The problems relating to time-scale (wavelet) transforms for spectral-time analysis of complex-shaped non-stationary signals in information measurement systems are discussed. They are encountered in speech signal processing, seismology, marine geophysics, radar, etc. The theory and methods of wavelet transform, bases, frames, their types and features are given. The main properties and classes of wavelet transforms are summarized in the table. Considerations for the problem-dependent choice of the wavelet basis type are presented.