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Representation frequency transforms by matrix direct sum

Spectral methods are widely used to analyzed the different dimensions signals. Wavelet transform, Discrete cosine transform, Fourier transform and its windowed version are the basis of modern software and hardware for digital signal processing. This article considers issues of formation the modified scheme wavelet transform in matrix form.

Showed examples for data processing based on the Haar and Daubechies wavelets giving an idea of the difference between traditional and modified approaches to the method implementation. Further, this approach is extended to the Windowed Fourier transform. Traditional and proposed matrix forms represented. The modified method has minimal effect on coefficient values in depending direction of processing in all cases.