Exercise · ZW-IMPULSE-RESPONSE-009 · ★★☆ Intermediate
If \(h[n]=\delta[n-2]\), what output does the input \(x[n]=\delta[n]+\delta[n-1]\) produce at \(n=2\)?
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- A. 1
Explanation
The output is \(y[n]=x[n-2]\), and at \(n=2\) it equals \(x[0]=1\). Taking \(y[2]=x[2]\) leads to zero, a common shifting error.
Review the concept: Impulse response
The impulse response \(h[n]\) is the output of an LTI system when its input is the unit impulse \(\delta[n]\).
\[y[n]=\sum_{k=-\infty}^{\infty} x[k]\,h[n-k]\]
More practice problems: impulse response
- ZW-IMPULSE-RESPONSE-001 What is the output of an LTI system called when the input is δ[n]?
- ZW-IMPULSE-RESPONSE-002 What value does δ[n] take at n=0?
- ZW-IMPULSE-RESPONSE-003 If h[n]=0 for n<0, what property does the system have?
- ZW-IMPULSE-RESPONSE-004 If h[n] is nonzero only for n=0,1,2, what is the system called?
- ZW-IMPULSE-RESPONSE-005 Which operation combines the input x[n] with the response h[n] to produce the output?
- ZW-IMPULSE-RESPONSE-006 A system has h[n]=(0.5)^n u[n]. What is h[2]?
- ZW-IMPULSE-RESPONSE-007 For h[n]=δ[n]+2δ[n-1] and input x[n]=δ[n], what is y[1]?
- ZW-IMPULSE-RESPONSE-008 A system has h[n]=u[n]-u[n-3]. What is h[1]?