Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 1
items per page: 25 50 75
Sort by:
Download PDF Download RIS Download Bibtex

Abstract

Time invariant linear operators are the building blocks of signal processing. Weighted circular convolution and signal processing framework in a generalized Fourier domain are introduced by Jorge Martinez. In this paper, we prove that under this new signal processing framework, weighted circular convolution also has a generalized time invariant property. We also give an application of this property to algorithm of continuous wavelet transform (CWT). Specifically, we have previously studied the algorithm of CWT based on generalized Fourier transform with parameter 1. In this paper, we prove that the parameter can take any complex number. Numerical experiments are presented to further demonstrate our analyses.
Go to article

Bibliography

  1.  N. Holighaus, G. Koliander, Z. Průša, and L.D. Abreu, “Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction Algorithm,” IEEE Trans. Signal Process., vol. 67, no. 15, pp. 3894–3908, 2019.
  2.  M. Rayeezuddin, B. Krishna Reddy, and D. Sudheer Reddy, “Performance of reconstruction factors for a class of new complex continuous wavelets,” Int. J. Wavelets Multiresolution Inf. Process., vol. 19, no. 02, p. 2050067, 2021, doi: 10.1142/S0219691320500678.
  3.  Y. Guo, B.-Z. Li, and L.-D. Yang, “Novel fractional wavelet transform: Principles, MRA and application,” Digital Signal Process., vol. 110, p. 102937, 2021. [Online]. Available: doi: 10.1016/j.dsp.2020.102937.
  4.  V.K. Patel, S. Singh, and V.K. Singh, “Numerical wavelets scheme to complex partial differential equation arising from Morlet continuous wavelet transform,” Numer. Methods Partial Differ. Equations, vol. 37, no. 2, pp. 1163–1199, mar 2021.
  5.  C.K. Chui, Q. Jiang, L. Li, and J. Lu, “Signal separation based on adaptive continuous wavelet-like transform and analysis,” Appl. Comput. Harmon. Anal., vol. 53, pp. 151‒179, 2021.
  6.  O. Erkaymaz, I.S. Yapici, and R.U. Arslan, “Effects of obesity on time-frequency components of electroretinogram signal using continuous wavelet transform,” Biomed. Signal Process. Control, vol. 66, p. 102398, 2021.
  7.  Z. Yan, P. Chao, J. Ma, D. Cheng, and C. Liu, “Discrete convolution wavelet transform of signal and its application on BEV accident data analysis,” Mech. Syst. Signal Process., vol. 159, 2021.
  8.  R. Bardenet and A. Hardy, “Time-frequency transforms of white noises and Gaussian analytic functions,” Appl. Comput. Harmon. Anal., vol. 50, pp. 73–104, 2021, doi: 10.1016/j.acha.2019.07.003.
  9.  M.X. Cohen, “A better way to define and describe Morlet wavelets for time-frequency analysis,” NeuroImage, vol. 199, pp. 81–86, 2019. doi: 10.1016/j.neuroimage.2019.05.048.
  10.  H. Yi and H. Shu, “The improvement of the Morlet wavelet for multi-period analysis of climate data,” C.R. Geosci., vol. 344, no. 10, pp. 483–497, 2012.
  11.  S.G. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way. Academic Press, 2009.
  12.  H. Yi, P. Ouyang, T. Yu, and T. Zhang, “An algorithm for Morlet wavelet transform based on generalized discrete Fourier transform,” Int. J. Wavelets Multiresolution Inf. Process., vol. 17, no. 05, p. 1950030, 2019, doi: 10.1142/S0219691319500309.
  13.  R. Tolimieri, M. An, and C. Lu, Algorithms for Discrete Fourier Transform and Convolution. Springer, 1997.
  14.  J.-M. Attendu and A. Ross, “Method for finding optimal exponential decay coefficient in numerical Laplace transform for application to linear convolution,” Signal Process., vol. 130, pp. 47–56, 2017.
  15.  W. Li and A.M. Peterson, “FIR Filtering by the Modified Fermat Number Transform,” IEEE Trans. Acoust. Speech Signal Process., vol. 38, no. 9, pp. 1641–1645, 1990.
  16.  M.J. Narasimha, “Linear Convolution Using Skew-Cyclic Convolutions,” Signal Process. Lett., vol. 14, no. 3, pp. 173–176, 2007.
  17.  J. Martinez, R. Heusdens, and R.C. Hendriks, “A Generalized Poisson Summation Formula and its Application to Fast Linear Convolution,” IEEE Signal Process Lett., vol. 18, no. 9, pp. 501–504, 2011.
  18.  R.C. Guido, F. Pedroso, A. Furlan, R.C. Contreras, L.G. Caobianco, and J.S. Neto, “CWT×DWT×DTWT×SDTWT: Clarifying terminologies and roles of different types of wavelet transforms,” Int. J. Wavelets Multiresolution Inf. Process., vol. 18, no. 06, p. 2030001, 2020, doi: 10.1142/S0219691320300017.
  19.  P. Kapler, “An application of continuous wavelet transform and wavelet coherence for residential power consumer load profiles analysis,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 69, no. 1, p. e136216, 2021, doi: 10.24425/bpasts.2020.136216.
  20.  J. Martinez, R. Heusdens, and R.C. Hendriks, “A generalized Fourier domain: Signal processing framework and applications,” Signal Process., vol. 93, no. 5, pp. 1259‒1267, 2013.
  21.  S. Hui and S.H. Żak, “Discrete Fourier transform and permutations,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 67, no. 6, pp. 995–1005, 2019.
  22.  Z. Babic and D.P. Mandic, “A fast algorithm for linear convolution of discrete time signals,” in 5th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Service. TELSIKS 2001. Proceedings of Papers (Cat. No.01EX517), vol. 2, 2001, pp. 595–598.
  23.  H. Yi, S. Y. Xin, and J. F. Yin, “A Class of Algorithms for ContinuousWavelet Transform Based on the Circulant Matrix,” Algorithms, vol. 11, no. 3, p. 24, 2018.
  24.  D. Spałek, “Two relations for generalized discrete Fourier transform coefficients,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 66, no. 3, pp. 275– 281, 2018, doi: 10.24425/123433.
Go to article

Authors and Affiliations

Hua Yi
1
ORCID: ORCID
Yu-Le Ru
1
Yin-Yun Dai
1

  1. School of Mathematics and Physics, Jinggangshan University, Ji’an, 343009, P.R. China

This page uses 'cookies'. Learn more