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Problem 3.) Find and plot X(w) and X(w), the magnitude and DTFT for the signal x[n]...
5. (4 pts) Let X(ej) be the DTFT of a signal x[n] which is known to be zero for n < 0 and n > 3. We know X(eja) for four values of N as follows. X(@j0) = 10, X(eja/2) = 5 – 5j, X(ejt) = 0, X(ej37/2) = 5 + 5j (a) (3 pts) Find x[n]. (Hint: Compute the IDFT) (b) (1 pts) Find X(ej?).
Problem 3.12 Find the DTFT of the following time-domain signals: (b) x[n] = alu. lal < 1 11:32 AM Wed 25 Mar '< ! Q 0 O Untitled Notebook (12) 5 * Untitled Notebook (12) W X hw3A_s2020.pdf Untitled Problem 3.14 Find the FT of the following signals: continuous la aperiodic (b) X(t) = e te n(jw) t 120
for the plot, provide the matlab code. 3. Let the input signal x[n] (defined for -<n < oo) to the system be x[n] = 3 cos( 0.05πn) + 4 cos( 0.45πn) + cos( 0.95 n) and the transfer function be 1-re-je a) Plot this signal as a function of n. b) Determine and plot the output y[n] produced by the system due to the input analyzed in part a) of this problem. Do this first with r 0.05 and then...
6. Let X(e2) be the DTFT of a signal nl which is known to be zero for n < 0 and n > 3. We know X(eim) for four values of N as follows X (ejm)0, X(en/2) X(eT/2)5 5j, X(ej0) 10, 55j = = = (a) Find n. (Hint: Compute the IDFT) (b) Find X(ei?)
2. Given x[n]— 1-ae-ja' find the DTFT of: (a) y[n] = nx[n],(b) z[n] = (n − 1)x[n] dX(92) Hint: nx[n]< > ; dΩ
2+z-1 1. The Z-transform of a signal x[n] is given as X(z) = }</21 < a) Find the signal x[n] [7] b) Draw the pole – zero plot of the z-transform .[3] c) Is x[n] causal or not? Justify your answer [2]
3.13 Determine the DTFT of the two-sided sequence y[n] = a1",jal < 1.
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
Compute and sketch the convlution of y[n] = x[n]*h[n] using the graphical method for discrete signal where x[n] = h[n] = 2.-1<n<3 0, other wise
6 3. Consider x = [<1 %)* 3. Consider x' = | (a) Find the general solution to the system and describe the behavior of the solution as t + +00 (b) Draw a direction field and plot a few trajectories of the system.