FORMING TIME-FREQUENCY REPRESENTATIONS (DYNAMIC SPECTRA)
OF A NON-STATIONARY SIGNAL BY MEANS
OF TRANSFORMING REPRESENTATIONS OF KNOWN TYPE
A. V. Merkusheva
Two-parameter representations used for
non-stationary signal analysis in an information-measurement sys-tem realize
mapping the signal into the time-frequency domain and provide dynamic spectrum
estimation. De-pending on the way of forming these representations, they
belong to one of two classes: Cohen’s class or affine class of wavelets.
These classes are designed on the basis of two different principles of
modifying (conveniently for applications) the time-frequency signal representation
at signal transformations related to time and frequency shifts (or
time shift and scale changing - for the affine class). The two classes differ
just by the form of signal-representation modification at transformations
of that signal. The modification rule itself is termed covariance.
The covariance has two forms: for time and frequency shift, and for time
shift and scale change. At the present time, the problem concerning the completeness
of the class number for signal time-frequency representations (TFR) is solved.
In the paper, a general methodology for creating the TFR-classes on the basis
of unitary equivalence principle is considered. It is shown that every possible
TFR class may be obtained using this principle.