Exercise · ZW-IMPULSE-RESPONSE-007 · ★★☆ Intermediate
For \(h[n]=\delta[n]+2\delta[n-1]\) and input \(x[n]=\delta[n]\), what is \(y[1]\)?
Choose one option.
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- C. 2
Explanation
With input \(\delta[n]\), the output is \(y[n]=h[n]\), so \(y[1]=2\). Adding the coefficients of \(h\) would give a different value and does not correspond to \(y[1]\).
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-008 A system has h[n]=u[n]-u[n-3]. What is h[1]?
- ZW-IMPULSE-RESPONSE-009 If h[n]=δ[n-2], what output does the input x[n]=δ[n]+δ[n-1] produce at n=2?