About: Polyphase matrix

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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 are two filters, then one level the traditional wavelet transform maps an input signal to two output signals , each of the half length: Note, that the dot means polynomial multiplication; i.e., convolution and means downsampling. The wavelet transformation reformulated to the split filters is: This can be written as matrix-vector-multiplication This matrix is the polyphase matrix.

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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 are two filters, then one level the traditional wavelet transform maps an input signal to two output signals , each of the half length: Note, that the dot means polynomial multiplication; i.e., convolution and 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: The arrows and denote left and right shifting, respectively. They shall have the same precedence like convolution, because they are in fact convolutions with a shifted discrete delta impulse. The wavelet transformation reformulated to the split filters is: This can be written as matrix-vector-multiplication This matrix is the polyphase matrix. Of course, a polyphase matrix can have any size, it need not to have square shape. That is, the principle scales well to any filterbanks, , wavelet transforms based on fractional refinements. (en)
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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 are two filters, then one level the traditional wavelet transform maps an input signal to two output signals , each of the half length: Note, that the dot means polynomial multiplication; i.e., convolution and means downsampling. The wavelet transformation reformulated to the split filters is: This can be written as matrix-vector-multiplication This matrix is the polyphase matrix. (en)
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  • Polyphase matrix (en)
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