Ece 429/529 Digital Signal Processing

ece 429/529

digital signal processing

ECE 429/529 © RNS SPRING 2007 SCHEDULE All dates are tentative. Learning outcomes Lesson Day Date Topics Textbook HW/PROJECT to be covered 1 W Jan 10 1 Introduction to DSP Chap. 1 2 F Jan 12 2-5 Sequences, digital frequency 1.2-1.3, 2.1 3 W Jan 17 6-7 Sampling, aliasing 1.4 HW1 4 F Jan 19 8-10 Quantization noise 1.4 5 M Jan 22 11-12 DT system components 2.2 6 W Jan 24 13-14 System properties 2.2 HW2 7 F Jan 26 15-17 Filter realizations, impulse response 2.3-2.5 8 M Jan 29 18-19 Convolution 2.3 HW3 9 W Jan 31 20 Correlation 2.6 10 F Feb 2 21 (Forward) z-transform 3.1 11 M Feb 5 22-23 Time-shifting, DtFt existence, sequence type from ROC 3.2-3.3 HW4 12 W Feb 7 24 (Inverse) z-transform 3.4 13 F Feb 9 25 Applying z-transform properties 3.2 14 M Feb 12 26-27 Poles & stability, system analysis using z-transform 3.3, 3.6 REVIEW 15 W Feb 14 REVIEW REVIEW F Feb 16 EXAM 1 REVIEW 16 M Feb 19 28-30 (Forward) Discrete-time Fourier transform (DtFt), symmetry 4.2-4.3 PROJ 1 17 W Feb 21 31-33 Frequency-shifting, modulation, filter design from lowpass prototypes 4.3 18 F Feb 23 33-34 Synthesis of filters using DtFt properties 4.3, 4.5 19 M Feb 26 35-37 DtFt analysis of downsampling, expansion, compression operations 4.3 HW5 20 W Feb 28 38-39 DtFt systems analysis 4.4 21 F Mar 2 40-41 Phase and group delay of filters 4.4 22 M Mar 5 42 Frequency response from poles & zeros 4.4 HW6 23 W Mar 7 43 Comb and notch filters 4.5 24 F Mar 9 44 Minimum-phase filters 4.5 25 M Mar 19 45-46 Forward DFT and Inverse DFT, relationship to DtFt 5.1 PROJ 2 26 W Mar 21 47 Applying DFT properties 5.2 27 F Mar 23 48-49 Convolution and correlation using DFT 5.2 28 M Mar 26 50-52 DFT symmetry, sinusoidal analysis and freq resolution 5.2 HW7 29 W Mar 28 53 Zero-padding and windowing 5.4 30 F Mar 30 54 Spectral analysis 5.4 31 M April 2 55 Mason’s gain rule - REVIEW 32 W April 4 REVIEW REVIEW F April 6 EXAM 2 REVIEW 33 M April 9 56-58 Filter architecture, filter comparisons, limit cycles 7.1-7.3, 7.7 34 W April 11 59-60 Linear phase FIR filter types 8.2 35 F April 13 61 FIR design by windowing 8.2 HW8 36 M April 16 61 FIR design by windowing 8.2 37 W April 18 62 IIR filter design using bilinear transforms 8.3 38 F April 20 62 IIR filter design using bilinear transforms 8.3 HW9 39 M April 23 63-64 DtFt analysis of sampling and aliasing 9.1-9.2 40 W April 25 65-66 Analog signal reconstruction, decimation and interpolation 10.1-10.3 41 F April 27 67-68 Digital audio applications of multirate DSP 10.9 REVIEW 42 M April 30 REVIEW REVIEW 42 W May 2 REVIEW Final Wednesday, May 9,

Exam 11:00-1:00 p.m.

ECE 429/529 © RNS LESSON: 1 PAGE: 1

WHAT DOES ECE 429/529 COVER?

Discrete-time signals & systems Discrete-time signals A/D & D/A conversion Convolution & correlation z-Transform & Discrete-time Fourier transform Discrete-time systems Frequency response: gain, phase and group delay Digital filter principles: linear-phase filters, minimum-phase filters, notch filters, comb filters Multirate processing: decimation & interpolation

Spectral analysis Digital filter design Discrete Fourier Transform (DFT) Mason’s gain rule DFT properties, frequency resolution Filter architectures Fast convolution & correlation FIR linear phase filters Zero-padding, spectral leakage, Window method of FIR design tapered windows Analog filters basics Interpretation of DFT results IIR design using bilinear transform

50 0 40 -10 30 -20 20 -30

10 dB dB -40

0 -50

-10 -60

-20 -70

-30 -80 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 digital frequency (rads) digital frequency (rads)

Applications/simulations using MATLAB®

ECE 429/529 © RNS LESSON: 1 PAGE: 2

DSP APPLICATIONS -Echo reduction -Signal multiplexing -Data acquisition -Filtering -Spectral analysis -Digital audio recording and effects -Simulation and modeling -Musical instruments -Oil and mineral prospecting -Image and sound compression for multimedia -Process monitoring & control presentation -Nondestructive testing -Movie special effects -CAD and design tools -Video conference calling -Radar -Diagnostic imaging (CT, MRI, ultrasound, and -Sonar others) -Ordnance guidance -Electrocardiogram analysis -Secure communication -Medical image storage/retrieval -Sound cards -Space photograph enhancement -Fax machines -Data compression e.g. JPEG, MPEG -Modems -Intelligent sensory analysis by remote space probes -Cellular phones -High-capacity hard disks -Digital TVs -Voice and data compression

Example

Listen to synthesized speech at www.ece.arizona.edu/~429rns/audiofiles/audiofiles.html

Speech synthesis

ECE 429/529 © RNS LESSON: 1 PAGE: 3

HOW IS DSP DONE?

Example…

Audio i/p Headphone o/p

Laptop PC High level PC SOUND CARD software

e.g. MATLAB

C-code

Cross- compiler

ECE 429/529 © RNS

LESSON: 1 PAGE: 4

Describe the distinctions between analog, continuous-time, discrete-time and digital signals, and describe the basic operations involved in analog-digital (A/D) and digital- analog (D/A) conversion.

LESSON: 1 PAGE: 5

TYPICAL DSP SYSTEM

x(nT) x(n) y(n) y(t) x(t) ZERO AAF SAMPLER DSP ARF Q CODER ORDER HOLD

ANALOG MIXED DIGITAL MIXED ANALOG

AAF: anti-aliasing filter (analog), removes frequencies > Fs/2 SAMPLER: effectively converts continuous-time t to discrete-time nT Q: B bits/sample quantizer, with 2B levels CODER: produces byte stream DSP: digital signal processing algorithms ZOH: converts discrete samples to analog staircase waveform ARF: analog reconstruction (lowpass) filter, converts staircase to smooth waveform

SIMPLIFIED DSP (DISCRETE-TIME) SYSTEM

x(n) y(n) x(t) y(t) C/D DSP D/C

T T (sampling interval)

T sampling interval (s)

Fs = 1/T sampling frequency or sampling rate (Hz or samples/s)