Design of IIR/FIR filters using a frequency domain bootstrapping technique and LPC methods

A technique is described for designing IIR/FIR digital filters which are specified by the number of poles and zeros, the sampling frequency, and a magnitude response versus frequency. The iterative technique to carry out the design bootstraps back and forth between the IIR (all pole) section and FIR (all zero) section, updating the design each time in the frequency domain using the data from the previous IIR or FIR section and the desired filter response. Coefficient calculations at each iteration are based upon standard LPC (linear prediction coefficient) and inverse LPC methods. An efficient computer program has been written to implement the technique using Levinson and FFT pruning algorithms. The combination of the efficiency from LPC and pruning methods, and the ease of iteration and interpretation in the frequency domain creates a straightforward and workable computer program for general digital filter design based upon spectral magnitude specifications. Examples of the filter design program illustrate how well the technique works as a function of the number of iterations.