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} > 2*f*_{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*) must be greater than 2_{s}*f*._{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 ...

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