Question

Specify the Nyquist rate and Nyquist interval for each of the following signals:

(a) g(t)=sinc(200t)
(b) g(t)=sinc2(200t)
(c) g(t)=sinc(200t)+sinc²(200t)
where Nyquist rate is twice the highest frequency of the analog signal g(t) and Nyquist nterval is the reciprocal of Nyquist rate.

Answer 1

The Nyquist rate for g(t)=sinc(200t), g(t)=sinc²(200t), and g(t)=sinc(200t)+sinc²(200t) is 400 samples per second. The Nyquist interval for these signals is 2.5 milliseconds.

Step-by-step explanation:

Nyquist Rate and Interval

For signals (a) g(t) = sinc(200t), (b) g(t) = sinc²(200t), and (c) g(t) = sinc(200t) + sinc²(200t), we need to specify the Nyquist rate and Nyquist interval. The Nyquist rate is twice the highest frequency component of the signal, and the Nyquist interval is the reciprocal of the Nyquist rate.

In the case of sinc(200t), the highest frequency component is 200 Hz. Thus, the Nyquist rate is 400 samples per second and the Nyquist interval is 1/400 seconds or 2.5 milliseconds. For sinc²(200t), the frequency content is the same since squaring the function does not change the bandwidth, so the Nyquist rate and interval remain the same. Finally, for the combined signal, the highest frequency component is still given by the sinc function, so the Nyquist rate and interval do not change.

We can conclude that for all three signals, the Nyquist rate is 400 samples per second and the Nyquist interval is 2.5 milliseconds.