Discrete powers-of-two kernels for time-frequency distributions

We introduce a new class of powers-of-two (PFT) kernels for fast real time implementations of time-frequency distributions. In this class, the local autocorrelation function is computed using a series of shifting and addition operations. PFT filter design techniques are not limited to the design of fixed kernels. They can also be used to design data-dependent kernels suitable for specific operating environments. In the time-frequency context, where the task is to identify the signal autoterms in the time-frequency domain, a discretized powers-of-two kernel shows little or no difference in performance from its infinite precision counterpart. A simple modification of the PFT design technique that significantly improves the approximation when small register lengths are used, is also introduced