A Simple Recursive (IIR) Filter

Using FIR filters to reproduce a desired frequency response often requires a very high-order filter, i.e., a greater number of coefficients and more computation.

It is often possible to reduce the number of feedforward coefficients by introducing feedback coefficients.

A simple first-order recursive low-pass filter is given by

$$y(n) = x(n) + .9y(n-1)$$

Figure 6: The spectral magnitude of the first-order FIR and IIR (recursive) lowpass filters.