11. Infinite impulse response filters#

an impulse and the result of applying an IIR low-pass filter

In the previous chapter, we saw how to use convolution to implement finite impulse response (FIR) filters, such as low-pass filters. FIR filters have many nice properties:

  • They’re easy to implement (by convolution);

  • They’re stable;

  • They can be analyzed by the DFT.

However, one big drawback to FIR filters is that they can be somewhat inefficient. As we saw in Filter Design and Analysis, achieving a desired stop-band attenuation can require a filter with thousands of coefficients!

In this chapter, we’ll develop infinite impulse response filters. This family of filters uses feedback to process signals, resulting in more powerful and efficient filters. This comes at the cost of sacrificing the nice properties of FIR filters mentioned above, but don’t worry: we’ll see in the final chapter how to recover similar properties.