Filter Response Design Methods

The total specification of the ideal filter includes the location
of passbands and stopbands, the minimum stopband
attenuation, the maximum passband ripple, the filter order,
and perhaps the shape of the response in some of the
specified bands.
Typically, there are three stages to the design of digital filter
responses for passband filters. First, the ideal filter response
is specified. Next, a floating point response is designed.
Finally, the floating point coefficients are quantized to yield a
fixed point response.
Creating a floating-point IIR filter response starts with a
prototype analog filter. Then an s-domain to z-domain
transformation is used to generate a set of digital filter
coefficients. Common methods of designing floating-point
FIR filter responses are windowing, frequency sampling, and
optimal. All are described in general digital signal processing
texts and are standard in most commercially available digital
filter design software packages.
Converting floating-point coefficients into fixed-point
coefficients requires quantizing the coefficients and
calculating the frequency domain impulse response of the
filter or filter model to verify that the filter meets the required
specification. If it does not, either the number of coefficient
bits can be increased, the filter response can be redefined
and step two repeated, or the filter arithmetic can be
redesigned, or a combination of these procedures can be
performed. When filter hardware is at a premium,
sophisticated simulated annealing techniques can be used
for both fixed-point FIR and IIR filters to produce the best set
of filter coefficients, given a fixed filter order and coefficient
width.