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Digital Filters: An Introductory Course

This course covers fundamental concepts in digital signal processing, focusing on digital filters. Learn about designing FIR and IIR filters, multirate systems, frequency transformations, DFT, FFT algorithms, and practical DSP problem-solving. Explore filter characteristics, different filter responses (Butterworth, Chebyshev, Elliptic), and applications in radar and image processing. Gain insights into analog vs. digital signal processing reliability and the power aspects of digital filters. Various algorithms and design techniques are also discussed. Numerous examples and demonstrations enhance understanding.

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Digital Filters: An Introductory Course

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  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

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