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Advanced Digital Signal Processing ????????

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Title: Advanced Digital Signal Processing Author: DJJ Last modified by: MD531 Created Date: 2/24/2010 5:03:40 AM Document presentation format – PowerPoint PPT presentation

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Title: Advanced Digital Signal Processing ????????


1
Advanced Digital Signal Processing ????????
  • ??? ? ? ?
  • Office???723?, TEL 33669652
  • E-mail djj1_at_ms63.hinet.net ,
    djj_at_cc.ee.ntu.edu.tw
  • ????http//djj.ee.ntu.edu.tw/ADSP.htm
  • ???????,???????????!

2
? ???? Basic 15 scores ???????????? 12
???, ??,??????,??????1? Homework 60 scores (5
times, ? 3 ???) ????,??????? ,?? 70
??? ??????????? 4095 ???, ????? 8 ?,??????
??????,?? E-mail ????,??????? ?? Ctrl-C Ctrl-V
???? Term paper 25 scores
3
Term paper 25 scores ????? (1) ????
10???(????),?????,11?12???,?????????????????? ???
???????????????,?? abstract, conclusion, ?
references,???? sections,????subsections?
References ???, ????? IEEE ?????? ?????????,??????
?? Ctrl-C Ctrl-V ???,??? 70 ??? (2) Tutorial
??????,?????????,? ?????18???(???????
tutorial,???? (2/3)N 13 ??,N ??? tutorial
???),???????,?????????????????????????,???????????
???,? Word ?? ?????????,????? 2.5?
4
(3) ???? ????,??? 3045??,?????????????????? ????
?? 5?10?(? 11 ?)?????????,?????,???????????
PowerPoint ?? ?????,??????(?????????,?????????????
??)????????,?????? 0.5 ?? ?????????,????? 2? (4)
?? Wikipedia ?????????,?? 2 ???,?????????????????
? 80???????????,????,??????????? ???? Wikipedia
???,?? 6?24??,??????????????(2 ???),??????????????
??,??????????????????? ??????? Wikipedia,???
6?28?
5
Tutorial ???????(? 18 ?,??????)
(1) Adaptive Wiener Filter (2) Bilateral
Filter (3) Tone Analysis (4) Image Deblurring (5)
Sharpness Measurement for Images (6) Image
Compression Based on Structural Similarity
(SSIM) (7) Medical Image Compression (8) JBIG and
Binary Image Compression (9) Arithmetic
Coding (10) Structure Similarity (??) (11) Jacket
Transform (12) Integer Transform (??) (?)
6
Tutorial ???????(??????)
(13) Fermat and Mersenne Numbers (14) Non-Linear
Time Variant System Analysis (??) (15) Support
Vector Machine (16) 3-D Accelerometer Signal
Analysis (17) Nonuniform Sampling (18)
Eletromyography (EMG ) Signal Analysis
7
????16 ?
2/22, 3/1, 3/8, 3/15, ? HW1 3/22, 3/29, ?
HW1 4/12, ? HW2 4/19,
4/26, ? HW2 5/3, ? HW3 5/10, Oral 5/17, ?
HW3 5/24, ? HW4 5/31, 6/7, ? HW4 6/14, ? HW5
6/28, ? HW5 ? term paper
??? 3n1 ????, 3n3 ???
8
Matlab
Download ??????? http//comm.ntu.edu.tw/matlab/re
quest.php ???? ???,Matlab ???????,???,??,2011.
???,Matlab 7 ????,??,???,2010. ???,????????
Matlab,??,???,2007. ????,????????-Matlab,??,2005.
?????????? 35 ?
9
?????????????????????
10
Question
Why should we use the Fourier transform?
11
I. Introduction
Contents
(1) Introduction 1 W (2) Digital Filter
Design (A) 2 W (3) Digital Filter
Design (B) 2 W (4) Homomorphic Signal
Processing 1 W (5) Applications (A)
Acoustics 1 W (6) Applications (B)
Data Compression, Others 2
W (7) Fast Algorithms Basis,
FFT and Convolution 3 W (8) Orthogonal Transform
(A) Walsh Transform 1 W (9) Orthogonal
Transform (B) Number Theoretic Transform 1
W (10) Orthogonal Transform (C) OFDM, CDMA ,
and Others 1 W
12
?? (1) ? Digital Signal Processing
??????????? (2) ?? Digital Signal Processing
????????????
13
13
Part 1 Filter
? Filter ???
IIR
digital
(??aliasing)
MSE (mean square error)
filter
FIR
minimax
frequency sampling
analog
(??????)
14
14
IIR filter ???(1) easy to design
(2) (sometimes) easy to implement
??
FIR filter ???
??
An FIR filter is impossible to have the ideal
frequency response of
15
15
Part 2 Homomorphic Signal Processing
? ??? convolution ?? addition
Part 3 Applications of DSP
filter design, data compression (image, video,
text), acoustics (speech, music), image analysis
(structural similarity, sharpness), 3D
accelerometer
16
16
? Part 4 Fast Algorithms
? Basic Implementation Techniques
Example one complex number multiplication
? Real number multiplication.
Trade-off Multiplication takes longer than
addition
17
17
? FFT and Convolution
Due to the Cooley-Tukey algorithm (butterflies),
the complexity of the FFT is
The complexity of the convolution is 3? DFTs,

18
18
? Part 5 Orthogonal Transforms
DFT ???????
Question DFT ???????
? Walsh Transform
? Number Theoretic Transform
  • Orthogonal Frequency-Division Multiplexing
    (OFDM)
  • Code Division Multiple Access (CDMA)

19
19
Review 1 Four Types of the Fourier Transform
(1) Fourier Transform
, Alternative
definitions
,

(2) Fourier series
T ??
??? m ?????
20
20
(3) Discrete-time Fourier transform (DSP ??)

,

?t sampling interval (4)
Discrete Fourier transform (DFT) (DSP ??)
,

??? m ?????
where fs 1/?t (sampling frequency)
21
21
? ?? Fourier transforms ???
time domain
frequency domain
(1) Fourier transform
continuous, aperiodic
continuous, aperiodic
(2) Fourier series
continuous, periodic (or continuous, only the
value in a finite duration is known)
discrete, aperiodic
(3) discrete-time Fourier transform
discrete , aperiodic
continuous, periodic
discrete, periodic (or discrete, only the value
in a finite duration is known)
(4) discrete Fourier transform
discrete, periodic
22
22
Review 2 Normalized Frequency
(1) Definition of normalized frequency F
where fs 1/?t (sampling frequency)
?t sampling interval
(2) folding frequency f0
?? normalized frequency ???, folding frequency
1/2
23
23
For the discrete time Fourier transform
(1) G(f) G(f fs) i.e.,
G(F) G(F 1).
(2) If gn is real G(F)
G(?F) ( means conjugation)
???? G(F) for 0 ? F ? ½ (? 0 lt f lt f0) ????????
G(F)
(3) If gn g?n (even)
G(F) G(?F), gn ?g?n (odd)
G(F) ?G(?F)
Analog filter H(f)
24
24
? Discrete time Fourier transform of the lowpass,
highpass, and band pass filters
high pass filter
?fs (F ?1) F ?0.5
0 (F 0) F 0.5 fs
(F 1)
band pass filter
?fs (F ?1) F ?0.5
0 (F 0) F 0.5 fs
(F 1)
25
25
Review 3 Z Transform and Laplace Transform
? Z-Transform
suitable for discrete signals
Compared with the discrete time Fourier
transform
26
26
? Laplace Transform
suitable for continuous signals
One-sided form
Two-sided form
Compared with the Fourier transform
27
27
Review 4 IIR Filter Design
Two types of digital filter (1) IIR filter
(infinite impulse response filter) (2) FIR
filer (finite impulse response filer) There
are 3 popular methods to design the IIR filter.
28
28
Method 1 Impulse Invariance
????,????? sampling
analog filter ha(t)
digital filter hn
Advantage Simple
Disadvantage
29
29
Method 2 Step Invariance
? step function ? response ? sampling
analog filter ha(t)
digital filter hn
step function (continuous form)
Laplace transform of u(t)
1
u(t)
Fourier transform of u(t)
0
t 0
step function (discrete form)
1
1
1
1
1
un
Z transform of un
0
0
0
0
n0
30
30
Step 1 Calculate the convolution of ha(t) and
u(t)
(????? ha(t) ???)
Step 2 Perform sampling for ha,u(t)
Step 3 Calculate hn from
Note Since
so
31
31
Advantage of the step invariance method
Disadvantage of the step invariance method
????,???????
32
32
Method 3 Bilinear Transform
Suppose that we have known an analog filter ha(t)
whose frequency response is Ha(f). To design the
digital filter hn with the frequency response
H(f),
fold ? (??, ?) fnew ? (?fs/2, fs/2)
fs 1/?t (sampling frequency)
? The relation between fnew and fold is
determined by the mapping function
s index of the Laplace transform z index of
the Z transform c some constant
33
33
??
? Suppose that the Laplace transform of the
analog filter ha(t) is Ha,L(s)
The Z transform of the digital filter hn is
Hz(z)
34
34
fold -? 0 ? 1
fnew
fnew/fs
c 2?
fold
35
35
analog filter
Ha(f)
-?
?
0
fc
-fc
digital filter H(f)
-fs/2
fs/2
0
fc,1
-fc,1
Advantage of the bilinear transform
Disadvantage of the bilinear transform
36
36
??? ?? DSP ???????
(1) Concepts ?????????????????
(2) Comparison ??????????,?????????
????????
(3) Advantages ?????????
(3-1) Why? ????????????
(4) Disadvantages ?????????
(4-1) Why? ????????????
(5) Applications ?????????????,?????
(6) Innovations ?????????????
???????????
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