It can be shown  that the most general conditions for perfect reconstruction are that
for some constant and some integer , where is any integer between 0 and .
Note that the more general form of above can be regarded as a (non-unique) square root of a vector unit delay, since
Thus, the general case is the same thing as
except for some channel swapping and an extra sample of delay in some channels.
Polyphase View of the STFT
Sufficient Condition for Perfect Reconstruction