Time-frequency signal synthesis on signal subspaces

Signal synthesis is an indispensable part of signal processing schemes based on bilinear time-frequency representations like Wigner distribution, ambiguity function or spectrogram. We present a comprehensive theory of signal synthesis in which a signal subspace constraint imparts flexibility to the synthesis process. Representing the signal subspace by a projection operator or an explicit basis results in two different types of synthesis algorithms. Subspace synthesis is particularly suited for Wigner distribution and ambiguity function.