FILTER RESPONSE DESIGN METHODS

The total specification of the ideal filter includes the locationof passbands and stopbands, the minimum stopbandattenuation, the maximum passband ripple, the filter order,and perhaps the shape of the response in some of thespecified bands.Typically, there are three stages to the design of digital filterresponses for passband filters. First, the ideal filter responseis specified. Next, a floating point response is designed.Finally, the floating point coefficients are quantized to yield afixed point response.Creating a floating-point IIR filter response starts with aprototype analog filter. Then an s-domain to z-domaintransformation is used to generate a set of digital filtercoefficients.
Common methods of designing floating-pointFIR filter responses are windowing, frequency sampling, andoptimal. All are described in general digital signal processingtexts and are standard in most commercially available digitalfilter design software packages.Converting floating-point coefficients into fixed-pointcoefficients requires quantizing the coefficients andcalculating the frequency domain impulse response of thefilter or filter model to verify that the filter meets the requiredspecification.
If it does not, either the number of coefficientbits can be increased, the filter response can be redefinedand step two repeated, or the filter arithmetic can beredesigned, or a combination of these procedures can beperformed. When filter hardware is at a premium,sophisticated simulated annealing techniques can be usedfor both fixed-point FIR and IIR filters to produce the best setof filter coefficients, given a fixed filter order and coefficientwidth.