The authors discuss the signal synthesis problem in the general framework of bilinear signal representations (BSRs), thereby obtaining a unified treatment which encompasses, e.g., the Wigner distribution and ambiguity function as special cases. The inclusion of a signal space constraint serves to impart flexibility to the signal synthesis process and to relax mathematical requirements. The characterization of signal spaces either by orthogonal projection operators or by orthonormal bases leads to two different signal synthesis methods. Both methods assume the BSR to be unitary (i.e., satisfy Moyal's formula) on the signal space on which signal synthesis is performed. As an application of the general signal synthesis methods, band-limited signal synthesis in the case of the Wigner distribution is considered.
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