2023
DOI: 10.3390/electronics12030745
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Increasing the Speed of Multiscale Signal Analysis in the Frequency Domain

Abstract: In the Mallat algorithm, calculations are performed in the time domain. To speed up the signal conversion at each level, the wavelet coefficients are sequentially halved. This paper presents an algorithm for increasing the speed of multiscale signal analysis using fast Fourier transform. In this algorithm, calculations are performed in the frequency domain, which is why the authors call this algorithm multiscale analysis in the frequency domain. For each level of decomposition, the wavelet coefficients are det… Show more

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Cited by 3 publications
(4 citation statements)
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“…We call the frequency shift caused by object movement as the Doppler effect or Doppler shift [37]. The frequency relationship [38] between the transmitter and the receiver is as follows. f=()v±vsvvs·f ${f}^{\prime }=\left(\frac{v\pm {v}_{s}}{v\mp {v}_{s}}\right)\cdot f$ f=|ff|, ${\increment}f=\vert {f}^{\prime }-f\vert ,$ Where f is transmitter frequency, f ′ is receiver frequency, v is the propagation speed of acoustic signal in the air, v s is speed of target object movement, and ∆ f is the frequency shift.…”
Section: System Designmentioning
confidence: 99%
See 1 more Smart Citation
“…We call the frequency shift caused by object movement as the Doppler effect or Doppler shift [37]. The frequency relationship [38] between the transmitter and the receiver is as follows. f=()v±vsvvs·f ${f}^{\prime }=\left(\frac{v\pm {v}_{s}}{v\mp {v}_{s}}\right)\cdot f$ f=|ff|, ${\increment}f=\vert {f}^{\prime }-f\vert ,$ Where f is transmitter frequency, f ′ is receiver frequency, v is the propagation speed of acoustic signal in the air, v s is speed of target object movement, and ∆ f is the frequency shift.…”
Section: System Designmentioning
confidence: 99%
“…We call the frequency shift caused by object movement as the Doppler effect or Doppler shift [37]. The frequency relationship [38] between the transmitter and the receiver is as follows.…”
Section: Doppler Shift Of Different Digitmentioning
confidence: 99%
“…There are well-known ways to implement the continuous wavelet transform (WT) using the fast Fourier transform (FFT) [7], [8]. The authors have developed ways to increase the speed of MSA in the frequency domain based on wavelets constructed in the frequency domain [9]. The authors proposed an MSA algorithm using wavelets based on derivatives of the Gauss function [10], [11].…”
Section: Introductionmentioning
confidence: 99%
“…Therefore, the appropriate threshold, threshold function, and wavelet base are the key to the denoising effect [ 7 ]. The design of soft and hard threshold functions has also become a hot research topic; the soft threshold function focuses on smoothing the image and retaining the image details, while the hard threshold function can remove the noise more thoroughly, but it will lose some detail information, resulting in a loss of accuracy [ 8 ]. Researchers have spent a lot of effort to integrate the respective advantages of the soft threshold function and the hard threshold function [ 9 ] to obtain a moderate threshold function.…”
Section: Introductionmentioning
confidence: 99%