Question

A continuous time, si spectrum illustrated below: 2 s, has the magnitude spectrum illustrated berioic signal,x(), with a fundamental period 7 - 2 -3 2 a) Plot the magnitude spectrum of x (3t). b) Plot the magnitude spectrum of eltx(t) c) Plot the magnitude spectrum of 2x(t) + d) Determine the average power of x(3t) co δ(t-3m)

Answer 1

Assume spectra of x (3t) = x_1 (B) x _1(k) = 1/3 times (k/3) but x (k) is discrete exits only for is = -1, -2, -3, 1, 2, 3 so x (k/3) exits for only k = -1, 1 i.e x _1 (k) = 1/3 times [3/3] = 1/3 times [1] x _1 [k] = 1/3 times [-3/3] = 1/3 times [-1] plot of magnitude of spectra of x (3t) b) spectrum of e^j pi t x (t) = x_2(k) By frequency shift property x (t) x (k) then e^j w_0 t x (t) x (k - w_0) so e^j pi t x (t) x _2 (k) = x [k - pi] \r\n so x_2 [k] = x [k - pi] x [k] is shift by 3.14 units and x [k] does not exist for this shift since they are not discrete c) plot of 2 x (t) + Sigma^infinity_m = -infinity delta (t-3 m) F.T of Sigma^infinity_m = -infinity delta (t - 3m) is period = 3 sec