Recursive (IIR) Filters

Using FIR filters to reproduce a desired frequency response often requires using a high order filter.

A high order filter means a long impulse response, 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

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