Wavelet filtering of signals without using model functions





recursive algorithm, root-mean-square error, numerical optimization, model signal, discrete wavelet transformation, noise filtering, decomposition level


The effective wavelet filtering of real signals is impossible without determining their shape. The shape of a real signal is related to its wavelet spectrum. For shape analysis, a continuous color wavelet spectrogram of signal level is often used. The disadvantage of continuous wavelet spectrogram is the complexity of analyzing a blurry color image. A real signal with additive noise strongly distorts the spectrogram based on continuous wavelet analysis compared to a pure signal. Therefore, the identification of a real signal by using a continuous color wavelet spectrogram is difficult. To solve this problem, for the first time, a comparative analysis of spectrograms of signals and correlation matrices is carried out. The spectrograms of signals are obtained based on continuous wavelet transformation in the form of images with areas of different colors of variable intensity. Correlation matrices are computed by using mathematical functions of the coefficients of discrete wavelet spectra.


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Form and wavelet power spectral density of HypChirps signal (two frequencies with hyperbolic functions of time)


2022-02-15 — Updated on 2022-09-30



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