## SC- and SS-wavelet transforms.(English)Zbl 1151.42313

Summary: A. M. Grigoryan [Fourier transform representation by frequency-time wavelets, IEEE Trans. Signal Process. 53 No. 7, 2489–2497 (2005; doi:10.1109/TSP.2005.849180)] has proposed an alternative representation of the Fourier transform, called A-wavelet transform. In that paper, the Cosine and Sine signals defined over one period have been used to develop the Cosine- and Sine-wavelet transforms and using those wavelet transforms the Fourier transform has been represented. For computing the Fourier transform at a given frequency, one does not require to compute the Cosine- and Sine-wavelet transforms at all time points in the time-frequency plane, but at specific time points that are separated out by $$2\pi /\omega , \omega$$ is the frequency variable. In this paper, we propose SC- and SS-wavelet transforms that help representing the Fourier transform of a signal in a better way. The SC- and SS-wavelet transforms use the Cosine and Sine signals defined over the smaller intervals (of length $$2\pi /(m\omega ), m \geqslant 1$$) than that (of length $$2\pi /\omega$$) used in the A-wavelet transform. The SC- and SS-wavelet transforms not only give sharper time-frequency localization but also much more information in a better localized form than the A-wavelet transform.

### MSC:

 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 65T50 Numerical methods for discrete and fast Fourier transforms
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### References:

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