This section details the polyphase implementation of filter bank multicarrier (FBMC)/offset quadrature amplitude modulation (OQAM) multi-carrier modulations.
The transmit filter G is a finite impulse response filter containing LG = KN coefficients, whose z transform is:
K is the overlapping factor. G(z) can be decomposed into N elementary filters. Thus, it generates a polyphase network:
where are the polyphase components of G(z).
Let us now denote by Gi(z) the filter deduced from G(z) by a frequency shift of i/N:
Using polyphase representation, Gi(z) is written as:
A uniform filter bank is obtained by shifting the response of G(z) on the frequency axis. It is thus deduced from G(z), which is, therefore, called the prototype filter of the filter bank.
If all filters are deduced from the prototype filter by frequency shift multiples in 1/N, then the filter bank has the following expression: ...