Question

1. A system has impulse response $h_1[n] = 2u[n - 5]$. a) Is this system causal? Explain; b) Is this system stable? Explain; c) Use convolution to determine the output of the system for input $x_1[n] = 2u[n + 1]$; d) Sketch the output, $y_1[n]$ over an appropriate range of n. 2. Repeat problem 1) above for and $h_2[n] = \left(\frac{3}{4}\right)^n u[n]$ $x_2[n] = u[n]$. 3. Repeat problem 1) above for and $h_3[n] = u[n] - u[n - 5]$ $x_3[n] = \left(\frac{3}{4}\right)^n u[n]$.

          1. A system has impulse response
$h_1[n] = 2u[n - 5]$.
a) Is this system causal? Explain;
b) Is this system stable? Explain;
c) Use convolution to determine the output of the system for input
$x_1[n] = 2u[n + 1]$;
d) Sketch the output, $y_1[n]$ over an appropriate range of n.
2. Repeat problem 1) above for
and
$h_2[n] = \left(\frac{3}{4}\right)^n u[n]$
$x_2[n] = u[n]$.
3. Repeat problem 1) above for
and
$h_3[n] = u[n] - u[n - 5]$
$x_3[n] = \left(\frac{3}{4}\right)^n u[n]$.

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1. A system has impulse response
h1[n] = 2u[n - 5].
a) Is this system causal? Explain;
b) Is this system stable? Explain;
c) Use convolution to determine the output of the system for input
x1[n] = 2u[n + 1];
d) Sketch the output, y1[n] over an appropriate range of n.
2. Repeat problem 1) above for
and
h2[n] = ((3)/(4))^n u[n]
x2[n] = u[n].
3. Repeat problem 1) above for
and
h3[n] = u[n] - u[n - 5]
x3[n] = ((3)/(4))^n u[n].

Added by Nicholas R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Vysakh M

Step 1

a) To determine if the system is causal, we need to check if the impulse response h[n] is nonzero only for n ≥ 0. In this case, h[n] = -2u[n-5]. Since u[n-5] is nonzero only for n ≥ 5, we can see that h[n] is nonzero only for n ≥ 5. Therefore, the system is Show more…

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Hello, the following has to do with Discrete LTI Systems. Please help with the following problems. I will thumbs up for full help. Please include all scratch work and if possible, please write legibly. Thank you very, very much! Note: Please use Convolution as instructed. Thank you again. 1. A system has impulse response h[n] = -2u[n-5] a) Is this system causal? Explain. b) Is this system stable? Explain. c) Use convolution to determine the output of the system for input x[n] = 2u[n+1]. d) Sketch the output, y[n], over an appropriate range of n. 2. Repeat problem 1) above for h2[n] = u[n] and x[n] = u[n]. 3. Repeat problem 1) above for h[n] = u[n] = u[n-5] and x[n] = u[n].

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