Forming time-frequency representations (dynamic spectra) of a non-stationary signal by means of transforming representations of known type

Two-parameter representations used for non-stationary signal analysis in an information-measurement system realize mapping the signal into the time-frequency domain and provide dynamic spectrum estimation. Depending 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.