Digital Signal Processing Basics
Which of the following 5-tap FIR filters has linear phase?
- Ah = {1, 2, 3, 2, 1}
- Bh = {1, 2, 3, 4, 5}
- Ch = {5, 4, 3, 2, 1}
Show answer and explanation
Answer: A. h = {1, 2, 3, 2, 1}
If the coefficients of an FIR filter are symmetric about the center (h[n] = h[N − 1 − n]), the phase is a straight line proportional to frequency, and every frequency component is delayed by the same (N − 1)/2 samples. {1, 2, 3, 2, 1} is symmetric about the central 3, so it is a linear-phase filter with a constant delay of 2 samples. {1, 2, 3, 4, 5} and {5, 4, 3, 2, 1} are neither symmetric nor antisymmetric, so their delay changes with frequency.
- A. Correct. It is symmetric about the center, so the delay is a constant 2 samples.
- B. The coefficients are not symmetric, so the delay changes with frequency.
- C. This is just {1, 2, 3, 4, 5} reversed, and it is not symmetric either.