We began a discussion of filters, frequency-shaping and frequency-selective.
Related this to the desirable form of the frequency response H(jw).
Explained how differentiating filters enhance edges in picture processing.
Described lowpass, highpass, and bandpass filters, cutoff frequencies,
and the passbands and stopbands.

We considered the following examples of continuous-time and discrete-time
filters described by differential or difference equations.

For the first-order RC circuit, we computed from first principles the
frequency response and showed that the RC filter is a nonideal lowpass
filter.  We discussed the tradeoff behavior between time and frequency
domain when choosing the RC value.

We considered two nonrecursive discrete-time filters: 1. When the output is
a weighted average of the neighboring input points, we expected intuitively
that the filter would be low pass.  From first principles, we computed
H(exp(jw)) and showed that the magnitude response indeed looks like nonideal
lowpass. 2.  When the output is half the difference between two successive
input samples (p.248), we intuitively expected the filter to approximate a
highpass filter, and indeed showed analytically that this was the case.