A new definition of discrete quadratic time-frequency distributions

Discrete time-frequency distributions (DTFDs) of discrete signals differ from their continuous counterparts. The DTFD is usually aliased and lacks some desirable mathematical properties inherent to the continuous distribution. The DTFD should, ideally, be free from aliasing and conserve all desirable properties. Two existing DTFD definitions, namely the generalised DTFD (GDTFD) and the alias-free GDTFD (AF-GDTFD), approximate this ideal: the GDTFD does not satisfy all desirable properties but is alias free; the AF-GDTFD satisfies most properties but is not always alias free. We propose, in this article, a new DTFD definition which is alias free and satisfies all desirable properties.