# Lecture 5: Ideal and Practical Filters

The ideal low-pass filter allows all signals below some cutoff of
rad/sec to pass through undistorted, while completely cutting off all
other frequencies. This is sometimes said to be the ideal "brick
wall'' filter. If
is strictly bandlimited to
rad/sec, then
the output is simply delayed:

The ideal filter has

The impulse response of the filter is then

Plot . Observe that it is

*noncausal*, and hence physically nonrealizable. We cannot build an ideal lowpass filter, or an ideal bandpass either, for that matter. We could get pretty close, but creating a system with a large , so that most of the sinc function would be included. One approach to determine the effect of this truncation of the impulse response

is to use the properties of F.T.

The effect is to smear the response by the convolution.