Analytical forms of signal processing for ims based on generalized modification of the Fourier transform

Generalized modification of the traditional Fourier transform (rotational Fourier transform, RFT) introduced by mathematicians comparatively long ago remained long unknown in the field of signal processing where RFT has quite a great potential for application. RFT depends on parameter a and is interpreted as time-frequency plane rotation. For a = pi/2, RFT is a usual Fourier transform, for a = 0 - identity operator, and the angles of RFT implemented sequentially are additive (as the angles of successive rotation). In analytical representation, RFT is a series expansion of signal in the basis consisting of a set of signals with rapidly changing frequency (into SRCF components). The basic elements of the theory of RFT, its properties, types of interpretation as operator, interrelations of RFT with time-frequency distributions of non-stationary signals (with Wigner distribution, short-time Fourier transform and spectrogram). These relations have closed analytical forms. RFT examples for some signals and RFT applications are given.