representation (1) is important to extract information, such as the underlying dynamics, hidden in x(t). Time-frequency (TF) analysis is widely used in engineering fields such as communication, radar and sonar as a powerful tool for analyzing time-varying non-stationary signals [1]. Time-frequency analysis is especially useful for signals containing many oscillatory components with slowly timevarying amplitudes and instantaneous frequencies. The short-time Fourier transform (STFT), the continuous wavelet transform (CWT) and the Wigner-Ville distribution are the most typical TF analysis, see details in [1]-[6]. Other TF distributions of Cohen's class include the exponential distribution [7], a smoothed pseudo Wigner distribution [8] and the complex-lag distribution [9].In addition, the TF signal analysis and synthesis using the eigenvalue decomposition method has been studied [10,11]. In particular, an eigenvalue decomposition-based approach which enables the separation of non-stationary components with overlapped supports in the TF plane has been proposed in [12].Recently a number of new TF analysis methods such as the Hilbert spectrum analysis with empirical mode decomposition (EMD) [13], the reassignment method [14] and synchrosqueezed wavelet transform (SST) [15] have also been proposed ...

show abstract

Instantaneous frequency estimation based on synchrosqueezing wavelet transform

Cited by 95 publications

References 28 publications

A new discrete wavelet transform appropriate for hardware implementation

A new discrete wavelet transform appropriate for hardware implementation

Analysis of adaptive short-time Fourier transform-based synchrosqueezing transform

Adaptive short-time Fourier transform and synchrosqueezing transform for non-stationary signal separation

Contact Info

Product

Resources

About