Signal Processing, Filtering, and Noise

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EE93 – Medical Mobile Devices and Apps

60 bpm

98

%

30 rpm

Lecture: Instrumentation & DSP

ECG Waveform on Strip Chart

12-lead – showing in 4 columns by 3 rows

One heartbeat cycle

5 mm by 5 mm reference square

0,200 s duration by

0.5 mV amplitude

1 mm by 1 mm reference square

0,040 s duration by

0.1 mV amplitude

EE93 – Mobile Medical Devices and Apps

1 mV, 10 mm high reference pulse

Length: 0.200 s

2

Measuring ECG (3-Lead)

3-lead ECG uses right arm (or chest), left arm

(or chest) and left foot

Able to obtain PQRST wave

Unable to obtain other leads and heart angle

60 bpm

98

%

30 rpm

EE93 – Mobile Medical Devices and Apps

Source for ECG slides: Computing the Electrical Activity in the Heart: 1 (Monographs in Computational Science and

Engineering) by Joakim Sundnes, Glenn Terje Lines, Xing

Cai and Bjørn Frederik Nielsen (2007)

3

Common Frequencies for ECG

Heart rate: 0.67 to 5 Hz (40 to 300 bpm)

P-wave: 0.67 to 5 Hz

QRS Complex: 10 to 50 Hz

T-wave: 1 to 7 Hz

High frequency potentials: 100 to 500 Hz

EE93 – Mobile Medical Devices and Apps 4

Common Frequencies for ECG Artifacts & Noise

Muscle: 5 Hz to 50 Hz

Respiratory: 0.12 to 0.5 Hz (8 to 30 bpm)

External Electric: 50 Hz or 60 Hz (AC Line)

Other Electrical: > 10 Hz (muscle stimulators, magnetic fields, pacemakers with impedance monitoring)

EE93 – Mobile Medical Devices and Apps 5

ECG Special Notes

Skin-electrode interface – largest source of interference – produces 200 to 300 mV

Skin-electrode interference is magnified by motion (patient movement, respiratory variation)

Electrical activity of heart – 0.1 to 2 mV

EE93 – Mobile Medical Devices and Apps 6

Power Spectra of ECG

Relative power spectra of QRS complex, P and T waves, muscle noise and motion artifacts based upon an average of 150 bpm

Source: http://www.ems12lead.com/wp-content/uploads/sites/42/2014/03/ecg-component-frequencies.jpg

EE93 – Mobile Medical Devices and Apps 7

V

2

+

ECG Amplifier

+

V

1

EE93 – Mobile Medical Devices and Apps 8

V signal

Signal & Noise Model

V noise

V signal

+ V noise

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V

1

V

2

Instrumentation Amplifier

+

R

4

R

3

R

2

R

1

+

R

2

R

3

R

4

+

V out

10 EE93 – Mobile Medical Devices and Apps

Instrumentation Amplifier (IA)

Provides capability to:

Reject common-mode signal components (noise & interference, undesired DC offsets)

Amplifies differential-mode signal

In practice, rejection of common-mode signal is not complete

 common-mode rejection ration (CMRR)

A differential

mode

CMRR

=

A common

mode

11 EE93 – Mobile Medical Devices and Apps

Instrumentation Amplifier (IA)

Provides impedance isolation between bridge transducers and differential amplifier stage

Signals V1 and V2 are amplified separately

Conditions the signals

Provide high CMRR if implemented with diligence

EE93 – Mobile Medical Devices and Apps 12

Instrumentation Amplifier

+

V

1 –

R

4

R

3

R

2

R

1

R

2

R

3

V

2

A

1 st

=

1

+

R

2

R

1

2

+

=

1

+

2 R

2

R

1

EE93 – Mobile Medical Devices and Apps

+

R

4

V out

V out

=

R

R

3

4

æ

ææ

1

+

2 R

2

R

1

æ

ææ

(

V

2

-

V

1

)

A

2 nd

=

R

4

R

3

13

Level Shifter

Wide spread use in medical applications

V

+

Adds or subtracts a

DC offset to or from signal

V ref

R s

+

R

F

V out

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Signal Processing

Instrumentation

Amplifier

High

Pass

Filter

Pulse

Indicator

Signal

Processing

WiFi

Patient

Monitor

ECG with

Noise

Stop Band

Filter

Square

Signal

Pulse Detect

EE93 – Mobile Medical Devices and Apps 15

DSP y [ n ]

+

N å i

=

1 a i y [ n

i ]

=

M å i

=

0 b i x [ n

i ]

IIR Filter y [ n ]

=

M å i

=

0 b i x [ n

i ]

 FIR Filter

16 EE93 – Mobile Medical Devices and Apps

H dB

Filter Specification

=

20 log

10

(

H ( w

)

)

20 log

10

(

1

+ d

2

)

20 log

10

(

“Ripple”

1

d

2

) w

C

= w

P

+

2 w

S

20 log

10

(

1

+ d

1

)

“Ripple”

20 log

10

(

1

d

1

) w

S w

C w

P

EE93 – Mobile Medical Devices and Apps 17

DSP Notes

IIR filter – has infinite impulse response

 need to limit

FIR filter – has finite impulse response

 h f

FIR filter advantages:

[n] = 0, n ≥ 0

Can have exact linear phase

Always stable (even under quantization)

Design methods are reasonable linear

Realize efficiently in hardware or software

Transients have finite duration

Disadvantages

Requires higher filter order that IIR to achieve similar performance

Delay is typically greater in FIR than IIR counterpart

EE93 – Mobile Medical Devices and Apps 18

FIR Filter Design Notes

IIR: H[Ω] = desired IIR filter with impulse h[n]

FIR: h d

[ n ]

=

ææ h [ n ],

0,

0

æ n

æ

N

-

1 otherwise h d

[ n ]

= h [ n ],

Transfer function:

DTFT:

ææ 0,

H d

[

W

]

=

N

-

1

å

n

=

0 h d

[ n ] z

jn

W

0

æ n

æ

N

-

1 otherwise

H d

[

W

]

»

H [

W

]

EE93 – Mobile Medical Devices and Apps 19

DSP – Analytically

• h d

[n] = w[n]

 h[n]

Where w[n] is a window function

 truncates the signal w [ n ]

=

ææ

1,

0,

0

æ n

æ

N

-

1 otherwise

Rectangular window causes abrupt transitions

Other windows allow gradual transitions

EE93 – Mobile Medical Devices and Apps 20

DSP – Other Windows

Hanning: w [ n ]

=

1

2

å

åå

1

cos

å

åå

2 p n

N

-

1

å

åå

å

åå

Hamming: w [ n ]

=

0.54

-

0.46 cos

å

åå

2 p n

N

-

1

å

åå

EE93 – Mobile Medical Devices and Apps 21

DSP – Windows

H d

(Ω) better approximates H(Ω) when main lobe of filter is narrow in bandwidth and side lobes are small in value

Hanning and Hamming, in general have much smaller sidelobes than rectangular window

 less ripple in frequency response of FIR filter

EE93 – Mobile Medical Devices and Apps 22

DSP – Procedure

•  signal that needs to be filtered

Design the filter

Normalize the Nyquist rate across the spectrum

Generate the filter coefficients in MatLab

Use MatLab command fir1

– Iterate until you “get an acceptable response”

Use MatLab command filter on signal

•  signal filter in iPad

Set up difference equation

Use filter coefficients from fir1

Compute filtered signal in code using add/multiply via difference equation

Program filter in Objective-C – rather than vDSP framework

EE93 – Mobile Medical Devices and Apps 23

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