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Signals and Systems by Smarajit Ghosh

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3.7 NYQUIST THEOREM

This theorem states that a signal which has a Fourier transform having only frequencies upto a certain maximum value fm, 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 fm present in the signal i.e., fs > 2fm.

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 fm.
  • The sampling rate (fs) must be greater than 2fm.
  • 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 ...

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