Determine the nyquist rate for the signal xt- what is the

Question

Answer the following questions:

1. Graphically convolve the following two functions:

2. Consider the continuous time signal
x(t) = 3 cos 600 ∏t + 2 cos 1800∏t

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) + 2(dy(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 functiom H(s) of the following block diagram:

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).