medical signal processing

KAD 2021.12.08

Medical signal processing

2

A signal is any kind of physical quantity that conveys/ transmits/stores information

e.g. (1)electrical voltage, that can be measured on the surface of the skin/head as a result of the heart-/muscle-/brain activities (ECG/EMG/EEG)

e.g. (2)gamma photon detection in radioisotope diagnostics

(1) (2)

1mV/cm

25 mm/s

3

Classification of signals

static – time-dependentperiodic – non-periodicrandom – deterministicpulsed – continuouselectric – non-electricanalog – digital

1mV/cm

25 mm/s

4

in a very special role

electric signals

non-electric signals are transferred to electric ones

advantages of electric signals:they are easy to transform, amplify, transmit

digital signals

analog signals are transferred to digital ones

advantages of digital signals:they are easy to store, the noise can be engineered and influence can be reduced

5

quantity that compares the magnitudes of two signals:

Signal level or Bel-number (or Decibel-number): n

(named after A. Bell)

unit of n : Bel (B) or decibel (dB)

BlgBlgBlg1

2

1

2

1

2

EE

JJ

PPn

decimal logarithm of ratio of two powers (intensities, energies)

6

arcradius

radiusarc

cf. radian

1radmm

dBlg101

2PPn (10d = 1)

instead of Bel number we are using decibel-number

cf. pH (power of Hydrogen)

M 1

HlgpH

7)7(110lgpH

M10H:..e7-

-7

g

7

the relation between power and voltage:

dBlg20dBlg10

dBlg10dBlg10

1

22

1

22

1

21

2

22

1

2

UU

UU

RURU

PPn

):Ohm(2

IRURUIUP

the characteristic unit: power (or intensity/energy),the practical unit: (electric) voltage

signal level with voltages:12 RR

8

3dBdB0,310

dB2lg1021

2

PP

3dB21

1

2 PP

10dBdB110

dB10lg10101

2

PP

20dBdB210

dB100lg101001

2

PP

cf. half life,half value thickness

9

empirical density function

spectrum, as a special density function

H

h

body height, h (cm)

n: number of data

body height, h (cm)

10

hH

h (cm) h (cm)

hn

cm101

160 170 180 190 200 210 160 170 180 190 200 210

Density function Spectrum

area under the curve: n

area under the curve: H

11

all (usual) periodic functions can be expressed as a sum of sine (and cosine) functions from the fundamental frequency and the overtones

where f is the frequency

the sine function, which has the same frequency as theperiodic function: fundamental frequency

2f, 3f, 4f, ... : overtones

(line spectrum)

periodic function: there is a period, T

T

t

Fourier’s theorem for periodic functions (signals)

,1 fT

in music: pitch

in music: timbre/tone color

12

square pulse trainfundamental fr(equency)

fundamental fr.+3rd overtone

fundamental fr.+3rd overtone +5th overtone

fundamental fr.+3rd overtone +5th overtone +7th overtone

spectrumfunction

0

0.5

1

0 5 10 15 20

0

0.5

1

0 5 10 15 20

0

0.5

1

0 5 10 15 20

0

0.5

1

0 5 10 15 20f

f

f

f

13

fundamental fr.+3rd overtone ++ ... +9th overtone

0

0.5

1

0 5 10 15 20

0

0.5

1

0 5 10 15 20

0

0.5

1

0 5 10 15 20

0

0.5

1

0 5 10 15 20f

f

f

f

spectrumfunction



fundamental fr.+3rd overtone ++ ... +15th overtone 14

0

0.5

1

0 5 10 15 20

0

0.5

1

0 5 10 15 20

.

.

.

.

.

.

f

f

spectrumfunction


fundamental fr.+3rd overtone ++ ... +17th overtone ++ ...

15

2...81

41

211...

21

21

21

21

21

32100

kkcf. infinite series

0 1 2 3

16Textbook, Figure VII.3.

Creating an ECG signal from sine functions

17

flute clarinet

Measured spectra

18

all (usual) functions can be expressed as a sum of sine (and cosine) functions

spectrum: continuous

cf. emission spectra of incandescentlight sources

Fourier’theorem for non-periodic functions (signals)

J

19

t

t

t

t

t

U

U

U

U

U

f

f

f

f

f

P

P

d P/df

d P/df

d P/df

T

T

T

f = 1/T0

f = 1/T0

f = 1/T0

f = 1/T0

A A’

B B’

C C’

E E’

D D’

T

line spectrum (1 line)

line spectrum

band spectrum

band spectrum

continuous spectrum

periodicfunction

sine function

non-periodic function

a few periods

more periods

eg. pulsed ultrasound

spectrumfunction

20

fsine

t

Music in time-frequency representation

pitch

timbre

fund

amen

tal

over

tone

s2n

d3r

d4t

h

21

Voiceprint

http://www.nrips.go.jp/org/fourth/info3/index-e.html

oscillogram (sound intensity vs. time)

time –frequency representation

pronounced consonants and vowels22

t (s)

f sine

(Hz)

systole diastole

Heart beats in time-frequency representation(+ oscillogram)

t (s)

U

23

Frequency and amplitude ranges of biological signals

Practical manual, titel page of meas. 1724

Frequency dependent unit: Electronic amplifier

functionssame:and)2()1(

outin

outin

PPPP

1where),()()2()1( outin PP AtPtPA

same: „fundamentalist“ requirementsimilar: realistic requirement

,in

out

PPAP

,in

out

UUAU

power gain (amplification)

voltage gain (amplification)

25

Uin Uout

R1

R2

in21

2out U

RRRU

(frequency independent) voltage-divider

Uin

Uout

R1

R2

frequency dependent voltage-divider: with capacitor26

CR 1

C

in222in2

22

out11

UCR

RCUR

C

RU

Uin Uout

C

R

High-pass/low-cut filter

0),0(if out0 Uat very low frequencies:

at low frequencies: inout0,if URCU

logf

n(dB)

↔ 6 dB/octave

because of the phase difference, the sum should be calculated as vectors

inout,if UU at high frequencies :

at high frequencies the capacitor is a shortcut

supplementarymaterial

stray/parasiticcapacitance

27

Low-pass/high-cut filter

Uin

R

C

in222in

222

out1

11

1

UCR

U

CR

CU

inout0 ),0(if UU at low frequencies:

at very high frequencies : 0),(if out0 U

logf

n(dB)

Uout

at high frequencies: inout01,if U

RCU

↔ -6 dB/octave

the capacitor at low frequencies is a discontinuity

CR 1

C

supplementarymaterial

28

for (1 [on page 24]): AP >1,

n=10 lg AP = 20 lg AU > 0 dB

for (2 [on page 24]): frequency characteristics

f (logarithmic scale)

n(dB)

fl futransfer band (passband)

fl : lower frequency limit fu : upper frequency limit

nmax

nmax-3

ideal amplifier

29

Amplifier with feedback

Without appropriate perspective we may not recognize our real position.

U

UUUUUU

UUUUUUU

U

U

AAAAAAA

AAAAUUA

UAUU

UAU

UUAc

UUAbUUUa

1

)()(

)()(

***

*

0

2

0

20

0

1

0

2*

1

2201

30

:

:,1

**

U

UU

UU

A

AA

AA

positiv feedback:(a) AU=1, amplification: „infinite“

– sine wave oscillatore.g.: ultrasound generator,

heat theraphy(b) AU 1, amplification: very big

– regenerative amplifiere.g.: hearing, outer haircells

negativ feedback: „all“ amplifier

voltage gain with feedback

voltage gain without feedback

> 0, positiv feedback (same phase), AU*> AU (advantage)

< 0, negativ feedback (in opposite phase), AU*< AU (disadv.)

31

3 dBpositiv feedback

without feedback

negativ feedback

positiv feedback: transfer band – narrrower (big disadvantage)higher gain (advantage)

negativ feedback: transfer band – broader (advantage)less gain (small disadvantage)

logf

n(dB)

transfer band

‐50

‐40

‐30

‐20

‐10

0

10

20

30

‐50

‐40

‐30

‐20

‐10

0

10

20

30

‐50

‐40

‐30

‐20

‐10

0

10

20

30

T 1T 2T 3T 4T 5T 6T 7T 8T 9T 10T 11T 12T

‐50

‐40

‐30

‐20

‐10

0

10

20

30

T 1T 2T 3T 4T 5T 6T 7T 8T 9T 10T 11T 12T

32

analog signal: time- and value-contin.

time-discrete value-contin.

time-cont. value-discrete

digital signal: time- and value-discrete

Analog signal – digital signal

33

Nyquist–Shannon sampling theorem:highest frequency component of the signal

fsampl = fmax, reconstructed signal is constant

fsampl = 1.5 fmax, freq. of reconstructed signal is wrong

fsamp = 2 fmax, freq. of reconstructed signal is correct

e.g.: hifi, fmax = 20 kHz

fsampl = 44.1 kHz > 2*20 kHz

time-discrete: the value of the signal is not known for all moments in time

value discrete: the value of the signal can not be arbitrarye.g.: hifi, 16 bit = 216 = 65 536 (CD standard)

24 bit = 224 = 16 777 216 (“best” audio card)

for complete reconstruction the minimum sampling frequency should be twice the frequency of the highest overtone of the signal

34

Pulse processing

integral discrimination differential discrimination

to select only those pulses that are larger than a preset amplitude

to select only those pulses whose amplitudes lie within a preset window

in in

out out

discr

Textbook, Figure VII.32.

35

Distribution functions and ID/DD ”spectra”

0

1

2

3

4

5

6

150 160 170 180 190 200 210 220

02468

101214

150 160 170 180 190 200 210 220

02468

101214

150 160 170 180 190 200 210 220

density function

h (cm)

h (cm)

h (cm)

ID-”spectrum”

DD-”spectrum”

”cumulative-distribution-function”

hN

cm101

M=N0-N

N

how many pulses are smaller than h?

cumulative-distribution-function

how many pulses are larger than h?

36

Concentration of white blood cells

Coulter counter

medical signal processing

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