Problem 2. Suppose the impulse response function h[n] of a DT system is: h[n] = (-−0.5)^u[n]. Determine the transfer function / eigenvalue H(z) of this DT system through its definition: assuming the input signal is the eigenfunction x[n] = z^, and calculate the absolute value and the phase angle of the eigenvalue H(z) at: 1 (a) z = √(1 + j) (Q5, Q6); (b) z = −0.5 + j; (Q7, Q8)

2. For the two continuous-time signals ?(?) shown below, please use decomposition to find and sketch their even ?e(?) and odd ?0(?) components. Be sure to clearly indicate (label) important time and amplitude values in your sketches.

Part a,b and c.

y(n) is output. x(n) is input

(a) The analog signal x(t) = sin(60rt) is sampled at 20 Hz. Derive and write down an expression for the sampled signal r[n]. What is the Nyquist frequency for this r(t)?

For the transfer functions given in the control system in the figure, find the relevant E(s) steady state error and approximately draw the response curve for the relevant input. Note: Find the kaher state error ess and the permanent state response yss and show the rise time tr, peak time tp, settling time ts, maximum overshoot M and steady state regions on the curve you drew.

4+ Page 4. For two systems with impulse responses hi[n] = (0.3)" u[n] h2[n] = (0.7)" u[n] pud (a) Write down their transfer functions, H1(z) and H2(z). Include the ROCS. (b)Determine the transfer function for the parallel interconnection of these two systems. Indicate the ROC and all the poles and zeros. Plot the pole-zero diagram as well. (c)Using the result of part (b) above: Determine all possible inverse systems, H1(z). (i) Indicate which inverse is causal, and whether this inverse is stable and/or FIR? Explain. O words

Q1: For the pole-zero diagram shown in Figure below, the lengths of poles and zeros from the origin are 0.5 and 0.8 respectively: a. Find the transfer function H(z), impulse response h(n) and the difference equation. b. Calculate and plot the magnitude and phase frequency responses. Im(z) Re(z)

Given the difference equation: y(n) = 0.2y(n-1) + 0.2y(n-2) + 0.1u(n-1) 1-Find the discrete transfer function H(z) = 2-Draw a block diagram of this discrete system using delays and gains. Y(z) (2) U(z)

The question is in the photo