The Ideal Low-Pass Filter

In this lecture, we examine the Ideal low pass filter and the process of reconstruction of a Band-limited signal.

Let us first see another way of interpreting the action of the Ideal low-pass filter.

 IMPULSE RESPONSE OF  IDEAL LOW PASS FILTER:

The Frequency response (the Fourier transform of the impulse response of an LSI system is also called its frequency response) of an ideal low pass filter which allows a bandwidth B, is a rectangle extending from -B to +B, having a constant height as shown in the figure.

Lets look at the Impulse Response of this Ideal low pass filter, taking its height in [-B, B] to be 1. Using the formula for inverse Fourier Transform we have :

             (note that )

Thus the impulse response of an ideal low pass filter turns out to be a Sinc function, which looks like: