Post on 15-Feb-2018
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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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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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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)