# IIR Response

The impulse response of our Chebyshev IIR filter is:

Notice that it also has the intuitively expected sinusoidal character, oscillating at 2100 Hz, but unlike the FIR filters, it decays exponentially to zero, never quite reaching zero (this is why it is called an infinite impulse response filter). In fact, it decays quite slowly to zero (2000 samples are shown above). The frequency response is much sharper than for either FIR example:

Thus, the IIR design achieves:

- A narrower passband,
- Greater stopband attenuation, and
- Much less computation per output sample (5%).

For this particular application, the FIR filter designs are not attractive. In general, IIR filters are much better at narrowband designs. For other applications, however, FIR filters can have significant advantages. Choosing the right filter is a sophisticated art.