Time-frequency distribution kernels using FIR filter design techniques

Time-frequency (t-f) distribution kernels are obtained using finite impulse response filter design methods. Two methods are considered: the window method and the frequency sampling method. The ideal kernel is first specified in the ambiguity domain. At each time-lag, an FIR filter approximating the desired response is designed using one of the above methods. The individual responses along the different lags are then assembled to construct a finite extent t-f kernel with desirable characteristics. Two different classes of kernels are therefore introduced. While the window based t-f kernels are simple, noniteratively generated, and can be used for all practical considerations, the frequency sampling class of kernels is computationally efficient and leads to recursive computations. Kernels from the two different classes are presented along with simulation examples which illustrate their performance.