Signals and Systems

3.7 NYQUIST THEOREM

This theorem states that a signal which has a Fourier transform having only frequencies upto a certain maximum value f_m, we can obtain the analog signal f(t) from the sampled signal f*(t) by passing the sampled signal f*(t) through a low pass filter provided that the sampling frequency fs is more than twice the maximum frequency f_m present in the signal i.e., f_s > 2f_m.

The required conditions for recovery of the analog signal f (t) from the sampled signal f*(t) are given below:

• The analog signal should be band limited to some maximum frequency f_m.
• The sampling rate (f_s) must be greater than 2f_m.
• We will be able to get hold of an ideal low pass filter.

Fig. 3.26 shows a typical band limited signal.

 

 

Fig. 3.26 Typical ...