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Realisation of a 2-dimensional f.i.r. digital filter using separable filters

Realisation of a 2-dimensional f.i.r. digital filter using separable filters

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The scheme for the expansion of a 2-dimensional f.i.r. digital filter function into a sum of separable functions is generalised. Using the generalised procedure a m × m order filter function can be expressed in as many as m!n!/(|mn| + 1)! ways. Further it is also proved that the number of terms in the expansion will be equal to the rank of the matrix.

References

    1. 1)
      • B.R. Suresh , B.A. Shenoi . Exact realisation of 2-dimensional digital filters by separable filters. Electron. Lett. , 242 - 244
    2. 2)
      • F.R. Gantmacher . (1959) , The theory of matrices.
    3. 3)
      • M. Lal . On the separability of multivariable polynomials. Proc. IEEE , 718 - 719
    4. 4)
      • S. Treital , J.L. Shanks . The design of multistage separable planer filters. IEEE Trans. , 10 - 27
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