Linear Phase Signals

In practice, a signal may be said to be linear phase when its phase is of the form

$$\Theta(\omega_k)= - \Delta \cdot \omega_k\pm \pi I(\omega_k),$$

where $\Delta$ is any real constant (usually an integer), and $I(\omega_k)$ is an indicator function which takes on the values 0 or $1$ over the points $\omega_k$ , $k=0,1,2,\ldots,N-1$ . An important class of examples is when the signal is regarded as a filter impulse response.^7.15 What all such signals have in common is that they are symmetric about the time $n=\Delta$ in the time domain (as we will show on the next page). Thus, the term ``linear phase signal'' often really means ``a signal whose phase is linear between $\pm\pi$ discontinuities.''