Adaptive Frequency Sampling Filters

We present two new structures for adaptive filters based on the idea of frequency sampling filters and gradient based estimation algorithms. These filters have a finite impulse response (FIR) and can be thought of as attempting to approximate a desired frequency response at given points on the unit circle. The filters operate in real time with no batch processing of signals as is the case when using the discrete Fourier transform. They result in a marked reduction in dimension of the time-domain problem of fitting an Nth-order FIR transversal filter to a collection of length 2 transversal filters and further to a collection of N scalar filters. The advantages of this are then discussed.