3) Express the waveform in the following figure in terms of unit step or ramp functions.

The continuous time signal xc (t)=sin(23t)+cos(k23mt)where k =6.is sampled with a sample period I to obtain the discrete-time signalc [n]=sin()+cos()where A =25Choose the smallest possible value of T in milliseconds/sample consistentwith this information.Provide a number as your answer with an accuracy of two decimal digits.

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 2. DISCRETE TIME SIGNAL FROM FOURIER COEFFICIENTS (i) Determine the signal x[n] from the Fourier coefficients given period N = 8.

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.

Topics: Signal recovery from Fourier coefficients Exercise 2. CONTINUOUS-TIME SIGNAL RECOVERED FROM FOURIER COEFFICIENTS (i) The Fourier series coefficients of a continuous-time signal that is periodic with period 4 is: (ii) A continuous-time periodic signal z(t) is real-valued and has a fundamental period T Fourier series coefficients for this signal are specified as: = 8. The nonzero

Consider the periodic signal x(t) which has the Fourier series coefficients (i) Determine whether r(t) is real or not. (ii) Determine whether z(t) is even or not. (iii) Determine whether dx(t/dt) is even or not.

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.

3.1. A continuous-time periodic signal x(t) is real valued and has a fundamental period T = 8. The nonzero Fourier series coefficients for x(1) are a₁ = a_₁ = 2, a3 = a_3 = 4j. Express x() in the form x(t) = Σ A. cos(w;! + Φι). k=0