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 = 1/17. 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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