Statistical design of autoregressive-moving average digital filters

Procedures are presented for the systematic design of digital filters that contain poles and zeros. The procedures are simple, fast, and effective. All of the important algorithms are of the Levinson-type. The first key idea in the paper is that one may begin a design by posing a linear prediction problem for a stochastic sequence. The second is that a high-order "whitening" filter may be constructed for this sequence and "inverted" to yield a high-order all-pole filter whose spectrum approximates the spectrum of the stochastic sequence. The third key idea is that the all-pole filter may be used to generate consistent unit-pulse and covariance sequences for use in the Mullis-Roberts algorithm. This algorithm is then used to obtain a low-order digital filter, with poles and zeros, that approximates the high-order all-pole filter. The results demonstrate that the Mullis-Roberts algorithm, together with the design philosophy of this paper, may be used with profit to reduce filter or stochastic model complexity and to design spectrum-matching digital filters.