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

TL;DR

This paper introduces a spectral method for modeling linear filters, enabling continuous-time output prediction and tested on popular filter types like Butterworth, Linkwitz-Riley, and Chebyshev.

Contribution

It presents a novel spectral approach for linear filter modeling using orthogonal expansions and non-stationary transfer functions, advancing filter simulation techniques.

Findings

Successfully modeled Butterworth, Linkwitz-Riley, and Chebyshev filters

Achieved continuous-time output prediction

Demonstrated effectiveness across different filter orders

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.