Variable digital filter design using the outer product expansion

Digital filters with adjustable frequency domain characteristics are referred to as variable digital filters. Variable filters are useful in the applications where the filter characteristics are required to be changeable during the course of signal processing. Especially in real time applications, variable filters are needed to change their coefficients instantaneously such that the real time signal processing can be performed. The present paper proposes a very efficient technique for variable 1D digital filter design. Generally speaking, the variable coefficients of variable digital filters are multidimensional functions of a set of spectral parameters which define the desired frequency domain characteristics. The authors first sample the given variable 1D magnitude specification and use the samples to construct a multidimensional array, then propose an outer product expansion method for expanding the multidimensional array as the sum of outer products of 1D arrays (vectors). Based on the outer product expansion, one can reduce the difficult problem of designing a variable 1D digital filter to the easy one that only needs constant 1D filter designs and 1D polynomial approximations. The technique can obtain variable 1D filters having arbitrary desired magnitude characteristics with a high design accuracy