Linear Phase

## Definition

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).

## Advantage

**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.

## Disadvantage

**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.

page revision: 3, last edited: 24 Apr 2010 00:47