TABLE OF CONTENTS Digital filters with sharp transition bands are difficult, sometimes impossible, to be implemented using single-stage structures. A serious problem with a single-stage sharp FIR filter is its complexity. The FIR filter length is inversely proportional to the transition width and complexity becomes prohibitively high for sharp filters, (Lim, 1986). IIR filters with sharp transition bands suffer from extremely high sensitivities of transfer function poles. In many practical cases, the multirate approach is the promising solution that could be applied for implementation of a sharp FIR or IIR filter.
In this chapter, we present two methods for designing filters having narrow transition bandwidths: multistage filtering suitable for narrowband filters, and the method based on multirate and complementary filtering, which may be used for filters of arbitrary bandwidths.
Multirate techniques provide efficient tools for constructing digital filters with equal input and output sampling rates. Multirate techniques are shown to be an appropriate solution for the specifications that require a single-rate filter of a very high order. Instead of designing the single-rate filter, one can achieve a more effective solution with a multirate filter constructed as a combination of several low-order Subfilters and sampling rate alteration devices. The benefits that can be achieved in comparison with the single-rate design are threefold:
The overall filtering problem can be shared between several lower-order Subfilters.
The final wordlength effects on the overall filter performances are considerably reduced.
The arithmetic operations in Subfilters can be evaluated at the reduced...
