ANALYTICAL  FORMS  OF  SIGNAL  PROCESSING
FOR  IMS  BASED  ON  GENERALIZED  MODIFICATION
OF  THE  FOURIER  TRANSFORM

A. V. Merkusheva

Saint-Petersburg

    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  alfa and is interpreted as time-frequency plane rotation. For alfa = pi/2, RFT is a usual Fourier transform, for alfa = 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.