whenever its impulse
response 
is symmetric, i.e.,
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Linear phase filters delay all frequencies by equal amounts, and this
is often a desirable property in audio and other applications. A
filter phase response is linear in
whenever its impulse
response
is symmetric, i.e.,
 |
(12.35) |
 |
(12.36) |
![$\displaystyle g\,e^{-j\omega d} \eqsp e^{-j\omega N}\left[ \left\vert H_0(\ejo )\right\vert^2 - (-1)^N\left\vert H_0(e^{j(\pi-\omega)})\right\vert^2\right].$](img2060.png) |
(12.37) |
is even, the right hand side of the above equation is forced
to zero at
. Therefore, we will only consider odd
,
for which the perfect reconstruction constraint reduces to
![$\displaystyle g\,e^{-j\omega d} \eqsp e^{-j\omega N}\left[ \left\vert H_0(\ejo )\right\vert^2 + \left\vert H_0(e^{j(\pi-\omega)}\right\vert^2\right].$](img2061.png) |
(12.38) |
