Problem 5 For the difference equation 0=2y[n+2]-3y[n+1]-2y[n]-4x[n+2]+2x[n+1] a. Put the difference equation in standard causal form y[n]=... b. Draw a block diagram (i.e., flow diagram, or digital filter structure) implementing this difference equation. c. For the input x[n] = [n] and the system at rest (i.e., zero initial conditions), compute y[-1],y[0], [1], [2], and y[3] by hand directly from the difference equation. d. Find the transfer function H(z). e. Compute the unit pulse response h[n],via inverse z-transform. Confirm that h[-1] through h[3] are identical to the samples of the unit pulse response computed above via direct iteration of the difference equation.

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Problem 5
For the difference equation
0=2y[n+2]-3y[n+1]-2y[n]-4x[n+2]+2x[n+1]
a. Put the difference equation in standard causal form_y[n]=...
b. Draw a block diagram (i.e., flow diagram, or digital filter structure) implementing
this difference equation.
c. For the input x[n] = [n] and the system at rest (i.e., zero initial conditions),
compute y[-1],y[0], y[1],y[2], and y[3] by hand directly from the difference equation.
d. Find the transfer function H(z).
e. Compute the unit pulse response h[n],via inverse z-transform. Confirm that [-1]
through h[3] are identical to the samples of the unit pulse response computed above
via direct iteration of the difference equation.
Transcribed Image Text:Problem 5 For the difference equation 0=2y[n+2]-3y[n+1]-2y[n]-4x[n+2]+2x[n+1] a. Put the difference equation in standard causal form_y[n]=... b. Draw a block diagram (i.e., flow diagram, or digital filter structure) implementing this difference equation. c. For the input x[n] = [n] and the system at rest (i.e., zero initial conditions), compute y[-1],y[0], y[1],y[2], and y[3] by hand directly from the difference equation. d. Find the transfer function H(z). e. Compute the unit pulse response h[n],via inverse z-transform. Confirm that [-1] through h[3] are identical to the samples of the unit pulse response computed above via direct iteration of the difference equation.
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