produces filters with a magnitude response for which the weighted ripple is evenly distributed over the passband and stopband and that have a sharp transition region. The advantage of this approach is the optimal response of the designed filter. The disadvantages are the complexity and length of time required to design. Park-McClellan design time is much longer than the Windowed approach. A specialization of the Parks-McClellan approach is equiripple FIR design. The only difference between them is the equiripple design weights the passband and stopband ripple equally. To design an FIR filter using the equiripple approach, you must specify the cut-off frequency, the number of taps, the filter type, and pass and stop frequencies. The cut-off frequency for equiripple designs specifies the edge of the passband and/or the stopband. Equiripple filters have a ripple in the passband that causes the magnitude response in the passband to be greater than or equal to 1. Similarly, the magnitude response in the stopband is always less than or equal to the stopband attenuation. For example, if you specify a lowpass filter, the passband cut-off frequency is the highest or largest frequency for which the passband conditions hold true. Similarly, the stopband cut-off is the lowest frequency for which the stopband conditions are met. Both design approaches deliver FIR filters with a linear phase characteristic.

When you use conventional techniques to design FIR filters with especially narrow bandwidths, the resulting filter lengths can be very long. FIR filters with long filter lengths often require lengthy design and implementation times and are more susceptible to numerical inaccuracy. In some cases, conventional filter design techniques, such as the Parks-McClellan algorithm, might fail the design altogether.

IIR Filters

IIR filters are filters that may or may not have ripple in the passband and/or the stopband. Digital IIR filter design derives from the classical analog designs. These designs are Butterworth, Chebyshev, inverse Chebyshev, Elliptic, and Bessel.

Butterworth Filters

A smooth response at all frequencies and a monotonic decrease from the specified cut-off frequencies characterize the frequency response of Butterworth filters. Butterworth filters are maximally flat, the ideal response of unity in the passband and zero in the stopband. The half power frequency or the 3 dB down frequency corresponds to the specified cut-off frequencies.