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 original support. From this extension of the time domain filter, we can get a causal filter. In this paper, GDFT-based algorithm for CWT, which has a more concise form than that of linear convolution proposed by Jorge Martinez, is constructed by using this causal filter. The analytic expression of the GDFT of this filter, which is essential for GDFT-based algorithm for CWT, is deduced in this paper. The numerical experiments show that the calculation results of GDFT-based algorithm are stable and reliable; the running speed of GDFT-based algorithm is faster than that of the other two algorithms studied in our previous work.

Multimodal Gait Recognition for Neurodegenerative Diseases

“…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].…”

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…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].…”

“…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)…”

“…If the CWT is computed directly by the linear convolution of signal and p, then this method is known as time-domain algorithm of CWT [12]. The discrete Fourier transform(DFT) of p is DFT p ≈ e −iaT ω ψ * (aω)…”

“…By considering the shift property of DFT and (2). It is natural to define a filter q such that [12] DFT q ≈ ψ * (aω)…”