Biosignal Processing 5

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Biosignal Processing 4

Prof. Jang-Yeon Park

Biosignal Processing 3

Prof. Jang-Yeon Park

Biosignal Processing 1

Prof. Jang-Yeon Park

건국대학교 의학공학부 교수 박장연

Biosignal Processing 5

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Biosignal Processing 5

1. The concept of a filter

2. Signal Averaging

- A low-pass filter

- A high-pass filter

- A band-pass filter

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1. Filters

 Filters are a special class of linear systems:

 A filter allows us to selectively remove an undesired signal component while preserving or enhancing some components of interest.

Examples:

a. Sunblock: A type of filter that removes an unwanted ultraviolet light from the sun.

b. Treble and bass controls in an audio system: A type of filter that enables boosting or suppressing the amount of a high

frequency (“treble”) and a low frequency (“bass”) sounds.

The output of a filter is the convolution of the input and the filter’s impulse response.

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1. Filters

 Filters plays an important role in the analysis of biological systems by removing unwanted noises which distort the signal waveforms and, thus, prevent a reliable diagnosis.

 Most filters can be subdivided into three broad classes:

A low-pass filter, A high-pass filter, A band-pass filter.

a. A low-pass filter: It removes the high frequencies from a signal, keeping the low frequencies.

b. A high-pass filter: It passes the high frequencies but removes the low frequencies (“exactly opposite to the low-pass filter).

c. A band-pass filter: It removes both high and low frequencies but selectively keep a small “band” of frequencies.

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1. Filters

a. A low-pass filter: It removes the high frequencies from a signal, keeping the low frequencies.

b. A high-pass filter: It passes the high frequencies but removes the low frequencies (“exactly opposite to the low-pass filter).

c. A band-pass filter: It removes both high and low frequencies but selectively keep a small “band” of frequencies.

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Low-pass, High-pass, and Band-pass Filters

(Introduction to Biomedical Engineering, by John Enderle et al.:p.591)

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An Ideal Low-pass (Analog) Filter

The transfer function of the ideal low-pass filter (b):







 

c c

LP W

H W

|

| ,

0

|

| ,

) 1

( 

 

 

frequency cutoff

filter A

f W

where

t W W

t h

c c

LP

: 2

, sinc

) (

 



The impulse response of the ideal low-pass filter (a):

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An Ideal High-pass (Analog) Filter

The transfer function of the ideal high-pass filter:







 





c c LP

HP W

H W

H 1, | |

|

| ,

) 0 ( 1

)

( 

 



 

^,

sinc )

( )

( W W t

t t

h t

t

h_HP _LP ^c _c

 

   



The impulse response of the ideal high-pass filter:

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An Ideal Band-pass (Analog) Filter

The transfer function of the ideal band-pass filter:

filter pass

- low a

of frequency cutoff

the

filter pass

- high a

of frequency cutoff

the

otherwise , ,

0

|

| ,

) 1 ( )

( )

(

2 1





  







W W where

W H W

H

H_BP _HP _LP 



) ( )

( )

( t h t h t

h

_BP



_HP



_LP

The impulse response of the ideal high-pass filter:

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Example 10.21:

An EMG signal contains energy within the frequencies 25 and 100 Hz. Design a filter to remove unwanted nosies:

Hint) We need a “band-pass” filter with pass-band frequencies 25 and 100 Hz.

 

^W^t ^t



^t



W t

t

h_HP( )  ( ) 2 ₁sinc ₁ ( ) 50sinc 50

 

^W ^t



^t



W t

h_LP( )  2 ₂sinc ₂  200sinc 200



^t

 

^t



^t

 

t h

t h t

h_BP( )  _LP( ) _HP( )  200sinc 200  ( ) 50sinc 50



The impulse response of the band-pass filter required is:

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2. Signal Averaging

 Biological measurements are often confounded by noises.

 If the spectrum of noise and signal components do not overlap in the frequency domain, a filter can be easily designed and used to remove the unwanted noises.

 However, a filter does not work well in some cases where biological signals and noise spectrums overlap.

 In this case, “signal averaging” is a good alternative way to eliminate the noises.

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2. Signal Averaging

Many biological signals can be modeled as the sum of an ideal noiseless signal component, x(t), and a separate

independent noise term, n(t):

) ( )

( )

( t x t n t

x

_i

 

x(t): the measured i^th trial or i^th measurement of the signal.

n(t): a random noise term which causes a trial-to-trial variability.

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2. Signal Averaging

) ( )

( )

1 ( )

( )

1 ( )

(

1 1

t t

x t

N n t

x t

N x t

x

N

i N

i

    

  



 If the noise terms, n(t), is purely random, (t) approaches 0 as N  . Thus, x(t)  x(t) for a very large N where

becomes very small.  “A very powerful result!”

Averaged signals:

 If we average a sufficiently large number of signal trials, the averaged signal closely approximates the true

noiseless signal waveform.

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2. Signal Averaging

(Introduction to Biomedical Engineering, by John Enderle et al.:p.553,p.600)

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