Transcript (DWT) and Distributed Source Coding (DSC)

Overview
•
•
•
•
•
•
•
•
BWSSN Recap
Skin Sensor Signal Types
DSC Brief Review
DWT Brief Review
ECG Signal
DWT ECG
DWT ECG Adapted for Wireless Transmission
DSC DWT ECG Wireless Transmission
Typical Skin Sensor Network
DCN 1
Rm 1
Sensor & Data
Acquisition Boards
Processor/Radio Boards (Motes)
Gateways & Network Interface
S1-Temperature
S2–Blood Pressure
Wired
Connection to
Internet and/or
PC
S3–Heart Rate
S4-Blood Oxygen
DCN
0
S5-Sweat: Na,Cl,K
S6-Sweat: pH, NH3, Lactate
DCN 2
Rm 2
S7-Sweat: Ca, Amino Acids
S8- Glucose
DCN 3
Rm 3
BWSSN Basic Sensor Processor Module
Sensing, Signal Processing, Wireless
Communication Module
Communications
Biomedical
Sensing
Signal
Processing
Low Power
Electronics
Wireless Comm. Node
Skin Sensor Signals
• Modules will incorporate sensing, signal
processing, RF communications and low
power electronics.
• Skin sensors for
– Temperature: Thermistor
– Heart Rate: ECG
– Blood Oxygen: Pulse Oximeter
– Blood Pressure
– Sweat component detectors:
Distributed Source Coding (DSC)
Typical Area of Application
Y1
Y2
Y3
X
Y4
Yi = hi*X + Zi
Zi: Noise
hi: LTI Filter
Wireless
Comm
networ
k
Central
Decoder
DSC SW Example Implementation
Source
X
000
Encoder
000
{000, 111} = 00
001
{001, 110} = 01
010
{010, 101} = 10
011
{011, 100} = 11
100
101
110
111
00
Decoder
Y
X={000, 111}
Y=000
dH(X,Y) ≤1
X-Y ≤1
X=000
X=000
Wireless Communication
General Data Packet Structure
Preamble sequence
Start of Packet Delimiter
PRE
SPD
LEN
PC
ADDRESSING
DSN
Link Layer PDU
CRC
CRC-16
Data sequence number
Addresses according to specified mode
Flags specify addressing mode
Length for decoding simplicity
TOSH Data Packet Used in Xbow Motes
A typical TOSH data packet comprises the following:
7E 42 FF FF 06 11 1D 81 02 01 00 B9 07 B0 07 BE 07 B5
07 7F 00 FF 01 FF 03 00 00 00 00 00 00 00 00 00 00 00 55
86 7E
In this frame:
7E 42 ==> SYNC and TYPE bytes is the Serial framing
protocol
The rest is the TOS_msg -- actual packet (detailed in file
tos/types/AM.h)
TOSH Data Packet
Breakdown is as follows:
uint16_t addr; // FF FF
uint8_t type; // 06 //
uint8_t group; // 11
uint8_t length; // 1D
int8_t data[TOSH_DATA_LENGTH];
// 81 02 01 00 B9 07 B0 07 BE 07
// B5 07 7F 00 FF 01 FF 03 00 00
// 00 00 00 00 00 00 00 00 00
uint16_t crc; // 55 86
Energy Consumption Reduction Via DSC
• TOSH_DATA_LENGTH is usually set equal to
29. Varying this number varies the length of the
data packet.
• Each packet carries node id, voltage,
temperature, light and other mote information.
• Each sensor’s data is encoded into two eight bit
words.
• One objective via DSC
– reduce the number of data bits per sensor that is
wirelessly transmitted from 16 to 8 with the receiver
still yielding the sensor reading without loss of
information.
Wavelet Transforms Introduction
• Wavelet
– A small wave
• Wavelet Transforms
– Convert a signal into a series of wavelets
– Provide a way for analyzing waveforms, bounded in both
frequency and duration
– Allow signals to be stored more efficiently than by Fourier
transform
– Be able to better approximate real-world signals
– Well-suited for approximating data with sharp discontinuities
• “The Forest & the Trees”
– See gross features with a large "window“
– See small features with a small "window”
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
TIME-DOMAIN SIGNAL
• The Independent Variable is Time
• The Dependent Variable is the Amplitude
• Most of the Information is Hidden in the Frequency Content
1
1
0.5
0.5
Magnitude
Magnitude
2 Hz
0
-0.5
-1
0
0.5
0
10 Hz
-0.5
-1
1
0
Time
1
4
0.5
2
0
-0.5
-1
0
0.5
1
Time
Magnitude
Magnitude
20 Hz
0.5
1
2 Hz +
10 Hz +
20Hz
0
-2
-4
0
0.5
1
Source: Fengxiang Qiao, Ph.D. Texas Southern
University
Time
Time
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
STATIONARITY OF SIGNAL
3
600
2
500
Magnitude
Stationary
Magnitude
2 Hz + 10 Hz + 20Hz
1
0
400
300
-1
200
-2
100
-3
0
0.2
0.4
Time
0.6
0.8
0
1
Occur at all times
0
5
10
15
20
Frequency (Hz)
25
Do not appear at all times
250
0.8
0.6
0.4
0.2
0
-0.2
Magnitude
NonStationary
1
Magnitude
0.0-0.4: 2 Hz +
0.4-0.7: 10 Hz +
0.7-1.0: 20Hz
200
150
100
-0.4
-0.6
50
-0.8
-1
0
0
0.5
1
0
5
10
15
Source: Fengxiang Qiao, Ph.D. Texas Southern
University
Time
Frequency (Hz)
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
20
25
• Wavelet Transform
– An alternative approach to the short time Fourier
transform to overcome the resolution problem
– Similar to STFT: signal is multiplied with a function
• Multiresolution Analysis
– Analyze the signal at different frequencies with
different resolutions
– Good time resolution and poor frequency resolution at
high frequencies
– Good frequency resolution and poor time resolution at
low frequencies
– More suitable for short duration of higher frequency;
and longer duration of lower frequency components
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
PRINCIPLES OF WAVELET TRANSFORM
• Split Up the Signal into a Bunch of Signals
• Represents the Same Signal, but all
Corresponding to Different Frequency
Bands
• Only Providing What Frequency Bands
Exists at What Time Intervals
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
PRINCIPLES OF WAVELET TRANSFORM
• Basically WT is a convolution of the
wavelet function with the signal
• WT analyzes signal info by modifying the
wavelets thru translation (location) and
dilation (scale)
• Wavelet function φa,b with Scale, a and
Location, b
T. Froese ECG Signal Classification using DWT:
http://www.cogs.susx.ac.uk/users/tf29/publications/Froese_04_ClassificationOfECGUsingDWT_MEng.pdf
DEFINITION OF CONTINUOUS WAVELET
TRANSFORM
1
CWT , s    , s  
s

x

x
t  

 xt     s dt
*
Translation
• Wavelet
(The location of the
window)
Scale
Mother Wavelet
– Small wave
– Means the window function is of finite length
• Mother Wavelet
– A prototype for generating the other window functions
– All the used windows are its dilated or compressed and
shifted versions
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
Translated 1 D Wavelet Example
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
DWT SCALE
• Scale
– S>1: dilate the signal
– S<1: compress the signal
• Low Frequency -> High Scale -> Nondetailed Global View of Signal -> Span Entire
Signal
• High Frequency -> Low Scale -> Detailed
View Last in Short Time
• Only Limited Interval of Scales is Necessary
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
Time Scaled 1D Wavelet
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
MATHEMATICAL EXPLANATION
1
CWT , s    , s  
s

x

x
t  

 xt     s dt
*
  X T    ,s t dt
1 t  
 t  


s  s 

,s
CWT can also be regarded as the inner
,s t 
product of the signal with a basis function
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
COMPUTATION OF CWT
1
CWT , s    , s  
s

x

x
t  

 xt     s dt
*
• Step 1: The wavelet is placed at the beginning of the signal,
and set s=1 (the most compressed wavelet);
• Step 2: The wavelet function at scale “1” is multiplied by the
signal, and integrated over all times; then multiplied by1 s ;
• Step 3: Shift the wavelet to t=  , and get the transform value
at t=  and s=1;
• Step 4: Repeat the procedure until the wavelet reaches the
end of the signal;
• Step 5: Scale s is increased by a sufficiently small value, the
above procedure is repeated for all s;
• Step 6: Each computation for a given s fills the single row of
the time-scale plane;
• Step 7: CWT is obtained if all s are calculated.
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
RESOLUTION OF TIME & FREQUENCY
Higher Frequencies
Better time
resolution;
Poor
frequency
resolution
Frequency
Lower Frequencies
Better
frequency
resolution;
Poor time
resolution
Time
• Each box represents a equal portion
Source: Fengxiang Qiao, Ph.D. Texas Southern University
• Resolution in STFT is selected once for entire analysis
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
Discrete Wavelet Transform
• Discrete form of Wavelet function
– m varies dilation,
– n varies translation,
– a0 is a fixed dilation step,
– b0 is the location parameter > 0
• Natural way to sample parameters a and b
is to use a log discretization of the ‘a’ scale
and link this in turn to the size of the steps
taken between ‘b’ locations
T. Froese ECG Signal Classification using DWT:
http://www.cogs.susx.ac.uk/users/tf29/publications/Froese_04_ClassificationOfECGUsingDWT_MEng.pdf
Discrete Wavelet Transform
• DWT of a continuous signal via a discrete
wavelet is given by
• Tm,n are known as wavelet or detail coefficients
• In the dyadic grid arrangement a0=2, and b0=1
• Discrete dyadic wavelets are usually selected to
be orthonormal (orthogonal and normalized to
have unit energy)
– Means that info stored in a wavelet coefficient, Tm,n is
not repeated elsewhere and allows for complete
regeneration of the original signal without redundancy
T. Froese ECG Signal Classification using DWT:
http://www.cogs.susx.ac.uk/users/tf29/publications/Froese_04_ClassificationOfECGUsingDWT_MEng.pdf
Discrete Wavelet Transform
• Sampling of the continuous signal is
accomplished by associating the orthonormal
dyadic discrete wavelets with scaling functions
• Scaling function is convolved with the
continuous signal to produce approximation
coefficients which are weighted averages of the
signal factored by 2m/2
• These approximation coefficients Sm,n constitute
a discrete approximation of the signal at scale m
T. Froese ECG Signal Classification using DWT:
http://www.cogs.susx.ac.uk/users/tf29/publications/Froese_04_ClassificationOfECGUsingDWT_MEng.pdf
Continuous Wavelet
Transform
Discrete Wavelet
Transform
T. Froese ECG Signal Classification using DWT:
http://www.cogs.susx.ac.uk/users/tf29/publications/Froese_04_ClassificationOfECGUsingDWT_MEng.pdf
1d DWT Algorithm
Starting from s, 1st step produces 2
sets of coeff: Approx coeff. cA1 and
Detail coeff cD1. These vectors are
obtained by convolving s with LPF
Lo-D for cA1 and with HPF Hi-D for
cD1 followed by dyadic decimation
Source: Matlab
Matlab DWT Decomposition Algorithm
Source: Matlab
DWT Matlab Implementation
Source: Matlab
SUBBAND CODING ALGORITHM
• Halves the Time Resolution
– Only half number of samples resulted
• Doubles the Frequency Resolution
– The spanned frequency band halved
0-1000 Hz
X[n]
512
Filter 1
256
S
S
D2
A2
A3
D3
Filter 2
A1
D1
A1
256
128
D1: 500-1000 Hz
128
Filter 3
A2
64
D2: 250-500 Hz
64
D3: 125-250 Hz
A3: 0-125 Hz
Matlab Illustration
Source: Matlab
Matlab Wavelet Decomposition
Source: Matlab
Matlab Wavelet Decomposition
Source: Matlab
WAVELET BASES
Time
domain
Frequency
domain
Wavelet Basis Functions:
-1
Morlet (0  frequency ) :  e
4
j0 2 2
e
2 m i m m!
Paul m  order  : DOG
1  im1
2m !
DOG m  devivative  :
Derivative Of a Gaussian
M=2 is the Marr or Mexican hat wavelet
- 1m1

d m 2 2
e
m
1 d
 m  
2


Various 1D Wavelets
Source: Fengxiang Qiao, Ph.D. Texas Southern University
www.missouri.edu/~sunc/TRB/ Introduction%20to%20Wavelet%20a%20Tutorial%20-%20Qiao.ppt
Wavelet Function Criteria
• For complex wavelets, FT must both be
real and vanish for negative frequencies
• Wavelet must have finite energy
• Wavelet must have zero mean meaning
that wavelet has no zero frequency
components
DWT of ECG
• DWT can be used to represent a discretely
sampled ECG signal by a finite amount of
time-invariant wavelet coefficients with
enough resolution for further signal
diagnostics.
• DWT can also be used to filter noise and
other signal deteriorating artifacts by
dropping out selected coefficients in the
reconstruction process
ECG Signal Origin
http://medicalcenter.osu.edu/patientcare/healthinformation/diseasesandconditions/he
artdisease/arrhythmias/
•http://your-doctor.com/healthinfocenter/medical-conditions/cardiovascular/conductiontutorial.html
ECG Signal Origin
Cardiac conduction system: The specialized network of cells in the heart that initiates an electrical signal in the heart and carries it throughout the
heart, causing it to beat.
Standard ECG Signal Detection
Typical ECG Signal
Ref: http://rnbob.tripod.com/index.htm
ECG Signal Points of Origin
[Diagram from Psychophysiology-Human Behaviour and Physiological Response
[Diagram from Psychophysiology-Human Behaviour and Physiological Response]
http://home.iprimus.com.au/rboon/HeartRhythmsandHRV.htm
ECG Wave Components
The P wave represents atrial activation; the PR interval is the time from onset of atrial activation
to onset of ventricular activation. The QRS complex represents ventricular activation; the QRS
duration is the duration of ventricular activation. The ST-T wave represents ventricular
repolarization. The QT interval is the duration of ventricular activation and recovery. The U wave
probably represents "afterdepolarizations" in the ventricles.
http://medstat.med.utah.edu/kw/ecg/mml/ecg_533.html
http://medstat.med.utah.edu/kw/ecg/image_index/index.html
Terminology for Contraction Phases
Marquette Electronics Copyright 1996,
http://medstat.med.utah.edu/kw/ecg/mml/ecg_compens.html
http://medstat.med.utah.edu/kw/ecg/image_index/index.html
http://medstat.med.utah.edu/kw/ecg/image_index/index.html
http://medstat.med.utah.edu/kw/ecg/mml/ecg_arrhythmia.html
http://medstat.med.utah.edu/kw/ecg/image_index/index.html
http://medstat.med.utah.edu/kw/ecg/image_index/index.html
http://medstat.med.utah.edu/kw/ecg/image_index/index.html
http://medstat.med.utah.edu/kw/ecg/image_index/index.html
Marquette Electronics Copyright 1996
http://medstat.med.utah.edu/kw/ecg/mml/ecg_compens.html
http://medstat.med.utah.edu/kw/ecg/image_index/index.html
Heart Rate Variability - HRV
Standards of Measurement, Physiological Interpretation, and Clinical Use
Task Force of the European Society of Cardiology the North American Society of Pacing
Electrophysiology. Correspondence to Marek Malik, PhD, MD, Chairman, Writing Committee of the Task
Force, Department of Cardiological Sciences, St George's Hospital Medical School, Cranmer Terrace,
London SW17 0RE, UK.
http://circ.ahajournals.org/cgi/content/full/93/5/1043
Normal Values of Standard Measures of HRV
Variable
Units
Normal Values (mean±SD)
SDNN
ms
141±39
SDANN
ms
127±35
RMSSD
ms
27±12
Time Domain Analysis of Nominal 24 hours
HRV triangular index
37±15
Spectral Analysis of Stationary Supine 5-min Recording
Total power
ms2
3466 ±1018
LF
ms2
1170±416
HF
ms2
975±203
LF
nu
54±4
HF
nu
29±3
LF/HF ratio
1.5-2.0
Typical Autonomic Response (ANS) Affecting
Heart Rate
[Diagram From The Institute of HeartMath]
http://home.iprimus.com.au/rboon/HeartRhythmsandHRV.htm
Typical ECG Signal Noise and Distortions
Clean
ECG
ECG+
noise
+60hz
DWT
Filtered
Signal
Sym5 Processed Signal
Clean
ECG
ECG+
noise+
60hz
DWT
Filtered
Signal
Db5 Processed Signal
Clean
ECG
ECG+
noise+
60hz
DWT
Filtered
Signal
Sym5 Processed Signal
Clean
ECG
ECG+
noise+
60hz
DWT
Filtered
Signal
Peaks
Detected
for signal
recovery
Db5 Processed Signal
Clean
ECG
ECG+
noise+
60hz
DWT
Filtered
Signal
Peaks
Detected
for signal
recovery
Matlab DWT Threshold Selection Choices
Matlab DWT Denoising function
[XD,CXD,LXD] = wden(X,TPTR,SORH,SCAL,N,'wname')
• Wavelet decomposition is performed at level N and 'wname' is a
string containing the name of the desired orthogonal wavelet
•
TPTR: Threshold Selection Rules:
– 'rigrsure' use the principle of Stein's Unbiased Risk
– 'heursure' is an heuristic variant of the first option
– 'sqtwolog' for universal threshold
– 'minimaxi' for minimax thresholding (see thselect for more information)
– SORH ('s' or 'h') is for soft or hard thresholding (see wthresh for more
information).
Multiplicative Threshold Rescaling
• SCAL defines multiplicative threshold
rescaling:
– 'one' for no rescaling
– 'sln' for rescaling using a single estimation of
level noise based on first-level coefficients
– 'mln' for rescaling done using level-dependent
estimation of level noise
DWT ARHOS LP Filter
R.H. Istepanian, L.J. Hadjileontiadis, S.M Panas, ECG Data Compression Using Wavelets and Higher Order
Statistics Methods, IEEE Transactions on Information Technology in Biomedicine, Vol 5, No.2 June 2001
Summary Research Goals
• Signal processing algorithms for wireless skin
sensors with the following optimization features
and objectives
– Higher signal to noise output with lower input signal
power
– Common interference signals identified and cancelled
– Common and typical artifacts characterized, reduced
and / or cancelled
– Reduced instruction set, software memory and
hardware requirements for processing of signal
Summary Research Goals
• Utilization of multiple wireless sensors to
improve desired signal via constructive signal
addition from the multiple sensor outputs.
• Processor hardware and software designed and
optimized for low power consumption
• Sensors to include types for measuring pulse,
respiration, blood oxygenation, glucose levels,
bio-impedance, skin hydration, and body
temperature.