Uniform sampling for signals with finite instantaneous bandwidth

One requires assumptions about signals in order to sample them such that the analog signal may be recovered from its samples. The assumption in Shannon sampling can be thought of as the signal´s Wigner-Ville distribution function (WDF) being confined to a strip centered on the time axis. Several other sampling theorems assume a signal´s WDF is confined to a strip about some other straight line through the origin of the WDF. This may be illustrated using an approach based on simplified time-frequency diagrams called phase space diagrams (PSDs). Reconstruction of signals sampled using these theorems may be simplified by this unified approach.