Using Methodology for MATLAB Designing the First-Order Chebyshev Analogue and IIR Digital Filters

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