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In signal processing, a polyphase matrix is a matrix whose elements are filter masks. It represents a filter bank as it is used in sub-band coders alias discrete wavelet transforms.
If h , g {\displaystyle \scriptstyle h,\,g} are two filters, then one level the traditional wavelet transform maps an input signal a 0 {\displaystyle \scriptstyle a_{0}} to two output signals a 1 , d 1 {\displaystyle \scriptstyle a_{1},\,d_{1}} , each of the half length:
Note, that the dot means polynomial multiplication; i.e., convolution and ↓ {\displaystyle \scriptstyle \downarrow } means downsampling.
If the above formula is implemented directly, you will compute values that are subsequently flushed by the down-sampling. You can avoid their computation by splitting the filters and the signal into even and odd indexed values before the wavelet transformation: