3 for each of the following impulse responses of lti

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3. For each of the following impulse responses of LTI systems, determine the stability and causality of the system. a. ] 1 [ ) 2 / 1 ( ] [ n u n h n b. ] 1 [ 3 ] [ ) 3 / 1 ( ] [ n u n u n h n n c. ] [ ) 3 / sin( ] [ n u n n h d. ) 4 / 4 / cos( ) 4 / 3 ( ] [ n n h n Please justify your answer for each property for each impulse response. 4. Plot each of the following signals using Matlab. Label the x-axis, y-axis and put titles on the plots. Turn in the Matlab code and plots for each part. a. a[n] = [ n+1 ]-2 [ n ]+3 [ n-1 ]-2 [ n-2 ]+ [ n-3 ], for n=-5:5 b. b[n] = sin(2 π n/128){u[n-32] – u[n-65]} for n=-128:127 c. c[n] = cos( 2 *960*n/1024){u[n] - u[n-128]} for n=-128:127 d. e[n] = .99 n cos(2 *128*n/1024) { u[n] – u[n-128] } for n=0:255
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5. Use a graphical approach to demonstrate the commutative property for convolution. Let x[n] = {1, 2, 3, 4, 5}, h[n] = {1, 2, 2, 1}. Note: You should do the convolution graphically two times and show that x*h gives you the same result as h*x. Also compute the convolution using Matlab to verify your solutions.
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