Digital Signal Processing Basics
Which of the following is the group delay of a 101-tap linear-phase FIR filter (with symmetric coefficients)?
- A50 samples
- B50.5 samples
- C101 samples
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Answer: A. 50 samples
The group delay of an N-tap FIR filter with symmetric coefficients is (N − 1)/2 samples at every frequency. For N = 101 this is (101 − 1)/2 = 50 samples, the position of the center coefficient (the 51st coefficient, h[50]). At a sampling frequency of 48 kHz this is a delay of 50 ÷ 48000 ≈ 1.04 ms, and in real-time processing it must be kept in mind that more taps mean more delay.
- A. Correct. (101 − 1)/2 = 50 samples.
- B. This is N/2 = 101/2. The delay is set by the position of the center coefficient, (N − 1)/2.
- C. This is the number of taps itself (the full length of the impulse response). The delay is set by its center.