Multiresolution of the Fourier Transform

Abstract

In this paper, the integral Fourier transform is described as a specific wavelet-like transform with a fully scalable modulated window, but not all possible translations. The transform is defined by sinusoidal waves of half periods. A geometrical locus of frequency-time points for the proposed wavelet-like transform is derived and the function coverage is described and compared with the short-time Fourier transform as well as with the wavelet transform.