Digital Filters

Aim

The aim of the course is to give the theoretical basis for analysis and synthesis of basic and advanced digital filters and knowledge about implementation of digital filters in hardware and software. After the course, the student should be be able to:

• Explain basic concepts and principles of basic and advanced digital filters as well as synthesize digital filters using standard methods and optimization methods.
• Realize and analyze basic and advanced digital filter structures as well as structures for interpolation and decimation.
• Analyze computational properties of basic and advanced digital filter structures.
• Use computer programs to synthesize, optimize, and implement digital filters.

Content

• Filter synthesis: Basic concepts and principles of digital filters, specifications, FIR and IIR filters, approximation theory, standard approximations, synthesis via optimization, optimization methods, frequency transformations, transformation of analog reference filters, applications, interpolation and decimation, polyphase structures.
• Realization and implementation: Analysis of different FIR and IIR filter structures, especially wave digital filters; transformation of analog reference structures, implementation in software.
• Computational properties: DSP algorithms, non-recursive and recursive realizations, signal-flow graphs, bounds on sampling frequency (data rate), impact of finite data and coefficient wordlengths, scaling of signal levels, roundoff noise, impact of scaling and roundoff noise on different filter structures.