# Appendix BPolyphase Implementation of FBMC/OQAM

This section details the polyphase implementation of filter bank multicarrier (FBMC)/offset quadrature amplitude modulation (OQAM) multi-carrier modulations.

## B.1. Polyphase representation

The transmit filter *G* is a finite impulse response filter containing *L*_{G} = *KN* coefficients, whose *z* transform is:

[B.1]
*K* is the overlapping factor. *G*(*z*) can be decomposed into *N* elementary filters. Thus, it generates a polyphase network:

[B.2]
where are the polyphase components of *G*(*z*).

Let us now denote by *G*_{i}(*z*) the filter deduced from *G*(*z*) by a frequency shift of *i*/*N*:

[B.3]
Using polyphase representation, *G*_{i}(*z*) is written as:

[B.4]
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: ...