Digital Signal Processing

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Digital Signal Processing Digital Filters

• An Introductory Course
• By
• Professor A G Constantinides
• MSc, EE4, ISE4, PhD

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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

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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?

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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?

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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

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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

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Course content

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

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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

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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

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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.

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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.

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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

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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

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DIGITAL FILTERS

• Digital Systems
•   No short or long term drifts.
•   Relative immunity to minor power supply
  variations.
•   Virtually identical components.
•   ICs have gt 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

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DIGITAL FILTERS

• Power aspects
• Size
• Dissipation

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Applications

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

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DIGITAL FILTERS

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

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DIGITAL FILTERS

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

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DIGITAL FILTERS

• Music
•  Music recording.
• Multi-track mixing.
• CD and DAT.
• Filtering / Synthesis / Special effects.

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DIGITAL FILTERS

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

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DIGITAL FILTERS

• In

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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