77 Consider the continuous signal found in Example 23 What w

7.7 Consider the continuous signal found in Example 2.3.

What would be an appropriate sample rate and sample period to use in sampling this signal if the resulting discrete series must have a size of 2^M, where M   is an integer and the signal is to be filtered at and above 2 Hz.

y(t) = infinite and n=1 Bn sin2 nt/T

Bn=4/nAn = 0 and n, Bn is identically 0.

Solution

Signal filtered with Frequency, f = 2 Hz

=> Sample period = 1 / f = 1/2 s = 0.5 s

Size of discrete series = 2^M

=> No. of signals = log₂2^M = M

Sampling rate = No. of signals / Time period = M / 0.5 = 2M signals per second