Filter Design by Modeling

Abstract

The two preceding chapters presented the traditional design methods for IIR and FIR digital filters. These methods are grounded in the mathematical theory of approximation, where upper and lower constraints are placed on the deviation of |H’(ω)| from the ideal response. Another class of design methods is based on the statistical modeling of spectra; and in these methods, the least-squares error (LSE) criterion is employed. These methods are especially appropriate when the filter design or model is derived from experimental data having random fluctuations. However, they can also be useful for deterministic designs when minimum-phase FIR filters are desired, when nonclassical specifications are given for IIR filters, when poles and zeros of unequal number (N ≠ M) are desired, and so forth. Complete coverage of this field, which is sometimes termed modern spectrum analysis, is beyond the scope of this book, and we will concentrate on deterministic filter design. However, the basics of statistical data modeling and spectrum analysis will also be included in section 10.5.