Objectives and outcomes
Knowledge of methods for designing and applying digital filters in signal processing and methods for frequency analysis of digital signals. Designing digital filters using software. Software implementation of filters. Upon completion of the course, students understand the use of frequency transformations and systems in signal filtering. They are qualified to apply fast Fourier transformation algorithms to the analysis of spectral characteristics of signals. Students use methods for designing digital filters based on the discretisation of analogue filters.
Lectures
Introduction to digital signal processing: overview of frequency characteristics of signals and systems, application of frequency transformations. Concept and application of discrete Fourier transform and the FFT algorithm in digital signal processing. Application of z-transformation for the analysis of discrete systems: determination of the transfer function on the basis of differential equations, understanding of poles and zeros, system properties management. Infinite impulse response filters. Design of discrete filters with infinite impulse response – IIR. Designing based on analogue prototypes: Butterworth filter, Chebyshev filter type 1 and type 2, elliptic filter, bilinear transformation. Finite impulse response filters. Designing FIR filters by windowing. Designing FIR filters by frequency selection. Optimal methods of designing FIR filters.
Practical classes
Application of software packages GNU Octave, Matlab for analysis of discrete signals. Calculation of signal spectrum using the FFT algorithm. Presentation of the software system. Determination of the frequency response of the system, the position of poles and zeros. Computer-aided design of IIR filters. Computer-aided design of FIR filters. Application of discrete filters in given situations.