Necessary and Sufficient Conditions for Perfect Reconstruction
It can be shown [287] that the most general conditions for perfect reconstruction are that
![]() |
(12.63) |
for some constant
![$ c$](http://www.dsprelated.com/josimages_new/sasp2/img2133.png)
![$ K\geq 0$](http://www.dsprelated.com/josimages_new/sasp2/img2134.png)
![$ L$](http://www.dsprelated.com/josimages_new/sasp2/img184.png)
![$ N-1$](http://www.dsprelated.com/josimages_new/sasp2/img300.png)
Note that the more general form of
above can be regarded as a (non-unique) square root of a vector unit delay, since
![]() |
(12.64) |
Thus, the general case is the same thing as
![]() |
(12.65) |
except for some channel swapping and an extra sample of delay in some channels.
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Sufficient Condition for Perfect Reconstruction