Frequency-domain Steiglitz-McBride method for least-squares IIR filter design, ARMA modeling, and periodogram smoothing

The classic Steiglitz-McBride (mode-1) time-domain algorithm for least-squares approximation of desired impulse responses for IIR digital filters or ARMA signal models is reformulated in the frequency domain to allow the direct least-squares approximation of either complex-valued or magnitude-only frequency responses, as well as power-density spectra, including periodograms. The resulting (stable) designs in the complex-valued case with both magnitude- and phase-response specifications can be either causal or noncausal, as appropriate to the phase, while the magnitude-only designs can always be made causal and minimum-phase. The periodogram models provide effective spectral smoothing without the need for averaging of data blocks, although averaging can be used, if desired, to reduce the computation. The filter coefficients can be either real- or complex-valued, corresponding to conjugate-symmetric or asymmetric frequency responses, respectively.