Signal Analysis & Synthesis

Analogue Modulation

Analogue Signal Processing

Digital signal processing

Digital modulation

Communication Systems

Ideal Low-pass Filter

As an important illustration, we now determine the output spectrum of an ideal low-pass filter having bandwidth B when its input is a sin_c pulse

The spectrum of the input sin e pulse is

Therefore, the output spectrum will be

Using H(f) given in Equation, we write

Thus the output time function is also a sin c pulse. That is,

We observe:

• When B > W, since the input signal is band-limited in W and all its frequency components are passed by the filter, the output is undistorted.
• When B < W, the filter rejects high-frequency components of the input, and the output is affected in two ways:

• the maximum signal amplitude is reduced by the factor B/W, and
• the duration of the output pulse is increased. Since the output-pulse duration can be measured by 1/B, the smaller the filter band-width, the more the output pulse is stretched in time.

• The output-pulse duration is determined by the filter band-width and not by the input signal.