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數位訊號處理Digital Signal Processing

吳炳飛 特聘教授

IEEE Fellow

國立交通大學 電機工程學系

2016 秋

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吳炳飛工五館 773 室，電話： x 31538

Office Hour: Tue. 6:30 p.m.-8:30 p.m. bwu@mail.nctu.edu.tw & http://cssplab.cn.nctu.edu.tw

教科書Oppenheim and Schafer, Discrete-Time Signal Processing,

3/e, Pearson: NJ, 2010.

助教 :Office Hours : Tue. 7:00-9:00 p.m.

朱允維：EE917 室 yunwei@cssp.cn.nctu.edu.tw, x 54428

先修課程：線性代數，訊號與系統評分作 業 ：20 % 兩次零分，此部分以零分計。期中考：40 %

期末考：40 %

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Important Date (Tentatively)

Homework due one week later

Midterm Exam. ：Nov. 7, 2016

Final Exam. ：Jan. 9, 2017

Raw Grade Post ：Jan. 16, 2017

Final Grade Post ：Jan. 17, 2017

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Contents

Part I: Review of Signals and Systems ( Chapter 2-3 )

1. DSP Systems and Applications

2. Introduction to Discrete-Time Signals and Processing

3. The Z-transform

Part II: Transform Methods for DSP ( Chapter 4-5,8-9 )

1. Sampling Theory

2. Examples of Digital Filters

3. The Discrete Fourier Transform ( DFT )

4. Fast Fourier Transform

Part III: Digital Filter Design ( Text Chapter 6-7 )

1. Type of Filters --- FIR and IIR

2. Filter Design Techniques

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Chapter 1

Introduction

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Introduction

Signals Speech( e.g. sampling frequency 8KHz:64Kbps 2.4Kbps),

Biomedical signals, Audio( e.g., MP3, sampling frequency 44.1KHz) and Sound, Video and Image, Radar signals…

Digital Signal Processing Sample an analog signals → Signals in digital form.

Process by digital processor.

Objectives Remove interference or noise from a signal.

Obtain the spectrum of data.

Transform the signal to a suitable form. (e.g. Fourier Transform, Wavelet Transform, Discrete Cosine Transform …)

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Introduction

Advantages Guaranteed Accuracy: depend on number of bits need.

Perfect Reproducibility: e.g. digital recording.

Advantages is always taken of the advances in semiconductor

technology.

Flexibility: reprogrammable.

Disadvantages Speed & cost: fast ADC/DAC are expensive. Bandwidth of 100

MHz increased are processed by analog signal method.

Design time: DSP hardware increasingly complicated.

Finite length effects: limited-bit number of DSP processor.

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DSP Applications

Image/Video Processing Pattern recognition, robot vision, facsimile, animation, data

compression…

Controls Spectrum analysis, position and velocity control of motors, noise

reduction…

Speech/Audio Speech recognition, speech/audio synthesis, text to speech, digital

audio, quantization…

Tele-communications Echo cancellation, adaptive equalization, video conference…

Vehicle Electronics Telematics, Navigation, Car Safety…

Biomedical signal processing Patient monitoring, EEG , EKG analysis, Biomedical image

processing…

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DSP Applications

Key DSP operations

Convolution

Correlation

Filtering

Discrete Transforms

DTFT、DFT 、 FFT 、 DCT 、 DWT 、 Z-Transform

Modulation

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Overview of Real-Time Signal Processing

Input

FilterS/H & ADC

Digital

ProcessorDAC

Output

Filter

Analog

MultiplexerDemultiplexer

x(t) y(t)x(n) y(n)

S/H : sample

& hold(Pre-filter)

maxf sf

e.g.

TI TMS320C5x

Low-Pass filter S/H : sample

& holdn bits ADC

sf

Logic

Circuit

encoder

( ADC )

x(t) x(n)

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Sampling Frequency

fs : Sampling frequency

fmax: Max frequency of the input signal

Sampling theorem:

∴Sampling rate ≧ Nyquist frequency

No distortion (ideally) e.g. Audio signal B.W.: 22KHz CD: 44.1KHz

Speech signal B.W.: 4KHz 8K↑ or 20KHz (recommended)

max2 ff s

max2 ff s

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Sampling Frequency

x(t)

p(t)

x(t)p(t) = x`(t)

Band-limited signals

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Aliasing

Anti-Aliasing Filter

Remove the undesired input signal or noise.

Aliasing22 max ffffff csccs

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For B-bit ADC:

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quantization noise error

SNR[Signal-to-Noise-ratio] 20log[ 1.5 2 ] in dBB

B

CD quality

B Amin (dB)

8 56

10 68

12 80

16 104CD quality

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Example

Ex. Determine fs to give an aliasing error of less

than 2% of the signal level in the passband.

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Solution:

12 2

2

1

1 12| ( ) |

1 1 21 (2 )

2

1 1 where 2

21 ( )

C

C

j fCH f

j fRCR fRC

j fC

f KHzRCf

f

Assume the analog input has a

wideband spectrum (assured

aliasing).

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2

1Passband @ 2 KHz 0.7071

2

2desired aliasing level 0.7071 0.01414

100

10.01414

1 ( )2

141.4 KHz

2 141.4 143.4 KHz

,say, 150 KHz

b

a

a

s C a

s

X

f

f

f f f

f

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Quantization & Encoding

For example ADC 0804. 0~5V, 8 bits Quantization error

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LSB= . 2

1 1 5Range of quantization error

2 2 2 2

fs

B

Vfs

B

V

VLSB

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2

10 2 2

2

Signal-to-Noise Ratio (SNR)

signal power 2 2SNR 10log 10log where

12 2

10log(1.5 2 ) 6.02 1.76dB

ADC bits 6 dB / bit signal quality

B

e

B

A A

B

/ 2 2/ 2

2 2 3

/ 2/ 2

( ) ( )

1 1( )

3 12e

e x t x n

e p e de e

Uniformly distributed

2For a sin wave sin average signal power / 2.A t A

ADCx(t) x(n)

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DAC: signal recover

DSP DAC LPFy(n) y(t)( )y t