Digital Signal Processing & Digital Filters

1. Digital Signal Processing & Digital Filters An Introductory Course By Professor A G Constantinides MSc, EE4, ISE4, PhD 1

2. DIGITAL FILTERS • In this course you will learn: • What are the general properties of a digital filter transfer function and amplitude response? • How to choose an appropriate filter response. • Why Butterworth responses are maximally flat. • Why Chebyshev and Elliptic responses are equiripple. • When to choose an IIR and when an FIR filter 2

3. DIGITAL FILTERS • How do you design FIR and IIR filters from specifications on amplitude performance? • What are multirate systems and their properties? • What is interpolation / Upsampling and Decimation / Downsampling? • How do you design efficient Decimation and Interpolation systems? • What are frequency transformations and how do you design these from performance specifications? • How accurate is the DFT as a spectrum estimator? 3

4. DIGITAL FILTERS • What are short FFT algorithms? • How do you choose the required wordlength? • What are Fast Convolutions and how are they realised? • How do you deal with a DSP problem in practice? 4

5. Course content • 1-Introduction 19 • 2-z transform 17 • 3-transfer functions 36 • 4-Signal Flow Graphs 25 • 5-digital filters intro 18 • 6-Digital Filters (FIR) 40 • 7-Digital Filters (IIR) 28 • 8-DFT 21 5

6. Course content • 9-DFT_one2two 29 • 10-Fourier transform & DFT 14 • 11-general transforms 10 • 12-running DFT 05 • 13-convolutions & transforms 07 • 14-interpolation_decimation 32 • 15-Finite Wordlength 27 • 16-applications 27 6

7. Course content  Filter Characteristics (Introductory) • ·        General Amplitude responses. • ·        Filter Characteristics • Butterworth • Chebyshev • Elliptic • ·        Interpreting Filter Specifications. • ·        The Bilinear z-Transform. • ·        Frequency Transformations. • Design Demonstrations. 7

8. DIGITAL FILTERS • FIR Filters, Structures and Design • ·        Lowpass Prototypes. • ·        Symmetry Conditions. • ·        Review of Windows. • ·        Optimisation Techniques for FIR filter Design. • ·        Realisation models. • ·        Differentiator and Hilbert Transform. • ·        Design Examples • Design Demonstrations 8

9. DIGITAL FILTERS • Multi-rate FIR and IIR Filters • ·        What is multirate filtering and why the need? • ·        Downsampling / Upsampling. • ·        Polyphase filtering techniques. • ·        Interpolation / Decimation. • ·        General Sample Rate Change. • ·        Design Examples. • Applications 9

10. DIGITAL FILTERS The Discrete Fourier Transform and the FFT • · Review and Definitions. • · Zero packing; zero extending. • · Radix 2/4/8 & Arbitrary Radix Transforms. • · Cook-Toom Algorithm. • · Thomas-Good Algorithm; The Chinese Remainder Theorem. • · Winograd Fourier Transforms. • · Prime Radix Transforms and Consequences. • · Wordlength; Scaling. • · Design Procedures in practice. 10

11. DIGITAL FILTERS • InThe DFT as a Filtering Operator • ·        Review of Fast Convolutions. • ·        Cyclic and Acyclic Convolutions. • ·        Overlap Add; Overlap Save. • ·        Narrow Band Filter Banks. • ·        Autocorrelation, Crosscorrelation. • ·        Performance measures. 11

12. DIGITAL FILTERS BOOKS • Course text book: Digital Signal Processing: A computer Based Approach, S K Mitra, McGraw Hill • Other books: • Introduction to Digital Signal Processing, Kuc, McGraw Hill • Digital Signal Processing, Roberts & Mullis, Addison Wesley • Digital Filters, Antoniou, McGraw Hill 12

13. DIGITAL FILTERS Analogue Vs Digital Signal Processing Reliability: Analogue system performance degrades due to: ·  Long term drift (ageing) ·  Short term drift (temperature?) ·  Sensitivity to voltage instability. ·  Batch-to-Batch component variation. ·  High discrete component count Interconnection failures 13

14. DIGITAL FILTERS Digital Systems: ·  No short or long term drifts. ·  Relative immunity to minor power supply variations. ·  Virtually identical components. ·  IC’s have > 15 year lifetime ·  Development costs *     * System changes at design / development stage only software changes. * Digital system simulation is realistic. DSP chips available as well as ASIC realisations 14

15. DIGITAL FILTERS Power aspects Size • Dissipation 15

16. Applications Radarsys / Sonarsys ·        Doppler filters. ·        Clutter Suppression. ·        Matched filters. ·        Target tracking. • Identification 16

17. DIGITAL FILTERS Image Processing •  Image data compression. • Image filtering. • Image enhancement. • Spectral Analysis. • Scene Analysis / Pattern recognition. 17

18. DIGITAL FILTERS Biomedical Signal Analysis • Spatial image enhancement. (X-rays) • Spectral Analysis. • 3-D reconstruction from projections. • Digital filtering and Data compression. 18

19. DIGITAL FILTERS Music •  Music recording. • Multi-track “mixing”. • CD and DAT. • Filtering / Synthesis / Special effects. 19

20. DIGITAL FILTERS Seismic Signal Analysis •  Bandpass Filtering for S/N improvement. • Predictive deconvolution to extract reverberation characteristics. • Optimal filtering. (Wiener and Kalman.) 20

21. DIGITAL FILTERS • In 21

22. DIGITAL FILTERS Telecommunications and Consumer Products • These are the largest and most pervasive applications of DSP and Digital Filtering • Mobile • Digital Recording • Digital Cameras • Blue Tooth or similar 22