Find ao, an's, b's, C's and D's. Also, evaluate an, bn, Cn and D' for n=3 (find a3, b3, C3 and D and _3.) n

Problem 4 [20 points] Use MATLAB command tf and bode, generate magnitude (in decibel) and phase plots (in degree) for the following voltage transfer functions.

Problem 5 [10 points] A signal z(t), bandlimited to 10 Hz, is sampled at 12 samples/s. what portion of its spectrum can still be recovered from its samples? Please draw a sketch (with an arbitrary signal shape of bandwidth 10Hz) that illustrates your findings.

Exercise 1. FOURIER SERIES REPRESENTATION OF A DISCRETE PERIODIC SIGNAL (i) Determine the Fourier series coefficients a, for the following signal, and write the signal z[n] in terms of its Fourier series coefficients (hint: solve "by inspection"):

Exercise 5.FORWARD TRANSFORMFor the following continuous time signals r(t),determine the Fourier transform X(jw)()x(t)=2-4

Exercise 3.6.1 Suppose G is a group, N, K < G with N normal in G, N K = [e], and G = NK. Prove that G/N=K.

Consider the discrete-time linear time-invariant system with transfer- function:

(This problem is a reproduction of the textbook Problem 1.22. (a), (d), (g), (h).) A discrete-time signal is shown in Figure P1.22. Sketch and label carefully each of the following signals.: (i) x[n - 4] (ii) x[3n + 1] (iⅲ) 호리미 + 호 (-1)"a[n] (iv) x[(n - 1)2²]

Given x[n] = {..., 12, 9, 6, 3, 6, 9, 12, 9, 6, 3, 6, 9, 12,...}, a. Compute its DTFS expansion. Hint: [n] has period = 6, is real, and is an even function. b. Compute its average power in the time domain. c. Compute its average power in the frequency domain. By Parseval's theorem, both should match. Note: fft in Matlab can be used to check the results, but all work needs to be shown for full credit.

Q1. Consider a CT LTI system with the following input-output relation: (D²+7D+6)y(t) = (D+1)x(t), with initial conditions y(0) = 1.8,ỳ (0) = -3.5 Find the response y(t), if x(t) = e^-4t u(t).