Multiresolution signal processing by Fourier transform time-frequency correlation analysis

In this paper, multiresolution signal processing is described, by the continuous Fourier transform, not the short-time Fourier transform. The inverse Fourier transform is defined by the integral Fourier formula which is referred to as the correlation of the function (signal) with cosine waveforms of various frequencies. This is a direct way to perform the time-frequency analysis of signals. The Fourier transform is described as the sum of wavelet-like transforms with the cosine analyzing function of one period. Properties of such transforms, including the inverse formula of reconstruction of the signal by the described wavelet-like transforms are described. Examples of application of such transforms to detect the exact location of a high-frequency signal are given.