Aim
The course provides solutions to problems in signal processing where filter design and efficient algorithms are in demand. The student should obtain sufficient insights on theory and application to independently formulate the mathematical problem, to solve it, and to implement the solution for processing of real signals.

Knowledge and understanding
For a passing grade the student must

• have knowledge on different approaches to filter design, derivation of efficient algorithms, e.g., the FFT, and filter banks.

• know how to apply the most common methods on real problems and signals related to audio and video (Matlab level)

• know how to define mathematical models within the area based on various situations.

Skills and abilities
For a passing grade the student must

• be able to understand the principles of different filter design methods (IIR and FIR and variants), and to design such filters in Matlab.

• be able to describe and analyze error sources present in the implementation of algorithms in the DSP environment.

• be able to describe efficient algorithms for the computation of the discrete-time Fourier transform.

• be able to describe and analyze the most common types of filter banks.

• be able to describe and implement algorithms for audio signal processing.

Judgement and approach
For a passing grade the student must

• be able to analyze, assess, and implement filters, filter banks, and efficient algorithms, and also to interpret and to describe their inherent principles.

• have insight on the fact that seemingly different technical problems can be dealt with using the same methods.

Contents
Filter design:
Digital IIR filter design; Bilinear transformation; Digital FIR filter design; Windowing, ideal filters, and the Gibbs phenomenon; Equirippel filters.

Implementation:
Structure verification; Efficient FFT algorithms; Different types of quantization.

Multirate signal processing and filter banks:
Up- and downsampling; Decimation and interpolation; Polyphase decomposition; Nyqvist filters; Uniform filter banks; Two-channel QMF; Multirate filters and wavelets.

Audio- and video signal processing:
Signal processing for sound effects (echo, reverb, and others); Signal processing for data compression of music (mp3); Signal processing for image and video compression.

Literature
Mitra S K: Digital Signal Processing, A Computer Approach, third edition, McGraw-Hill 2006. ISBN: 0-07-286546-6, and additional material provided by the department.