Linear Phase


When we say a system has linear phase, it means the systems's phase response is linear function(straight line) of frequency(excluding phase wraps at +/- 180 degrees).


  • constant delay — when a system is linear phase, its has the same delay at all frequency. To consider the formula of system delay, it is obvious that when "theta" is a straight line, the delay is constant.


  • larger delay — linear phase system has larger delay than a minimum phase system.

System Delay

We can compute system delay by the formula: -d(theta)/d(w), where "theta" is the system's phase response, w is angular frequency. Here is a simple example, consider the system with impulse response delta[n - 3], then its frequency response is e-jw3. We know that phase response of this system is -jw3. We can use the above formula to obtain -3, and that is exactly the system delay.

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