Finding the zeros of linear phase FIR frequency sampling digital filters

The need for finding the zeros of FIR filters often arises in digital signal processing applications. If we want to convert linear phase finite-impulse response (FIR) filters into minimum phase FIR filters [1], [2], the problem of finding the zeros of the filter is encountered. This problem has been addressed in [3], but not solved. Here we introduce the idea of using frequency sampling filters for obtaining its zeros. The advantage of using this kind of filter resides in the fact that all the zeros on the unit circle are known. Furthermore, the zeros off the unit circle can be obtained with some simple processing. This type of filter is especially useful when high-order narrow-band filters are involved. Finding the zeros of very high-order equirriple low-pass filters can be a difficult, if not impossible, task.