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EE 7345/5345, SMU Electrical Engineering Department, 2000 224

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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EE 5345, SMU Electrical Engineering Department, 1996 225

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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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

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