Introduction to Multirate, Polyphase, and Wavelet Filter Banks

Julius Smith $<$jos at ccrma$>$ (CCRMA)

This two-hour talk contains tutorial introductions to

• multirate digital systems,
• perfect reconstruction filter banks,
• quadrature mirror filters,
• polyphase filter bank analysis,
• multi-input, multi-output allpass filters,
• paraunitary filter banks, and
• wavelet filter banks (particularly the dyadic wavelet filter bank).

Additionally, it is demonstrated how polyphase filterbank analysis naturally converts the ``filter bank summation'' (FBS) representation of the STFT to an ``overlap add'' (OLA) representation, while simultaneously showing that the STFT implements a perfect reconstruction filter bank (usually oversampled).

This talk is a synthesis of Music 420 lecture overheads with contributions from past teaching assistants Scott Levine and Harvey Thornburg. They can be perused (on campus) at http://ccrma/~jos/JFB/.