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EE 5345
Biomedical Instrumentation
Lecture 11: slides 224-241
Carlos E. Davila, Electrical Engineering Dept.
Southern Methodist University
slides can be viewed at:http:// www.seas.smu.edu/~cd/ee5345.html
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Turning Point Algorithm
n Processes 3 points at a time: x0, x1, x2
n At each iteration:
n
x0 is the reference pointn either x1, or x2 is retained
n retained point becomes x0 for the next iteration
n Retaining rules:
n retain x1
if there is a slope sign change in going
from x0 - x1 - x2
n otherwise retain x2
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Turning Point Algorithm (cont.)
retained
discarded
xx00
xx11
xx22 x
x00 x
x11 x
x22
compression ratio is 2:1
original sample intervals are lost
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ex)
retained
discarded
first sample always retained
n
n
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Fan Algorithm U1
L1
U2
L2
U3
L3
retaineddiscarded
xx22xx00
xx11
xx33
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Fan Algorithm (cont.)
n Draw cone (U1, L1) from x0 about x1.
n If x2 lies outside (U1, L1) , retain x1, otherwise draw second
cone (U2, L2) about x2.
n If x3 lies outside smallest cone containing x2 (U2, L1) ,
retain x2, etc.
n At each step always retain the last point to fall within the
most restrictive cone.
n determines the amount of compression.n Must also store number of sampling intervals between
retained points.
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Zero-order Interpolator (ZOI)
n If a sequence of points, x0, x1, x2, , xNlie within of
n Discard x0, x1, x2, , xN-1 and replace xNby xavg
x
x x
avg =
+max min2
xmax = max(x0, x1, x2, , xN)xmin = min(x0, x1, x2, , xN)
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ex)
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Amplitude Zone Time Epoch Coding
(AZTEC )
n ECG is covered by slopes and plateaus.
n Plateaus (horizontal regions) are produced with a ZOI.
n Store plateau length (number of samples) and xavg
.
n Slope starts when number of points used to form a plateau
is less than 3.
n When a plateau of 3 or more samples can be formed, slope
is saved.
n Store slope length (number of samples) and amplitude of
last sample in slope.
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ex)
plateau
slope
plateau
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Differential Quantization
n Previous methods discard some of the samples, a subset of
the total samples are retained.
n Differential quantization relies on the use of quantizers. All
samples are retained, use a smaller number of bits to
represent each sample.
n Decreasing number of bits per sample increases
quantization error.
n Differential quantization transforms the input signal tomake it small, thereby reducing quantization error.
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Quantizers
Q[ ]
x$x
x takes on any value
takes on only a finite number of values$x
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Quantization Characteristic
7
2
5
2
3
2
2
2
32
5
2
7
2
2 3 4 2 3 4x
$
x
mid-riser
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Mid-Riser Encoder
$x b2b1b0
7/2 011
5/2 010
3/2 001/2 000
-/2 100
-3/2 101
-5/2 110
-7/2 111
sign-magnitude
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Mid-Tread
7
2
52
32
3
2
5
2
7
2
x
2
3
2
3
4
$
x
1
1
2
9
2
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EE 5345, SMU Electrical Engineering Department, 1996 239
Mid-Tread Encoder
$x b2b1b0
3 011
2 010
1 00100 000
- 111
-2 110
-3 101
-4 100
twos complement
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Analog to Digital Converter Model
quantization error = e[n] = x n x n[ ] $[ ]
Q[ ]encoder
x n[ ] $[ ]x n b b b2 1 0quantizersample/hold
x t( )
T= sampling interval
( )x n x nT [ ]
2 2
e n[ ]
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Quantizer Signal-to-Noise Ratio (SNR)
[ ]
[ ]
SNRE x n
E e n
x
e
=
2
2
2
2
[ ]
[ ]
SNR
X
N
x
=
3 22
2
max
2N= number of quantizer levels
E[ ] : expectation
operation