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The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
The group velocity is positive (i.e., the envelope of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward). The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes —known as the modulation or envelope of the wave—propagates through space.
In signal processing, linear phase is a property of a filter where the phase response of the filter is a linear function of frequency.The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the slope of the linear function), which is referred to as the group delay.
Gain and group delay of the third-order Butterworth filter with = The group delay is defined as the negative derivative of the phase shift with respect to angular frequency and is a measure of the distortion in the signal introduced by phase differences for different frequencies. The gain and the delay for this filter are plotted in the graph ...
So, a minimum phase system with all zeros inside the unit circle minimizes the group delay since the group delay of each individual zero is minimized. Illustration of the calculus above. Top and bottom are filters with same gain response (on the left : the Nyquist diagrams , on the right : phase responses), but the filter on the top with a = 0. ...
Propagation of a wave packet demonstrating a phase velocity greater than the group velocity. This shows a wave with the group velocity and phase velocity going in different directions. The group velocity is positive, while the phase velocity is negative. [1] The phase velocity of a wave is the rate at which the wave propagates in any medium.
A closely related yet independent quantity is the group-delay dispersion (GDD), defined such that group-velocity dispersion is the group-delay dispersion per unit length. GDD is commonly used as a parameter in characterizing layered mirrors, where the group-velocity dispersion is not particularly well-defined, yet the chirp induced after ...
The contents of the True time delay page were merged into Group delay and phase delay on 21 July 2017. For the contribution history and old versions of the redirected page, please see ; for the discussion at that location, see its talk page.