???????????????????????? Advanced Digital Signal Processing Chapter 1 Introduction to ADSP

1
????????????????????????Advanced Digital Signal
ProcessingChapter 1 Introduction to ADSP

• Asst. Prof. Dr. Peerapol Yuvapoositanon, PhD,DIC
• Department of Electronic Engineering
• and
• Graduate School of Electrical Engineering
• Mahanakorn University of Technology

2
Course Web page

• http//embedsigproc.wordpress.com/eeet0772/

3
What is DSP ?

• ?????? (Signals) ??? ???????????????????????????
  ??????????????????? ??????????????????
  ???????????????????????? ?????????????????????
• ???????????? ???????? ????????? ???????????
  ????????? ??????????????????? ???????????
  ????????????????? ????????? ????????? ??? ?????
  ?????????...

4
Digital Signal Processing v.s. Advanced Digital
Signal Processing

• Digital Signal Processing ????????? (Process)
  ??????????????????????????? ????????? (signals)
  ????????????????????????? ?? ?? ???? ???? ??????
  ??????????????????????????? (deterministic
  signals)
• Advanced Digital Signal Processing ?????????
  DSP ?????????????????????? (Random Signals)

5
Radar System

• ?????????? ?????????????????????????
  ????????????????????? (delay) ????????????????????
  ?????????????????

?????????????????
???????????????????????????
6
Transmitted and Received Sine Radar Signal

• ??????????? 1 ????????

• ??????????????????????? ????

??????? ???? ????? ?????????????
(???????????????????? ????) ??????????????????????
? ??????????
7
Received Radar with Noise

• ?????????????????????????? ??? ?????? Noise
  ???????
• ??????????????? ????????????????????? (??????)
  ???????????????????????
• ?????????????????????????????????????????????
  (Operation) ????? ??????????????????????????

Noise
8
Correlation

• ????? Correlation ???????? ????????????
  ????????????
• ????????? ?????? Correlation ???
• ???????? ??? ???????????? (???? Integration)

A
A

X
C
C
B
B
9
Detected Radar SignalNo Noise

• ?????? Correlation ???????????????????????????????
  ????????????? ????????? Noise

A
B
10
Detected Radar SignalWith Noise

• ??????????????? Correlation ???
  ????????????????????????????????? delay ?????????
  Noise

C
A
B
11
Mobile Communication

• ??????????????????????
• ?????????????? Channel
• ????? channel ?????????? ?????????? Multipath
  channel

1
2
12
Channel Model

• ?????????????????????????????? FIR

Multipath Channel (FIR)
13
Equalisation of Signal

• ?????????????????????????? ????????????????

Multipath Channel
Equaliser
14
Continuous-Time V.S. Discrete-Time Signals

• ??????

15
Sampled Signal

• ?????????????? sampled output ????????????
  ??????

Input
Sampled Output
16
Other Discrete-time
17
DSP System Block Diagram
DSP Processor
A/D
D/A
18
Sampling

• ????????????? x(t) ?????????????? x(n)
• ?????????? x(n) ?????????

???????????????
...
19
Combination of Sampling

• ?????? x(n) ?????????? s(n) ??? ?????? x(t)
• S(n) ????????? ????????????? ??? ????????

t
n
n
T
20
Elements of the Sampling Signal

• S(n) ??????????????????????

n

s(n)
n


n
T
n

n
T
2T
3T
21
An Impulse is Delta Function

• ???????? ??? ??????????????
  ?????? 1 ????? n0
• ??? ?????? 0 ????? n ????????????
• ?????????

1
????????
n
0
22

• ????????????????????????? s(n) ??????????????????

1
????????????????????????????
n
0
1
?????????????????????????????? 1 ?????
n
1
0
23
Summing of Shifted Delta
n


n



n


n
T
2T
3T
0
n
24
Sampling SignalsSumming of Impulses

• ?????????????????????????????????????
  ?????????????????????????????????????????
• ???? ?????????????????????????????

25
Discrete-time Signal x(n)

• x(n) ???????? ???????? x(t) ??? s(n)

n

X
t
n
26
System with Delta function
???????????????
????
27
Sampled Signal
n


n



n


n
1
2
0
3
28
System with Delayed Delta function
???????????????
????
29
Delayed Signal
n0

n1


n2


n3


1
2
0
3
30
Convolution

• ???????????????? ???????????????????????????
• ?????????????????????????? Convolution ????
  ?????????

????
31
Convolved Signal
n0


n1



n2


n3
1
2
0
3
1
2
0
3
32
Convolution Effect

• ????????????????

????? h(1)
????? h(0)
?????????
???????????????????
33
Nyquist Frequency

• ??????????????????????????????????????? 2
  ????????????????????????
• ????? Fs ??????????? sampling ??? B
  ?????????????????
• 2B ????? ????????????? (Nyquist Rate)
• ??? ????? Fs/2 ??????? ??????????????? (Nyquist
  Frequency)

Fs gt 2B
34
Aliasing

• ???????????????????????????????????????? ???????
• ????? ????????? (moire pattern) ????????????????
  ???????? Image processing

??????????????????
?????????????????????
35
Signal Reconstruction

• ????????????????????????????????? (filter)
  ??????????? copy ?????
• ?????????????????? copy ?????????

filtering
f
f
36
Fourier Transform Pair
sinc(t)
Rectangular(f)
FT
f
t
sinc(f)
Rectangular(t)
FT
f
t
37
DFT Discrete Fourier Transform

• ??????????????????????????????????????
  ???????????????????????????????
• Fourier Transform ?????????????????????????? (t)
  ?????????????????? (f)

FT
t
???????
????
38
Time Domain Signal and its Frequency

• ???????????????? time domain

39
DFTs of Various Functions

• ???? DC ????? ????????
• ???? ???????? ????? DC
• ???????????
• ???? sine
• ?????????

40
DFT Fundamental

• ????????? FT ??????????????????????
• DFT ???? FT ??????????--?????????????????????????

x(t)
FT
t
f
x(n)
DFT
n
k
41
DFT Frequency

• ?????????????????

radians
0
f
Fs
Fs/2
Hz
fnorm
0

1
1/2
42
Number of Points in DFT

• ????????? DFT ??????????? ???????????? ????? k
• N ???? ???????? (N-point) ??? DFT

4-point
0
1
2
3
k
????????? DFT ??? x(n)
????????? FT
43
8-point DFT

• ????????????????????????????? 8 ???
  ????????????????????

8-point
k
0
1
2
3
????????? DFT ??? x(n)
????????? FT
44
16-point DFT

• ????????????????????????????? 16 ???
  ???????????????????? ??????????? resolution

16-point
k
15
0
8
????????? DFT ??? x(n)
????????? FT
45
FFT Fast Fourier Transform

• FFT ?????????????????????? DFT ?????????????
  ???????????????????????????????????
• ??????????
• ????????? Matlab ??? Simulink ?????????????????
  ????????????? DFT ?????????? FFT

FFT DFT
46
Fourier Series

• ??????????????????? (Fourier) ???????????????????
  ???????????????????? (periodic) ??? ????
  ??????????????????????????????????????????????????
  ?? ??? Sine ??? Cosine ????????????????????????
• ??????????????????????????????? ??????????????
  (Fourier Series)

47
Fourier Series of Square Wave

• ?????????????? ??????????
• ????????? ?????????????????

?????????
????????????
48
Fourier Series of Sawtooth

• ??????????? ?????????????????????? ??. ????
• ????????????????????????(Sawtooth)

49
Part IIDigital Filters Design
50
Digital Filters

• ?????????????? (Digital Filters) ???
  ??????????????????? ??????? ??????
  ??????????????? ??? ????????
• ???????????????????? Finite Impulse Response
  (FIR) ??? Infinite Impulse Response (IIR)
• ?????????????? ?????????? ????????????? ??????
  ???????????? ??? ????????????
• FIR ???????????? feedback
• IIR ?????? feedback

51
Finite Impulse Response (FIR)

• FIR ???????????? feedback

Delay
52
Infinite Impulse Response (IIR)

• IIR ????????? feedback

Feedback
53
Transfer Function I

• ??????????????? (transfer function) ???
  ??????????????????? ??????? z ???????????
  ??????????????
• ??????? z ????????????????????????

z -Transform
????????? ???????????? k ?????????????? z-k
54
Transfer Function VS Frequency Response
???????????????
??????????????????????????????????? ???????
????? (zero) (o) ??? (pole) (x)
55
Z-Transform

• ??????????

?????????????????????
??????????????????????????
56
Frequency Response from Poles and Zeros

• ???????????????????????? ????????????
  ???????????????????? ??????? ?????????????????????
  ????????? ? ????????????

A
B
???????
57
Example for Frequency Response
???????? ??? .8 ????? 0
??????????
????????????
??????????
B
A
B
A
A
B
B gt A
B A
B lt A
???
?????
????
58
Example for Frequency Response
???????
59
Basic Filter Topology
Lowpass filter (LPF )
Highpass filter (HPF)
Bandpass filter (BPF)
Bandstop filter (BSF)
60
FIR Filter Design
Ideal lowpass
61
FIR Filter Design Parameters
Ideal
???????
???????
??? ???????
62
FIR Design with Window Method

• ????????? FIR ??????????????????????????????????
  ?????????????????????????????
• ??????????? Sinc Function ????????????????????????
  ???????? inf ??? inf ????????????????????? nlt0
  ????

Sinc function
Inverse FT


f
63
Realizable Filter

• ?????????????????????? ??? sinc ??? ????????
  ????????

w(n)
Sinc function
1
x
f
n
0
N-1
h(n)
?????????????????? ???????????????????????
n
0
N-1
64
Different Windows

• ???????????????? ????????????????????????

1
1
1
n
n
n
0
N-1
0
N-1
0
N-1
Rectangular
Hamming
Kaiser
65
Windows Performance
Big sidelobes Narrow transition
Small sidelobes Broad transition
66
Analogue Filter Prototypes

• ??????????????????????????????????????????????????
  
• ????????????????????????
• ????????????????????????????????????????????
  ????????????
• Butterworth, Chebychev, Elliptic

67
IIR Filter Design
0 dB
-3 dB
????????????? ???
Cutoff Frequency
Attenuation Frequency
68
Filter Design and Analysis (FDA) Tool

• ?????? FDA Tool ?? Signal Processing Toolbox ???
  MATLAB ?????????????? digital filter
  ???????????????
• gtgtfdatool

69
FIR Design by FDA Tool

• ???????? ????????? FIR ???????????????????

• ????????????????????????????????
• ????????????
• ?????? (order)

70
FIR Design by FDA Tool
Realize Filter
Realize Filter
71
Frequency Response of Filter
Lowpass




Lowpass


72
Two ways to find Freq. Resp.

• ???????????????????????????????? --- Chirp Signal
• ?????????????????? ??????? --- White Noise

Lowpass
Chirp
Lowpass
f
f
73
White Noise Generator

• ?????????????????????????????????????????? ???
  ??? Random Source

time
frequency
74
Lab 4 Filter Testing

• Chirp Signal input ????????????? IIR

75
Lab 4 Filter Testing
76
Lab 4 Filter Testing

• Impulse response ??????? FIR

77
Lab 4 Filter Testing

• ???????? Random Source ??? Digital Filter

Short-Time FFT
White noise Generator
???????
FFT
?????
78
Lab 4 Filter Testing

• ?????????? ???????????????????????????????????????
  ?????

79
Lab 5 FIR Design by Fdatool

• ?????????????????? FIR ???? fdatool

80
Lab 5 FIR Design by Fdatool
81
Lab 5 FIR Design by Fdatool
82
Lab 5 FIR Design by Fdatool
83
Lab 5 FIR Design by Fdatool
84
Lab 5 FIR Design by Fdatool
85
Lab 5 FIR Design by Fdatool
86
Lab 5 FIR Design by Fdatool

• ??? export ?????????????????????? simulink

87
Lab 5 FIR Design by Fdatool
88
Lab 5 FIR Design by Fdatool

• ???????? sine wave ??? scope ?????

89
Lab 5 FIR Design by Fdatool

• ?????????

90
Lab 5 FIR Design by Fdatool
91
Lab 5 FIR Design by Fdatool
92
Lab 5 FIR Design by Fdatool
10,800 Hz -6 dB (0.5V)
93
Lab 5 FIR Design by Fdatool
15,100 Hz -20 dB (0.1 V)
94
Lab 5 FIR Design by Fdatool
95
Lab 5 FIR Design by Fdatool
96
Lab 5 FIR Design by Fdatool
97
Lab 5 FIR Design by Fdatool
10.8 kHz -6 dB
98
Lab 6 IIR Design by Fdatool

• IIR design ???????????? Butterworth

99
Lab 6 IIR Design by Fdatool

• ?????????????? order ??????

-3 dB _at_Fc
100
Lab 6 IIR Design by Fdatool

101
Lab 6 IIR Design by Fdatool
102
Lab 6 IIR Design by Fdatool
103
Lab 6 IIR Design by Fdatool
104
Lab 6 IIR Design by Fdatool
105
Lab 6 IIR Design by Fdatool

• ??????????????????????????????????????????????????

106
Lab 6 IIR Design by Fdatool

• Lattice

107
Lab 6 IIR Design by Fdatool
108
Lab 6 IIR Design by Fdatool

• ?????????? sos2tf ?? MATLAB

109
Lab 6 IIR Design by Fdatool
110
Lab 6 IIR Design by Fdatool
12 kHz -3 dB
111
Part IIIFundamental of Random Signals
112
Random Signals

• ??????????????????????????????????????????????
• ??????????????????????????????????????????????
  (Random Signal)
• ???????????

??????????? Matlab
113
Statistics Values

• ???????????? ??? spectrum ????????????????????????
  ???? ???
• ?????? ???????? (Statistics)
• ????????? (Mean)
• ??? Correlation

114
Expectation Value

• ?????????????????? (mean) ???? ???????????????????

Ex(n) ?????????? (expected value) ?????????
115
Correlation

• ??? correlation ??????????????????????????????????
  ??????????????? ??????????????????????
• ??????????????????????????????????????????????
• ?????????????????????????????????? ??????????
  (expectation value)
• ??????????? correlation ??? A ??? B ?? ?????????

Cross-correlation
Auto-correlation
E Expectation operator
116
Auto and Cross correlation

• Autocorrelation
• Cross-correlation

A
C
A
A
D
B
117
Random Signal

• ???????? ?????????? (???? ????????) ??????????

118
AutoCorrelation

• ?????????? autocorrelation ??? ??????????

A
A
119
Different Signals

• ??????????????? B ??? ????????? A

120
Different Random Signals

• ???????????

A
A
A
B
A-A
A-B
121
Cross Correlation

• ?????????????????????????????????????
  (????????????) ??? ??????? ???????????? cross
  correlation ??????????

A
B
122
Cross Correlation

• ??????????????????????????? ????? crosscorrelation

A
C
123
Communication Signal

• ????????????????????????? ???? ???????????????????
  ??????????????????????????????? (information)
• ?????????????? (Information Theory) ??? C.E.
  Shannon ???? ?????????????????????????????
  ?????????????????????????????????

1
0
1
0
1
0
1
1
1
0
0
1
????????????? ??????????
124
Cross Correlation ApplicationCode Division
Multiple Access (CDMA)

• ??????????????

DATA
1
1
0
.
0
1
0
1
1
1
Modulation
X
Code
Chip
1
.
1
0
1
0
1
0
1
1
1
0
1
1
Bit 1
Bit 2
125
CDMA Receiver
Bit 2
Chip
Bit 1
1
.
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
X
Correlation
Code
Integration
1
1
0
126
Simulink Model of CDMA

• Note ???????????? ?????? 1 ??? -1 ????????? 1
  ??? 0 ????????

127
Decoding
?????? mod
?????? Demod
Code ???????
?????? mod
?????? Demod
Code ??????????
128
Adaptive Signal Processing

• ????????????????????????????????? ??????????
  ???????? ?????? ??????????????????????????????
  (adaptive signal processing)
• ?????????????? ????????????????????????? ????
• ????? channel ???????? Equalisation
• ????? room ??????????? Echo Cancellation
• ????? transfer function ?????????????????? ecg

129
Channel Equalisation
Multipath Channel
????? multipath
I)
1
0
1
0
1
?? multipath
II)
1
2
0
1
?
?
130
Transfer Function

• ?????????????? channel ???????????????? z
• ????????? multipath H(z) 1
• Multipath ?????????????????????????????????
• ?????????????????????? Multipath ???????????????

H(z)1
????? multipath
1
z
f
t
?? multipath
1
H(z)?
z
2
f
t
131
Basic Equalisation I

• ?????? Equaliser ???????????? channel ???
• ????? H(z) ???? 1 ????????? inverse

Channel
Equaliser
H(z)
1/H(z)

132
Basic Equalisation II

• ??????? ??????? channel H(z) ???????????????????
  ????????? error

d

y
x
Channel
e
Adaptive Equaliser
-

H(z)
1/H(z)

133
Adaptive Algorithm

• ?????????? error d-y

??????? ??????? ???? ????????????????
???????? Least-Mean Square (LMS) algorithm
134
LMS Algorithm Block

• ????? LMS

Normalization
135
Adaptive Equalisation

• ??????????????????? LMS ????????? Adaptive
  Equaliser

136
Noise Cancellation

• ???????????????????????????????????
• ????????????????????????? ??????? ?????????????

137
Basic of Noise Cancellation

• ?????????????????????????????????????????
• Active Noise Canceller ???????????????????????????
  ????? DSP

n
???????????
-n
Loudspeaker
n
Pilot Mic
???????????
Feedback ANC
138
Active Noise Cancellation Headphones

• ????????? ANC ?????????? ??? ?? Headphones

LX-18 Active Noise Cancelling Headphones
139
Diagram of Active Noise Cancellation Headphones
Quiet Zone
Pilot Mic
n
1
n
2
1. ?????????? n ??? Ext.Mic 2. n ?????????????? n
??? H(z) ??? Pilot Mic. 3. ANC ??????????? y ????
n ?????????? (??? n)
H(z)
3
Ext.Mic
y
H(z) ???????????? Acoustic
140
ANC
n

• ?????????

Loudspeaker
Pilot Mic
Exterior Mic
FIR
n
y

e
Algorithm
ANC
141
ANC Simulink Model

• Dspanc_win32.mdl

142
Adaptive Time Delay Estimation

• ????????????????? Adaptive Time Delay

d

d
y
x
error
Adaptive Equaliser
-
Delay


Noise
143
ADTE Simulink Model

• lmsadte.mdl

?????????????????????? ??????????????????????
9
9
144
ECG Measurement

• ?????? ECG ?????????????????? ???????????????????
  ?????????? ??? ?????

145
ECG Signal

• ??? Matlab ?????????? ecg

146
ECG Measuring Circuit

• ???????????????????????????????? ECG

147
Diagram of ECG Measurement with Noise
3
ECG
???????
????????????? 220 V ?????????????????? H(z)
1
2
ECG Sensor
H(z)
50 Hz
220 Vac 50Hz
H(z) ????Transfer Function ??????????
50 Hz
4
148
50Hz Notch Filtering

• ??????????????????? 50 Hz ???? Notch filter

From ECG Sensor
Filtered ECG
Notch Filter
50 Hz
f
50 Hz
149
Lab 7 50Hz Canceling in ECG

• ?????? Notch filter ???? Fdatool ??????? Simulink

Fpass2 55 Hz
Fpass1 40 Hz
Fstop2 60 Hz
50Hz
Fstop1 45 Hz
50 Hz
f
150
Lab 7 50Hz Canceling in ECG

• ???? 50Hz Canceling ???? Notch filter

Notch Filter
151
Lab 7 50Hz Canceling in ECG
152
Lab 7 50Hz Canceling in ECG

• ?????????????????????? distortion ????
  ????????????? sine ??????? ???? ????? clipping

Transfer Function??????????
Nonlinear Wave
153
Lab 7 50Hz Canceling in ECG

• ??????????????

154
Lab 7 50Hz Canceling in ECG

• ?????????? adaptive filter ????????? nLMS

155
Lab 7 50Hz Canceling in ECG
????????? ????
156
Conclusion

• Matlab ??? Simulink ?????????????????????????????
  DSP ???????????????????????????
• DSP BLockset ?????????????????????????????????????
  ????? DSP???????????
• ?????? DSP ???? Matlab Simulink ??? DSP BLockset
  ??????????????????????? ??????????????????????????
  ?????????????????????
• ??????????? DSP ??????????????????????????????????
  ?????????

157
Thank You