Using Matlab Functions for Designing Chebysev Filters

This paper deals with using MATLAB function and tools for designing first-order analogue Chebysev filters and IIR Chebysev filters. The first part of this paper is focused on a design of analogue filter via Chebyshev approximation approach, i. e. features and mathematical background of this iso-extremal approximation, approximation of normalized low-pass (NLP, also NDP in Czech) filter, and mathematical formulas for calculating fundamental parameters of NLP, such as constructing a tolerance scheme, Chebyshev approximation order, poles of transfer function, characteristic equation, and group delay. Due to frequency transformation formulas implemented in MATLAB, un-normalized forms of frequency functions for low-pass (LP, also DP in Czech), high-pass (HP, also the same in Czech), band-pass (BP, also PP in Czech), and band-stop (BS, also PZ in Czech) analogue filters are also available. The second part of this paper describes designing the first-order IIR Chebyshev filter via implemented MATLAB functions and Filter Visualization Tool (FVT), whereas conversion from an analogue form into a digital form is done and discussed for bilinear (Tustin) transformation only. Naturally, both design approaches are illustrated in form of some practical examples.