Recursive digital filter synthesis, noniteratively

The application of a generalized least-squares approach to the synthesis of recursive digital filters is discussed. The desired impulse-response is processed by a set of measurement units to yield a family of sequences. The Gram matrix of these measurement signals and the impulse responses of the measurement units is shown to yield a parameter vector consisting of the coefficients, both numerator and denominator, of the recursive approximant. Computationally efficient, the method possesses a closed-form solution. In typical designs it yields an error of fit comparable to those achieved by certain iterative methods.