Let x(t) be a signal with Nyquist rate w 0 . Determine the Nyquist rate for each of thefollowing signals:(a) x(t) + x(t - 1)(b) d~;t)(c) x2 (t)(d) x(t) cos wot

(a) x(t) + x(t - 1): The Nyquist rate for this signal is the same as the original signal, w0. This is because the signal x(t - 1) is just a delayed version of x(t), and the delay does not change the frequency content of the signal.

(b) dx(t)/dt: The Nyquist rate for this signal is 2w0. This is because the derivative of a signal can increase the highest frequency component of the signal, in this case doubling it.

(c) x^2(t): The Nyquist rate for this signal is 2w0. This is because squaring a signal can create frequency components at twice the original frequency.

(d) x(t) cos w0t: The Nyquist rate for this signal is 2w0. This is because multiplying a signal by a cosine can shift the frequency components of the signal, in this case potentially doubling the highest frequency.