AGC DSP Digital Signal Processing Digital Filters An

AGC DSP Digital Signal Processing & Digital Filters An Introductory Course By Professor A G Constantinides MSc, EE 4, ISE 4, Ph. D Professor A G Constantinides© 1

AGC DSP Digital Signal Processing & Digital Filters Contents 1 -Introduction 1) Introduction to Digital Signal Processing n n n Review of background DSP Review of mathematical methods Review of discrete-time random processes and linear systems Professor A G Constantinides© 2

AGC DSP Digital Signal Processing & Digital Filters 2) Multirate techniques and wavelets n Introduction to short-time Fourier analysis n Filter-banks and overlap-add methods of analysis and synthesis n Introduction to generalised time-frequency representation n Wavelet analysis n Multirate signal processing n Interpolation and decimation n Efficient filter structures for interpolation and decimation Professor A G Constantinides© 3

AGC DSP Digital Signal Processing & Digital Filters 3) Classical spectrum estimation methods n Power spectrum, power spectral density functions, random processes and linear systems n Introduction to statistical estimation and estimators n Biased and unbiased estimators n Einstein/Wiener Khintchine Theorem n Estimation of autocorrelations n Means and variances of periodograms n Smoothed spectral estimates, leakage Professor A G Constantinides© 4

AGC DSP Digital Signal Processing & Digital Filters 4) Modern spectrum estimation methods n Introduction to modern spectral estimation: Principles and approaches n Cramer-Rao Lower Bound (CRLB) and Efficient estimators n The Maximum Entropy Method (MEM) or Autoregressive Power Spectrum Estimation: Principles. n The MEM equations and Levinson/Durbin algorithm Professor A G Constantinides© 5

AGC DSP Digital Signal Processing & Digital Filters 4) Modern spectrum estimation methods (continued) n Introduction to Linear Prediction n Linear Predictive Coding using covariances and correlations n Cholesky decomposition n Lattice Filters n Linear Prediction of Speech Signals Professor A G Constantinides© 6

AGC DSP Digital Signal Processing & Digital Filters 5) Adaptive signal processing n Introduction to adaptive signal processing n Objective measures of goodness n Least squares and consequences n Steepest descent n The LMS and RLS algorithms n Kalman Filters Professor A G Constantinides© 7

AGC DSP Digital Signal Processing & Digital Filters 6) Applications § Communications § Biomedical § Seismic § Audio/Music Professor A G Constantinides© 8

AGC DSP DIGITAL FILTERS Digital Filters n In this course you will learn: n How to choose an appropriate filter response. n Why Butterworth responses are maximally flat. n Why Chebyshev and Elliptic responses are equiripple. n When to choose an IIR and when an FIR filter Professor A G Constantinides© 9

AGC DIGITAL FILTERS DSP § § § 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? How accurate is the DFT as a spectrum estimator? Professor A G Constantinides© 10

AGC DIGITAL FILTERS DSP n n 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? Professor A G Constantinides© 11

AGC DSP Course content Assumed DSP background DSP Background folder n n n 1 -Introduction 2 -z transform 3 -transfer functions 4 -Signal Flow Graphs 5 -digital filters intro Professor A G Constantinides© 12

AGC DSP Course content 2 -Digital Filter Design § 1 -Digital Filters (FIR) § 2 -Digital Filters (IIR) 3 -Multirate 1 -Interpolation_Decimation Professor A G Constantinides© 13

AGC DSP Course content 4 -Tranforms n 1 -DFT n 2 -DFT_one 2 two n 3 -general transforms n 4 -Wavelets 5 -Finite Wordlength n 1 -Finite Wordlength Professor A G Constantinides© 14

Course content AGC DSP 6 -Spectrum Estimation (Assumed n n n background in Mathematical Background folder) 1 -Fourier transform & DFT 2 -FFT-based Power Spectrum Estimation 3 -Modern Spectrum Estimation 4 -Intro-Estimation 5 -Eigen-based methods 6 -A Prediction Problem Professor A G Constantinides© 15

AGC DSP Course content 7 -Adaptive Signal Processing n 1 -Adaptive Signal Processing 8 -Applications § 1 -Applications § 2 -Applications Professor A G Constantinides© 16

AGC DSP Digital Signal Processing & Digital Filters BOOKS n Main Course text books: Digital Signal Processing: A computer Based Approach, S K Mitra, Mc. Graw Hill n Mathematical Methods and Algorithms for Signal Processing, Todd Moon, Addison Wesley n Other books: n Digital Signal Processing, Roberts & Mullis, Addison Wesley n Digital Filters, Antoniou, Mc. Graw Hill Professor A G Constantinides© 17

AGC DSP 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 Professor A G Constantinides© 18

AGC DSP 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. Professor A G Constantinides© 19

AGC DIGITAL FILTERS DSP Power aspects n Size n Dissipation n DSP chips available as well as ASIC/FPGA realisations Professor A G Constantinides© 20

AGC DSP Applications Radar systems & Sonar systems · Doppler filters. · Clutter Suppression. · Matched filters. · Target tracking. n Identification Professor A G Constantinides© 21

AGC DSP DIGITAL FILTERS Image Processing n Image data compression. n Image filtering. n Image enhancement. n Spectral Analysis. n Scene Analysis / Pattern recognition. Professor A G Constantinides© 22

AGC DSP DIGITAL FILTERS Biomedical Signal Analysis n Spatial image enhancement. (X-rays) n Spectral Analysis. n 3 -D reconstruction from projections. n Digital filtering and Data compression. Professor A G Constantinides© 23

AGC DSP DIGITAL FILTERS Music n Music recording. n Multi-track “mixing”. n CD and DAT. n Filtering / Synthesis / Special effects. Professor A G Constantinides© 24

AGC DIGITAL FILTERS DSP Seismic Signal Analysis n n n Bandpass Filtering for S/N improvement. Predictive deconvolution to extract reverberation characteristics. Optimal filtering. (Wiener and Kalman. ) Professor A G Constantinides© 25

AGC DIGITAL FILTERS DSP Telecommunications and Consumer Products These are the largest and most pervasive applications of DSP and Digital Filtering n n Mobile Communications Digital Recording Digital Cameras Blue Tooth or similar Professor A G Constantinides© 26