Exercise · ZW-IMPULSE-RESPONSE-006 · ★★☆ Intermediate
A system has \(h[n]=(0.5)^n u[n]\). What is \(h[2]\)?
Choose one option.
Show answer
- D. 0.25
Explanation
Since \(u[2]=1\), we have \(h[2]=(0.5)^2=0.25\). The value 0.125 corresponds to \((0.5)^3\), a common indexing 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-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]?
- 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?