Several new algorithms are presented for the optimal approximation and design of various classes of digital filters.
An iterative algorithm is developed for the efficient design of unconstrained and constrained infinite impulse response (IIR) digital filters. Both in the unconstrained and constrained cases, the numerator and denominator of the filter transfer function are designed iteratively by recourse to the Remez algorithm and to appropriate design parameters and criteria, at each iteration. This makes it possible for the algorithm to be implemented by means of a short main program which uses (at each iteration) the linear phase FIR filter design algorithm of McClellan et al. as a subroutine. The approach taken also permits the filter to be designed with a desired ripple ratio. Also, the algorithm determines automatically the minimum passband ripple corresponding to the prescribed orders and band edges of the filter. The filter is designed directly without guessing the passband ripple or stopband ripple.
Another algorithm, based on similar principles, is developed for the design of a nonlinear phase finite impulse response (FIR) filter, whose transfer function optimally approximates a desired magnitude response, there being no constraints imposed on the phase response.
A similar algorithm is presented for the design of two new classes of FIR digital filters, one linear phase and the other nonlinear phase. A filter of either class has significantly reduced number of multiplications compared to the one obtained by its conventional counterpart, with respect to a given frequency response. In the case of linear phase, by introducing the new class of digital filters into the design of multistage decimators and interpolators for narrow-band filter implementation, it is found that an efficient narrow-band filter requiring considerably lower multiplication rate than the conventional linear phase FIR design can be obtained. The amount of data storage required by the new class of nonlinear phase FIR filters is significantly less than its linear phase counterpart.
Finally, the design of a (finite-impulse-response) FIR digital filter with some of the coefficients constrained to zero is formulated as a linear programming (LP) problem and the LP technique is then used to design this class of constrained FIR digital filters. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI