Lec1 Introduction

Digital Signal & FilteringFilter Design, Applications in Adaptive Filter Design, Applications in Adaptive

Filtering & Communications

Pham Van TuanElectronic & Telecommunication EngineeringDanang University of Technology

Course Administration

Courses sequence: EE235, EE233, EE341 The prerequisite of this course

Discrete time signals Linear time invariant (LTI) systems Fourier transform (continuous/discrete time) Fourier transform (continuous/discrete time) Laplace transform and Z transform

Credits: 3 Grading policies:

IIR: 50% (Final); FIR: 30% (Midterm); Writing exam: 20% (HW)

Goals

To provide students fundamental knowledge of Digital filter characteristics Design principles & design specifications Applications to communications Applications to adaptive filtering

Textbooks: Textbooks: V.K. Ingle, J.G. Proakis, “Digital Processing Using

Matlab”, 2nd Ed., Thomson Learning, 2007 References:

S. S. Haykin, “Adaptive Filter Theory”, 4th Ed., Prentice Hall, 2002. PP. Vaidyanathan, Multirate System and Filter Banks, Prentice Hall, 2004 Nguyễn Quốc Trung, “Xử lý số tín hiệu”, Tập 1,2. Matlab Software 2007 and later versions EE 442, Digital Signals & Filtering, EE Dept., University of Washington

Schedules

Reviews: Discrete-Time Signals, DTFT: 1 week (chapter 2,3) Z Transform, DFT, FFT: 1 week (chapter 4,5)

Digital Filter Structures: 1 week (chapter 6)Finite Impulse Response (FIR) Filter Design: 2 weeks Finite Impulse Response (FIR) Filter Design: 2 weeks (chapter 7)

Infinite Impulse Response (IIR) Filter Design: 2 weeks (chapter 8)

Applications in Adaptive Filtering : 1 week (chapter 9) Applications in Communications: 1 week (chapter 10) Projects (midterm & final) will be announced on-site

Lecture 1Fundamentals of Digital Signals

and Digital Filteringand Digital Filtering(chapter 1)

Why Need Signal Processing ?

Signal processing is an operation designed for extracting, enhancing, storing and transmitting expected (useful) information.

Which are expected (useful) and unwanted (noisy) information ? Very much depend on subjective and objective of application. objective of application. Teamwork and give examples

How to process signals? In practice, mostly deal with analog signals. They are processed by analog devices (active and passive elements ?): Analog Signal Processing

Draw scheme ?

What Is DSP ?

Equivalent analog signal processor

Process signals based on digital hardware containing: adders, multipliers, logic elements

Can be general-purpose computer or specific-purpose microp. or digital hardware

PrF ADC DSP DAC PoFAnalog Analog

Equivalent analog signal processor

PrF: Pre-filter or antialiasing Filter ADC/DAC: Analog-to-digital and Digital-to-Analog

converters PoF: Post-filter to smooth out staircase waveform

Why DSP ?

It seems that ASP is simpler looking than DSP. Advantages of DSP over ASP:

Relatively develop, test on general purpose computer Extremely stable processing capability Easily and flexibly be modified in real time Easily and flexibly be modified in real time Normally with higher precision Can be cost-effective (DSPs, VLSI, FPGA, ASIC)

Disadvantages ?

Lecture #1:Lecture #1: A big picture about A big picture about Digital Signal Processing Digital Signal Processing

Duration: 1 hr

Outline:

1. Signals1. Signals

2. Digital Signal Processing (DSP)

3. Why DSP?

Learning Digital Signal Processing is not something you accomplish; it’s a journey you take.

R.G. Lyons, Understanding Digital Signal Processing

* * * * * * *

Given a continuous-time (CT) signal x(t), we can sample it to generate the discrete-time (DT) signal x(n)

period sampling theis T where),()( ∆∆= Tnxnx

Signals ?

1-D signals: speech, audio, biosensor, ECG, etc. 2-D signals: image (optical, X-ray, MRI), remote sensing

data, etc. 2.5-D signals: video, ultrasound images (2-D + time) 3-D signals: graphics and animation Multi-D signals: multi-spectral data, sonar array etc.

period sampling theis T where),()( ∆∆= Tnxnx

11--D signalsD signals

ECG

EEG

Color imageSpeech signal

22--D image signalsD image signals

Binary image??? Color imageGrey image

(indexed image)

ICAECA

PlaqueImaging

2-D images (MRI)

CCA Bifurcation ICA

Plaque

CCA

Imaging location

2.52.5--D video signalsD video signals

33--D animated signalsD animated signals

Information Technologies Are Driving Fast

Image Sensors: Digital Still Camera (DSC), PC Camera (CCD and CMOS), Digital Camcorder, portable scanners, etc.

Powerful Computers: faster and multi-core CPU, low power embedded CPU, USB2 ports, CD/DVD RW, power embedded CPU, USB2 ports, CD/DVD RW, flash memory & mini disk, etc.

Data Compression: audio/image/video coding (data compression) standards. HDTV and digital radio.

2D/3D graphics/video cards: faster display and better quality.

Communication: Internet, ATM, ADSL, wireless LAN, WiMAX, WDM in optics, transceiver/modem, etc.

Two Main Categories of DSP

APPLICATIONSSpectrum analysisFeature extraction

APPLICATIONSNoise removal

Interference separationSignal compression

Analyze

ProcessedMeasures

Feature extractionSignal detectionSignal estimationSignal verificationSignal recognitionSignal modeling

Signal codingSignal synthesis

Spectrum shaping

Filter

Rad

ar

BiomedicalBiomedical

Analysis of biomedical signals, diagnosis, patient monitoring, preventive health care

Image processingImage processing

Image enhancement: processing an image to be more suitable than the original image for a specific application

It makes all the difference whether one sees darkness through It makes all the difference whether one sees darkness through It makes all the difference whether one sees darkness through It makes all the difference whether one sees darkness through

the light or brightness through the shadowsthe light or brightness through the shadowsthe light or brightness through the shadowsthe light or brightness through the shadows

David LindsayDavid LindsayDavid LindsayDavid Lindsay

Image processingImage processing

Image compression: reducing the redundancy in the image data

UW Campus (bmp) 180 kb UW Campus (jpg) 13 kb

MusicMusic

Recording, encoding, storing

Playback

Manipulation/mixing

CommunicationCommunication

Digital telephony: transmission of information in digital form via telephone lines, modern technology, mobile phone

Speech compressionSpeech compression

Speech Speech recognitionrecognition

Fingerprint recognitionFingerprint recognition

Image Image restorationrestoration

Image restoration: reconstruct a degraded image using a priori knowledge of the degradation phenomenon

Noise removalNoise removal


Duration: 1 hr

Outline:

1. Signals


3. Why DSP?

What is Digital Signal Processing?What is Digital Signal Processing?

Represent a signal by a sequence of numbers (called a "discrete-time signal ” or "digital signal").

Modify this sequence of numbers by a computing processto change or extract information from the original signal

The "computing process" is a system that converts one digital signal into another— it is a "discrete-time system” or "digital system“.

Transforms are tools using in computing process

DiscreteDiscrete --time signal vs. time signal vs. continuouscontinuous --time signaltime signal

Continuous-time signal:- define for a continuous duration of time- sound, voice…

Discrete-time signal:- define only for discrete points in time (hourly, every second, …) - an image in computer, a MP3 music file- amplitude could be discrete or continuous- if the amplitude is also discrete, the signal is digital.

CT signal vs. DT signalCT signal vs. DT signal

CT signal DT signal

00 10 00 10 11

Signal processing systemsSignal processing systems

ProcessingAnalog signal

x(t)Analog signal

y(t)

Analog signal processing

ProcessingA/D D/A

Analog signal x(t)

Analog signal y(t)

Digital signal processing

Digital signal processing Digital signal processing implementationimplementation

Performed by:

Special-purpose (custom) chips: application-specific integrated circuits (ASIC)circuits (ASIC)

Field-programmable gate arrays (FPGA)

General-purpose microprocessors or microcontrollers (µP/µC)

General-purpose digital signal processors (DSP processors )

DSP processors with application-specific hardware (HW) accelerators



Use basic operations of addition, multiplication and delay

Combine these operations to accomplish processing: a discrete-time input signal another discrete-time output signal

An example of main step: An example of main step: “DT signal processing”“DT signal processing”

From a discrete-time input signal:

1 2 4 -9 5 3

Create a discrete-time output signal: Create a discrete-time output signal:

1/3 1 7/3 -1 0 -1/3 8/3 1

What is the relation between input and output signal?


Duration: 1 hr

Outline:

1. Signals


3. Why DSP?

Advantages of Digital Signal Advantages of Digital Signal ProcessingProcessing

Flexible: re-programming ability

More reliable

Smaller, lighter less power Smaller, lighter less power

Easy to use, to develop and test (by using the assistant tools)

Suitable to sophisticated applications

Suitable to remote-control applications

Limitations of Digital Signal Limitations of Digital Signal ProcessingProcessing

A/D and D/A needed aliasing error and quantization errorquantization error

Not suitable to high-frequency signal

Require high technology

Lecture #2:Lecture #2: AnalogAnalog --toto--Digital and Digital and DigitalDigital--toto--Analog conversion Analog conversion

Duration: 2 hr

Outline: Outline:

1. A/D conversion

2. D/A conversion

AD

CA

DC

SamplingSampling

Continuous-time signal discrete-time signal

Analog world

Digital worldSampling

SamplingSampling

Taking samples at intervals and don’t know what happens in between can’t distinguish higher and lower frequencies: aliasing

How to avoid aliasing?

Nyquist sampling theoryNyquist sampling theory

To guarantee that an analog signal can be perfectly recovered from its sample value

Theory: a signal with maximum of frequency of W Hz must be sampled at least 2W times per second to make it possible to reconstruct the original signal from the samplesreconstruct the original signal from the samples

Nyquist sampling rate: minimum sampling frequency

Nyquist frequency: half the sampling rate

Nyquist range: 0 to Nyquist frequency range

To remove all signal elements above the Nyquist frequency antialiasing filter

AntiAnti--aliasing filteraliasing filterm

agni

tude

frequency

Analog signal spectrum

Anti-aliasing filter response

0 W 2W =fs 3W 4W

frequency

0 W 2W =fs 3W 4W

mag

nitu

de

frequency

Filtered analog signal spectrum

Some examples of sampling frequencySome examples of sampling frequency

Speech coding/compression ITU G.711, G.729, G.723.1:

fs = 8 kHz T = 1/8000 s = 125µs

Broadband system ITU-T G.722:

fs = 16 kHz T = 1/16 000 s = 62.5µs

Audio CDs:

fs = 44.1 kHz T = 1/44100 s = 22.676µs

Audio hi-fi, e.g., MPEG-2 (moving picture experts group), AAC (advanced audio coding), MP3 (MPEG layer 3):

fs = 48 kHz T = 1/48 000 s = 20.833µs

Sampling and HoldSampling and Hold

Sampling interval Ts (sampling period): time between samples

Sampling frequency fs (sampling rate): # samples per second

Analog signal Sample-and-hold signal

0 1 2 3 4

QuantizationQuantization

Continuous-amplitude signal discrete-amplitude signal

Quantization step

Quantization errors & codingQuantization errors & coding

Quantized sample N-bit code word

1.5V

0.0V

0.5V

1.0V

1.5V

0.82V

1.1V1.25V

Example of quantization and codingExample of quantization and codingAnalog pressures are recorded, using a pressure transducer, as voltages between 0 and 3V. The

Digital code

000

001

010

Quantization

Level (V)

0.0

0.375

0.75

Range of analog

inputs (V)

0.0-0.1875

0.1875-0.5625

0.5625-0.9375signal must be quantized using a 3-bit digital code. Indicate how the analog voltages will be converted to digital values.

010

011

100

101

110

111

0.75

1.125

1.5

1.875

2.25

2.625

0.5625-0.9375

0.9375-1.3125

1.3125-1.6875

1.6875-2.0625

2.0625-2.4375

2.4375-3.0

Example of quantization and codingExample of quantization and coding

An analog voltage

between -5V and 5V

must be quantized

using 3 bits. Quantize

Digital code

100

101

110

Quantization

Level (V)

-5.0

-3.75

-2.5

Range of analog inputs (V)

-5.0 -4.375

-4.375-3.125

-3.125-1.875each of the following

samples, and record

the quantization error

for each:

-3.4V; 0V; .625V

110

111

000

001

010

011

-2.5

-1.25

0.0

1.25

2.5

3.75

-3.125-1.875

-1.875-0.625

-0.6250.625

0.6251.875

1.8753.125

3.1255.0

Quantization parametersQuantization parameters

Number of bits: N

Full scale analog range: R

Resolution: the gap between levels Q = R/2N

Quantization error = quantized value – actual value

Dynamic range: number of levels, in decibel Dynamic range: number of levels, in decibel

Dynamic range = 20log(R/Q) = 20log(2N) = 6.02N dB

Signal-to-noise ratio SNR = 10log(signal power/noise power)

Or SNR = 10log(signal amplitude/noise amplitude)

Bit rate: the rate at which bits are generated

Bit rate = N.fs

Noise removal by quantizationNoise removal by quantization

Q/2

NoiseError

Q

Quantized signal + noise After re-quantization

NonNon--uniform quantizationuniform quantization

Quantization with variable quantization step Q value is variable

Q value is directly proportional to signal

Non-uniform

Output

proportional to signal amplitude SNR is constant

Most used in speech Input

Uniform

AA--law compression curvelaw compression curve

≤<+

+

≤≤+=

1)t(sA

1,

Aln1

))t(sAln(1

A

1)t(s0,

Aln1

)t(sA

)t(s

1

1

1

1

2

1.0

s2(t)

- 1.0

- 1.0

1.00

A=87.6

A=1

A=5

s1(t)

ITU G.711 standardITU G.711 standardInput range Step size Part 1 Part 2 No. code

wordDecoding output

0-1

...

30-31

2 000 0000...

1111

0...15

1

...

31

32-33

...

62-63

2 001 0000...

1111

16...31

33

...

63

64-67

...

124-127

4 010 0000...

1111

32...47

66

...

126

128-135 8 011 0000 48 132128-135

...

248-255

8 011 0000...

1111

48...63

132

...

252

256-271

...

496-511

16 100 0000...

1111

64...79

264

...

504

512-543

...

992-1023

32 101 0000...

1111

80...95

528

...

1008

1024-1087

...

1984-2047

64 110 0000...

1111

96...

111

1056

...

2016

2048-2175

...

3968-4095

128 111 0000...

1111

112...

127

2112

...

4032

ITU G.711 AITU G.711 A--law curvelaw curve

2

17/8

6/8

1.0

Code-word format: Sign bit0/1

Part 1 (3bits)000 111

Part 2 (16bits)0000 1111

1.01/21/41/81/16

1/88

6

7

5

4

35/8

4/8

3/8

2/8

0

Example of G.711 code wordExample of G.711 code word

A quantized-sample’s value is +121

Sign bit: 0

Part 1: 010

Part 2: 1110 Part 2: 1110

Code word: 00101110

Decoding value: +122

A quantized-sample’s value is -121

Code word: 10101110

Lecture #2:Lecture #2: AnalogAnalog --toto--Digital and Digital and DigitalDigital--toto--Analog conversion Analog conversion

Duration: 2 hr

Outline: Outline:

1. A/D conversion

2. D/A conversion

DA

CD

AC

AntiAnti--imaging filterimaging filter

ImagesAnti-imaging filter

mag

nitu

de

0 W 2W =fs 4W = 2fsfrequency

Original two-sided analog signal spectrum

Prob.1. An analog signal is converted to digital and then back to analog signal again, without intermediate DSP.

HWHW

In what ways will the analog signal at the output differ from the one at the input?

Prob.2. An analog signal is sampled at its Nyquist rate 1/Ts, and quantized using L quantization levels. The derived signal is then transmitted on some channels.

HWHW

(a) Show that the time duration, T, of one bit of the transmitted binary encoded signal must satisfy

(b) When is the equality sign valid?

)L/(logTT 2s≤

Prob.3. A set of analog samples, listed in table 1, is digitized using

HWHW

Digital code

000

Quantization

Level (V)

0.0

Range of analog inputs (V)

0.0 0.3125

n 0 1 2 3 4 5 6 7 8

Sample(V) 0.5715 4.9575 0.6250 3.6125 4.0500 0.9555 2.8755 1.5625 2.7500

is digitized using the quantization table 2. Determine the digital codes, the quantized level, and the quantization error for each sample.

000

001

010

011

100

101

110

111

0.0

0.625

1.250

1.875

2.500

3.125

3.750

4.375

0.0 0.3125

0.31250.9375

0.93751.5625

1.56252.1875

2.18752.8125

2.81253.4375

3.43754.0625

4.06255.0

Prob.4. Consider that you desire an A/D conversion system, such that the quantization distortion does not exceed ±±±±2% of the full scale range of analog signal.

(a) If the analog signal’s maximum frequency is 4000 Hz, and

HWHW

(a) If the analog signal’s maximum frequency is 4000 Hz, and sampling takes place at the Nyquist rate, what value of sampling frequency is required?

(b) How many quantization levels of the analog signal are needed?

(c) How many bits per sample are needed for the number of levels found in part (b)?

(d) What is the data rate in bits/s?

Prob.5. An analog voice signal with voltage between -5V and 5V must be quantized using ITU G.711 standard. Encode each of the following samples; and

HWHW

standard. Encode each of the following samples; and record the quantization error for each:

(a) -3.45198 V

(b) 1.01119 V

Prob.6. A 3-bit D/A converter produces a 0 V output for the code 000 and a 5 V output for the code 111, with other codes distributed evenly between 0 and 5 V.

HWHW

other codes distributed evenly between 0 and 5 V.

Draw the zero order hold output from the converter for the input below:

111 101 011 101 000 001 011 010 100 110

Lecture #2Lecture #2The concept of frequency in The concept of frequency in CT & DT signalsCT & DT signals

Duration: 2 hrs

Outline: Outline:

1. CT sinusoidal signals

2. DT sinusoidal signals

3. Relations among frequency variables

Functions:

+∞<<∞−θ+π=+∞<<∞−θ+ω=

t),tf2cos(A

t),tcos(A)t(x a

Mathematical description of CT Mathematical description of CT sinusoidal signalssinusoidal signals

Plot:

+∞<<∞−θ+π= t),tf2cos(A

t

xa(t)

AcosθTp = 1/f

Properties of CT sinusoidal signalsProperties of CT sinusoidal signals

1. For every fixed value of the frequency f, xa(t) is periodic: xa(t+Tp) = xa(t)

Tp = 1/f: fundamental period Tp = 1/f: fundamental period

2. CT sinusoidal signals with different frequencies are themselves different

3. Increasing the frequency f results in an increase in the rate of oscillation of the signal (more periods in a given time interval)

Properties of CT sinusoidal Properties of CT sinusoidal signals (cont)signals (cont)

For f = 0 Tp = ∞

For f = ∞ Tp = 0

Physical frequency: positive Physical frequency: positive

Mathematical frequency: positive and negative

The frequency range for CT signal:

-∞ < f < +∞

)()(

22)cos()( θθθ +Ω−+Ω +=+Ω= tjtj

a eA

eA

tAtx

Functions:

+∞<<∞−θ+π=+∞<<∞−θ+Ω=

n),nF2cos(A

n),ncos(A)n(x

Mathematical description of DT Mathematical description of DT sinusoidal signalssinusoidal signals

Plot:

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0-2

-1 . 5

-1

-0 . 5

0

0 .5

1

1 .5

2

T im e in d e x n

Am

plitu

de

x(n N) x(n) n+ = ∀

Properties of DT sinusoidal signalsProperties of DT sinusoidal signals

1. A DT sinusoidal signal x(n) is periodic only if its frequency F is a rational number

x(n N) x(n) n+ = ∀

n)nF2cos(A)])Nn(F2cos[A 00 ∀θ+π=θ++π

k2NF2 0 π=π

N

kF0 =

2. DT sinusoidal signals whose frequencies are separated by an integer multiple of are identicalπ2

)ncos()n2ncos(]n)2cos[()n(x θ+Ω=θ+π+Ω=θ+π+Ω=


All

are identical

)ncos()n2ncos(]n)2cos[()n(x 000 θ+Ω=θ+π+Ω=θ+π+Ω=

πππθ

+≤Ω≤−+Ω=Ω=+Ω=

00 ,2

...,2,1,0),cos()(

k

knAnx

k

kk

3. The highest rate of oscillation in a DT sinusoidal signal is obtained when:


or, equivalently,

)or( π−=Ωπ=Ω

)2

1For(

2

1F −==

0 5 10 15 20 25 30-1

-0.5

0

0.5

1F = 3/24

0 5 10 15 20 25 30-1

-0.5

0

0.5

1F = 3/12

F0 = 1/8 F0 = 1/4

)2cos()( 0 nFnx π=Illustration for Illustration for property 3property 3

0 5 10 15 20 25 30 0 5 10 15 20 25 30

0 5 10 15 20 25 30-1

-0.5

0

0.5

1F = 3/6

0 5 10 15 20 25 30-1

-0.5

0

0.5

1F = 3/4

F0 = 1/2 F0 = 3/4

-π ≤ Ω ≤ π or -1/2 ≤ F ≤ 1/2: fundamental range

CT signal Sampling DT signal

xa(t) x a(nT)

θ+π )nTf2cos(A

Sampling of CT sinusoidal signalsSampling of CT sinusoidal signals

sf

fF =

)tf2cos(A θ+π

θ+π=

θ+π

Sf

nf2cosA

)nTf2cos(A

Normalized frequency

CT signals DT signals

2 FΩ = π2 fω = π

Relations among frequency variablesRelations among frequency variables

+∞<<∞−+∞<ω<∞−

f

2/1F2/1 +≤≤−π+≤Ω≤π−

2/ff2/f

T/T/

ss +≤≤−π+≤ω≤π− sf

fF =

sfT

1=

Exercise Exercise

Consider the analog signal

a) Determine the minimum sampling rate required to avoid aliasing

][,100cos3)( stttx π=

b) Suppose that the signal is sampled at the rate fs = 200 Hz. What is the DT signal obtained after sampling?

c) Suppose that the signal is sampled at the rate fs = 75 Hz. What is the DT signal obtained after sampling?

d) What is the frequency 0 < f < f s/2 of a sinusoidal signal that yields samples identical to those obtained in part (c)?

Prob.7. Consider the analog signal

ax (t) 3cos2000 t+5sin6000 t+10cos12000 t= π π π

HWHW

a) Determine the minimum sampling rate required to avoid aliasing

b) Suppose that the signal is sampled at the rate fs = 5000 samples/sec . What is the DT signal obtained after sampling?

c) What is the analog signal we can reconstruct from the samples if we use ideal interpolation?

Prob.8. Consider the analog signal

a) Sketch the signal for t from 0 to 30 ms

HWHW

][,100sin3)( stttx π=a) Sketch the signal for t from 0 to 30 ms

b) The signal is sampled at the rate fs = 300 samples/s . Determine the frequency of the DT signal x(n) and show that it is periodic.

c) Compute the sample values in one period of x(n). Sketch x(n) on the same diagram with x(t). What is the periodic of x(n) in ms?

d) Can you find a sampling rate so that x(n) reaches its peak value?

Date post:	02-May-2017
Category:	Documents
Upload:	tran-ngoc-lam
View:	220 times
Download:	2 times

Lec1 Introduction

Documents