2019
DOI: 10.1142/s0219691319500309
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An algorithm for Morlet wavelet transform based on generalized discrete Fourier transform

Abstract: Continuous wavelet transform (CWT) is a linear convolution of signal and wavelet function for a fixed scale. This paper studies the algorithm of CWT with Morlet wavelet as mother wavelet by using nonzero-padded linear convolution. The time domain filter, which is a non-causal filter, is the sample of wavelet function. By making generalized discrete Fourier transform (GDFT) and inverse transform for this filter, we can get a geometrically weighted periodic extension of the filter when evaluated outside its orig… Show more

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Cited by 8 publications
(24 citation statements)
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“…The timedomain generator calculates statistics including mean, root mean square, skewness, kurtosis, waveform factor, peak factor, impulse factor and margin factor ( X, X rms , S, K, W, C, I, M ) as the features of the signals (S 2 ). On the other hand, the frequency-domain generator uses discrete Fourier transform (DFT) to extract the frequency characteristics of the signals, which captures the dynamics of the data sources [35].…”
Section: B Data Fusion In Feature Level Using Spacial Feature Extractormentioning
confidence: 99%
“…The timedomain generator calculates statistics including mean, root mean square, skewness, kurtosis, waveform factor, peak factor, impulse factor and margin factor ( X, X rms , S, K, W, C, I, M ) as the features of the signals (S 2 ). On the other hand, the frequency-domain generator uses discrete Fourier transform (DFT) to extract the frequency characteristics of the signals, which captures the dynamics of the data sources [35].…”
Section: B Data Fusion In Feature Level Using Spacial Feature Extractormentioning
confidence: 99%
“…Time invariant linear operators, such as linear convolution and circular convolution, play an important role in classic discrete signal processing algorithms [11,12]. Circular convolution has a FFT-based fast algorithm due to convolution theorem [13].…”
Section: Introductionmentioning
confidence: 99%
“…CWT is a linear convolution of signal and wavelet function for a fixed scale [9]. In general, the time domain sampling of wavelet function has the following form [12] p = h(−aT ), h(−aT + 1), •• • , h(−1), h(0), h (1)…”
Section: Introductionmentioning
confidence: 99%
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