Algorithms for discrete quadratic time: frequency distributions

Time-frequency distributions (TFDs) are computationally costly to compute. We address this problem by presenting algorithms to reduce the computational load for computing TFDs. Before we can compute the TFDs, however, we first must define a discrete version of the TFD. Defining a discrete TFD (DTFD) is, unfortunately, not a straightforward process--for example, a popular DTFD definition does not satisfy all desirable mathematical properties that are inherent to the continuous 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 these definitions and show that the DTFD-C requires only 50% of the computational complexity and memory required to compute the DTFD-B.