This video introduces a class of low-pass filters called Butterworth Filters. We sketch the amplitude response of filter for different values of filter order n.

Before considering design of a Butterworth filter with arbitrary cutoff frequency, we first analyze a Butterworth filter with a cutoff frequency of wc = 1. This filter is called the "normalized filter". We examine the poles of such a filter in the s-plane. This normalized filter is the building block for designing Butterworth filters with arbitrary cutoff frequency and gain design criteria (investigated in the next videos).

We now investigate how to modify the normalized Butterworth filter to yield a low-pass filter with a desired cutoff frequency and other frequency/gain design criteria. The key results of this video is a collection of equations that can be used to select the correct Butterworth filter order and to compute the actual filter cutoff frequency.

We conclude this sequence of videos on the Butterworth filter with a filter design example. Given a set of filter specifications (i.e. desired stopband frequencies and gains and passband frequencies and gains) we use the equations derived in the previous video to select the filter order and cutoff frequency. We plot the amplitude response of the newly designed filter to show it meets the desired filter specifications.