Designing IIR filters with a given 3-dB point

Often in infinite impulse response (IIR) filter design, our critical design parameter is the cutoff frequency at which the filter´s power decays to half (-3 dB) the nominal passband value. This article presents techniques that aid in the design of discrete-time Chebyshev and elliptic filters given a 3-dB attenuation frequency point. These techniques place Chebyshev and elliptic filters on the same footing as Butterworth filters, which traditionally have been designed for a given 3-dB point. The result is that it is easy to replace a Butterworth design with either a Chebyshev or an elliptic filter of the same order and obtain a steeper rolloff at the expense of some ripple in the passband and/or stopband of the filter.