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.