The generalized sliding-window spectrum

The sliding-window spectrum is the Fourier transform of the windowed version of a signal where the window is shifted over the signal. This concept can be extended by replacing the Fourier transformation by an arbitrary orthogonal transformation resulting in what we call the generalized sliding-window spectrum (GSWS). The information in the GSWS is redundant. Thus, partial knowledge of the GSWS can be sufficient to reconstruct the signals. For a GSWS obtainable by causal filtering of the input signal the conditions under which simple reconstruction schemes (in terms of necessary filtering operations) apply are considered.