Digital Signal Processing: Filters Made of Pure Arithmetic
Difference equations, the FFT, FIR and IIR filters and spectral estimation: how adding and multiplying numbers reshapes sound, images and radio.
Digital Signal Processing · 50 questions
Try 3 questions
1. A filter computes y[n] = x[n] + 0.5·y[n−1]. What does its response to a single impulse look like?
- It ends after exactly two samples
- It decays but never fully ends
- It grows without any bound
Show the answer
Answer: It decays but never fully ends
Each output feeds back at half strength, giving 1, 0.5, 0.25... an infinite impulse response that shrinks forever.
2. For a causal discrete-time system to be stable, where must all its poles lie?
- Outside the unit circle
- Inside the unit circle
- In the left half-plane
Show the answer
Answer: Inside the unit circle
Each pole p contributes pⁿ to the response, which decays only if |p| < 1; the left half-plane rule is for continuous time.
3. A system outputs the average of the last four input samples. What kind of filter is it?
- A high-pass IIR filter
- A band-stop IIR filter
- A low-pass FIR filter
Show the answer
Answer: A low-pass FIR filter
Averaging smooths rapid changes, passing slow trends, and it uses only a finite number of past inputs with no feedback.
The whole quiz comes before your apps
BrainTok asks a few questions like these before the apps you choose open, so your screen time turns into learning. For iPhone.
Join the beta