(Created 2009-08-11.)

SIGNAL PROCESSING - DESIGN AND IMPLEMENTATION | ETIF01 |

**Aim**

The course provides solutions to problems in signal processing where design of filters, filter banks and fast 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 and understanding on different approaches to the design of filters and filter banks, derivation of efficient algorithms, e.g., the FFT, and have an understanding of how such algorithms are implemented in a digital signal processor (DSP).
- know how to apply the most common methods on real problems and signals in communication, medicine, audio and economics (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 the most common types of filter banks and how these are applied in compression applications.
- 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 Fourier and wavelet transforms.

*Judgement and approach*

For a passing grade the student must

- be able to analyze, assess, and implement filters, filter banks, and fast 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.

*Architecture and programming of the DSP*

**Literature**

ProakisJ G, Manolakis D G: Digital Signal Processing. Principles, Algorithms and Applications, 4:e upplagan, Pearson Prentice Hall, ISBN 0-13-187374-1, 2007.