Time-varying system characterization for wideband input signals

Wavelet and group theoretic Fourier transforms are powerful tools for characterizing time-varying linear systems and propagation channels for wideband input signals. It is shown that for such systems and channels, the usual impulse response and transfer function characterizations are invalid. We derive a valid representation for the effects of a time-varying channel on a wideband signal. It is shown that the continuous wavelet transform of the output signal with respect to the input signal provides the correct system characterization. The necessary background for this important application of continuous wavelet transforms and group Fourier transforms is developed.