Novel Short-Time Fractional Fourier Transform: Theory, Implementation, and Applications

Shi, Jun; Zheng, Jiabin; Li, Xiaoping; Wang, Xiang; Zhang, Qinyu

doi:10.1109/tsp.2020.2992865

Cited by 66 publications

(20 citation statements)

References 59 publications

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“…In order to obtain a more canonical TF filter, i.e., parameters σ and β have a clear role in determining the shape of W h σ,β (t, ω), we use the fractional Fourier transform (FrFT) [67,68] to rotate Gaussian window g(t) with parameter β, which is given by…”

Section: Ct With Rotation Windowmentioning

confidence: 99%

“…In this paper, we first theoretically analyze the effect of variance and CR parameters on the TF resolution of CT and prove that a narrow window limits the matching capacity of chirp basis. We compare the CT with its extension that employs a rotating Gaussian window by fractional Fourier transform [67,68]. By comparison, we conclude that the parameters of rotation-window CT have a clearer geometric meaning than that of the standard CT, but this rotation extension is actually the CT with a special parameter combination and thus can not localize a signal in both time and frequency precisely.…”

Section: Introductionmentioning

confidence: 99%

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High-resolution chirplet transform: from parameters analysis to parameters combination

Zhu¹,

Li²,

Zhang³

et al. 2021

Preprint

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The standard chirplet transform (CT) with a chirpmodulated Gaussian window provides a valuable tool for analyzing linear chirp signals. The parameters present in the window determine the performance of CT and play a very important role in high-resolution time-frequency (TF) analysis. In this paper, we first give the window shape analysis of CT and compare it with the extension that employs a rotating Gaussian window by fractional Fourier transform. The given parameters analysis provides certain theoretical guidance for developing high-resolution CT. We then propose a multi-resolution chirplet transform (MrCT) by combining multiple CTs with different parameter combinations. These are combined geometrically to obtain an improved TF resolution by overcoming the limitations of any single representation of the CT. By deriving the combined instantaneous frequency equation, we further develop a high-concentration TF post-processing approach to improve the readability of the MrCT. Numerical experiments on simulated and real signals verify its effectiveness.

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Section: Ct With Rotation Windowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-resolution chirplet transform: from parameters analysis to parameters combination

Zhu¹,

Li²,

Zhang³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Signal processing in the short-time domain [9] is a suitable technique for carrying out time-frequency analysis and processing of quasi-stationary signals. It can be applied to ECG signal processing [10], spectral analysis and speech processing [11], adaptive digital filtering [12], [13], radar emitter recognition [14], spectral analysis of biological signals [15], heart sound classification [16], time-frequency analysis of high-rate dynamic systems [17], etc. Short-time processing in the orthogonal transform domain can be realized by processing the signal in a window moving along the signal with an integer step.…”

Section: Introductionmentioning

confidence: 99%

Fast Hopping Discrete Sine Transform

Kober

2021

IEEE Access

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Discrete sine transform (DST) is widely used in digital signal processing such as image coding, spectral analysis, feature extraction, and filtering. This is because the discrete sine transform is close to the optimal Karhunen-Loeve transform for first-order Markov stationary signals with low correlation coefficients. Short-time (hopping) discrete sine transform can be employed for time-frequency analysis and adaptive processing quasi-stationary data such as speech, biomedical, radar and communication signals. Hopping transform refers to a transform computed on the signal of a fixed-size window that slides over the signal with an integer hop step. In this paper, we first derive a second-order recursive equation between DST spectra in equidistant signal windows, and then propose two fast algorithms for computing the hopping DST based on the recursive relationship and input-pruned DST algorithm. The performance of the proposed algorithms with respect to computational costs and execution time is compared with that of conventional sliding and fast DST algorithms. The computational complexity of the developed algorithms is lower than any of the existing algorithms, resulting in significant time savings.

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“…The study and the interpretation of multi-component non-stationary signals require a powerful analysis tool. Time-frequency (TF) analysis methods are used to measure how a signal's frequency components vary with time and provide an effective tool in non-stationary signals analysis [1][2][3][4][5][6][7]. The most frequently used TF representation is the linear TF analysis method, mainly including the short-time Fourier transform (STFT) [8], the continuous wavelet transform (CWT) [9], the Stockwell transform [10], and the chirplet transform (CT) [11].…”

Section: Introductionmentioning

confidence: 99%

IF equation: a feature extractor for high-concentration time-frequency representation

Zhu¹,

Yang²,

Zhang

2021

Preprint

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High-concentration time-frequency (TF) representation provides a valuable tool for characterizing multicomponent non-stationary signals. In our previous work, we proposed using an instantaneous frequency (IF) equation to sharpen the TF distribution and its effectiveness has been verified in experiments. In this paper, we systematically discuss why the IF equation-based TF analysis methods work and how to use the IF equation to improve the TF sharpness. By theory analysis, many popular TF post-processing methods, such as the synchroextracting transform, the multi-synchrosqueezing transform, and the time extracting transform, fall into the IF equation-based category. A comparison of the IF equation-based method with the popular synchrosqueezing transform is made. Numerical examples of the theoretical derivations are presented to illustrate the performance of the proposed IF equation-based TF analysis method.

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Novel Short-Time Fractional Fourier Transform: Theory, Implementation, and Applications

Cited by 66 publications

References 59 publications

High-resolution chirplet transform: from parameters analysis to parameters combination

High-resolution chirplet transform: from parameters analysis to parameters combination

Fast Hopping Discrete Sine Transform

IF equation: a feature extractor for high-concentration time-frequency representation

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