Question

Consider the following discrete-time LTI system y[n] - 0.3y[n - 1] - 0.04y[n - 2] = x[n] + 2x[n - 1], with the input x[n] = (0.4)^n u[n]. (a) Determine the impulse response h[n]. (b) Determine the zero-state response via convolution.

          Consider the following discrete-time LTI system
y[n] - 0.3y[n - 1] - 0.04y[n - 2] = x[n] + 2x[n - 1],
with the input
x[n] = (0.4)^n u[n].
(a) Determine the impulse response h[n].
(b) Determine the zero-state response via convolution.

Consider the following discrete-time LTI system
y[n] - 0.3y[n - 1] - 0.04y[n - 2] = x[n] + 2x[n - 1],
with the input
x[n] = (0.4)^n u[n].
(a) Determine the impulse response h[n].
(b) Determine the zero-state response via convolution.

Added by Salvador P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Scott Stetson

Step 1

First, we need to find the impulse response h[n]. To do this, we will replace x[n] with the impulse function δ[n] and solve for y[n]. y[n] - 0.3y[n - 1] + 0.04y[n - 2] = δ[n] + 2δ[n - 1] Show more…

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Consider the following discrete-time LTI system y[n] - 0.3y[n - 1] - 0.04y[n - 2] = x[n] + 2x[n - 1], with the input x[n] = (0.4)^n u[n]. Determine the impulse response h[n]. Determine the zero-state response via convolution.