What is Group delay?

A quantity that describes how much each frequency component of a signal passing through a filter is delayed, defined as the negative derivative of the phase response φ(ω) with respect to frequency (−dφ/dω). If the group delay is the same at all frequencies, the whole waveform is simply delayed with its shape intact. An N-tap FIR filter with symmetric coefficients has a constant group delay of (N − 1)/2 samples. In IIR and analog filters the group delay varies with frequency and often peaks near the cutoff frequency, distorting pulse shapes. Bessel filters are designed for a flat group delay.

Japanese name: 群遅延

Group delay appears in 2 practice questions across 2 topics, including Digital Signal Processing Basics, Analog and electronic circuits.

Field: Digital Signal Processing Basics

Try it: questions about Group delay

Which of the following is the group delay of a 101-tap linear-phase FIR filter (with symmetric coefficients)?

  1. A50 samples
  2. B50.5 samples
  3. C101 samples
Show answer and explanation

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.

Group delay in the explanations

Questions that mention Group delay (2)

  1. Which of the following is the group delay of a 101-tap linear-phase FIR filter (with symmetric coefficients)?
  2. Which correctly describes a Butterworth low-pass filter?

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Related terms

Linear phase FIR filter Aliasing Convolution Decimation Difference equation Discrete Fourier transform Fast Fourier transform (FFT) Frequency resolution IIR filter

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