A discrete-time signal is passed through a discrete-time lowpass filter with frequency response H(F ) = rect(8.5F) ? ?1(F ). If every Nth point of the filter’s output signal is sampled, what is the maximum numerical value of N for which all the information in the original discrete-time signal is preserved?

What will be an ideal response?


The highest frequency in the signal from the filter is F = 1/14. Twice that value is F = 2/17. So the time between samples must be chosen so that 1/N > 2/17.

That implies that N <17/2. Since N must be an integer, the maximum value for N is 8.

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