Abstract
Multirate fast-convolution (FC) processing can be used for realizing low-complexity filter banks (FBs) and transmultiplexers (TMUXs). The main advantage of the FC-based realizations when compared with the polyphase FBs is the increased configurability, that is, the number of subchannels, their bandwidths, and the center frequencies can be adjusted independently. In general, FC-based FBs are linear periodically shift-variant systems. In this brief, novel matrix representations for the FC synthesis and analysis FBs are first derived. These representations give all the shift-variant impulse responses of the FC-based FBs. Then the TMUX optimization criteria are expressed using these representations. Two examples are included to demonstrate the performance of the optimized designs as well as to illustrate the flexibility of the resulting FC-based TMUXs.
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