Efficient algorithms for discrete time-frequency distributions

Time-frequency distributions (TFDs) are computational costly to compute. This paper presents algorithms to reduce this computational load. Before we can compute the TFDs, however, we must define a discrete version of the TFD. Defining a discrete TFD (DTFD) is not a straightforward process--for example, a popular DTFD definition does not satisfy all desirable mathematical properties that are inherent to the TFD. In this paper, we define a new DTFD definition, the DTFD-C. This definition is closely related to another DTFD definition which we recently proposed, the DTFD-B. The DTFD-B and DTFD-C satisfy all desirable properties. We provide algorithms for both DTFD definitions. We find that the DTFD-C has the advantage: the DTFD-C requires only 50% of the computational load required to compute the DTFD-B.