P1. Sketch and calculate the average value of the following signals: ct (22) + rect(t − 1) (a) rect - =-∞ II (t-nto), where x = 0.5s, and to = 2s. (6) Σ.Ξ.

The spectrum, X(ƒ), of a periodic signal x(t) is shown in Figure Q1. 8e.j0.5m 8e-jo.5n TH "Lik. 2ej0.25n -32 -24 -16 16 24 32 f(Hz) Figure Q1 (a) Find the de value and average power of x(t). (b) Express x(t) as a function of real sinusoids. 2e-j0.25m

For each signal, if it is periodic, find the fundamental period To and the fundamental frequency wo. Otherwise, prove that the signal is not periodic. (a) x(t) (b) x(t): = cost sint. = cos 3t+sin 5t. (c) x(t) = cos (3t) + sin (9t) (d) x(t) = cos (3πt) + sin (4πt) + cos (5t)

5. Are the following signals periodic? If yes, determine its period. Plot the periodic signals in Matlab for two fundamental periods 1 1 a. x(t) = cos(271) --cos(67)+-cos10t) -cos(147t) 5 3 7 x(1) = cos(27rt) –cos(6/Zzt) b. с. x() %3 sin' (2лі) d. x(t)= cos (27) e. x[n]=sin(n)