Applying the Spectral Method for Modeling Linear Filters: Butterworth, Linkwitz-Riley, and Chebyshev filters

Abstract

This paper proposes a new technique for computer modeling linear filters based on the spectral form of mathematical description of linear systems. It assumes the representation of input and output signals of the filter as orthogonal expansions, while filters themselves are described by two-dimensional non-stationary transfer functions. This technique allows one to model the output signal in continuous time, and it is successfully tested on the Butterworth, Linkwitz-Riley, and Chebyshev filters with different orders.