Determine the nyquist rate for the signal - what is the

Question

1. Graphically convolve the following two functions:

2. Consider the continuous time signal

x(t) = 3 cos 600Πt + 2cos1800Πt

a) Determine the Nyquist rate for the signal x(t).

b) Suppose that the signal is sample at f_s = 2000 Hz, what is the discrete-time signal obtained after the sampling? What are the frequencies in the resulting discrete-time signal?

c) If the sampling rate is f_s = 600Hz, then what is the maximum frequency that can be recovered from the discrete-time signal?

3. Solve for system response y(t)

d²Y(t)/dt² + 2dy(t)/dt + 5y(t) = -8x(t)

Y(0^-) = 1, Y'(0^-) = 0, x(t) = e^-3tu(t)

4. Find the response of the system described by the following difference equation:

y[k] + 0.7y[k - 1] - 0.3y[k - 2] = 2δ[k]
y[0] = 2, y[-1] = 1, x[k] = δ[k]

5. Find the transfer function H(s) of the filter represented by the following Bode plot. Write your reasons.

6. Find the transfer function H(s) of the following block diagram: F(s)

7. The impulse response of a system is given by

h(t) = (e^-t e^-2t)u(t)

Determine the response to the following input:

x(t) = u(t) - u(t - 2)