Matrix Filter Representations Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

## MatrixFilter Representations

It is illuminating to look at matrix representations of digital filters.6.7Every linear digital filter can be expressed as a constant matrix multiplying the input signal (the input vector) to produce the output signal (vector) , i.e., For simplicity (in this section only), we will restrict attention to finite-length inputs (to avoid infinite matrices), and the output signal will also be length . Thus, the filter matrix is a square matrix, and the input/output signal vectors are column vectors.

More generally, any finite-order linear operator can be expressed as a matrix multiply. For example, the Discrete Fourier Transform (DFT) can be represented by the DFT matrix'' , where the column index and row index range from 0 to [83, p. 111].6.8Even infinite-order linear operators are often thought of as matrices having infinite extent. In summary, if a digital filter is linear, it can be represented by a matrix.

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