D 9 9 9 4 5 0 0 4

林穎聰

Time-Frequency Analysis of EMG and the Application

Time-Frequency Analysis of Myoelectric Signals During Dynamic Contractions: A Comparative Study.Stefan Karlsson*, Jun Yu, and Metin Akay. P228-238. IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 47, NO. 2, FEBRUARY 2000

Skeletal Muscle Tissue

Motor unit: a single motor neuron and all of the corresponding muscle fibers it innervates

Two types by color:A) Red fibers: more myoglobin, slow

contraction, small muscle forceB) White fibers: fewer myoglobin, fast

contraction, large muscle force

What is EMG?

Electromyogram (EMG): the electrical potential generated by muscle cells when these cells are electrically or neurologically activated. Application: Detection of medical abnormalities,

activation level, recruitment order. The biomechanics analysis of human or

animal movement. Human–Computer Interface

How to Gather EMG

Intramuscular EMG:A needle electrode or a needle containing two fine-wire electrodes is inserted through the skin into the muscle tissue.

Surface EMG:Surface electrode over the skin.

STFT

Gabor extended the applicability of Fourier transform method by dividing the input signal into segments. The signal in each window can be assumed to be stationary.

*( , ) ( ) ( ) jwxSTFT t w W t x e d

2*( ) tW t e Gabor transform:

WVD

Since energy is a quadratic signal representation, a quadratic time-frequency representation such as the Wigner distribution can be used to represent it.

*1( , ) ( ) ( ) ( )

2 2 2jw

xW t w h x t x t e d

pseudo Wigner-Ville distribution:

h(τ): a regular window

CWD

2

22 *42

( , ) 2 ( ) ( ) ( ) ( )4

jx N MRWED n W e W e x n x n

Running Windowed Exponential Distribution:

The larger the value of σ is, the better the autoterm resolution, otherwise the cross-termreduction will be worse. (σ:0.1~10)

2

*22

1( , ) exp( ) ( ) ( )

4 / 2 24 /

j tx

tCWD t e x x d d

Choi-Williams Distribution:

( ) 0, ; ( ) 1,2 2 2 2N M

N N M MW for W for

Wavelet Transform

*,

,

( , ) ( ) ( )

1( ) ( )

x a b

a b

CWT a b x t t dt

t bt

aa

Wavelet replaces the frequency shifting operation in STFT by a time scaling operation

a: the scale parameter; b: translation parameter

Larger a : useful for analysis the low-frequency components of the signal.

Smaller a : useful for analysis the high-frequency components of the signal.

Computer Synthesized Signals

Linearly decreasing MNF

Decreasing MNF from 160Hz to 72Hz with 100 steps in 3.2 secand 50 steps in 1.6 sec.

Sampling rates: 1k Hz

Burst

Different time and frequency ranges with bandpass filter:

72-160Hz with 512ms & 256ms 54-120Hz with 512ms & 256ms

Surface EMG Signals

Maximum static voluntary contraction(MVC)Ramp contraction (RC)Repeated dynamic contractions until exhaustion (RDC)

Kin-Com 500H

Vastus laterials muscle

Four healthy male volunteers

Exam System

Electrode

Kim-com 500H

DAP 2400 with MYSAS

MATLAB

Surface EMG(mV)

Force (N) Velocity(Deg/sec)

Sampling rates: 2k Hz

Low pass: 800Hz

High pass: 10HzSignal processing toolboxTime-frequency toolbox

Estimates of Time-Frequency Analysis

Mean frequencies (MNF) as the indicators of spectral changes are M1(t)

01

0

10

0

( , )( )

( , )

( ) ( , )( ) , 2,3, 4

( )

F

F

F k

ck F

P t dM t

P t d

M t P t dM t k

P t d

22

31 3

42 4

( ) ( )

( ) ( ) / ( )

( ) ( ) / ( )

c

c

c

M t t

t M t t

t M t t

Dispersion index

Skewness index

Kurtosis index

Relative error:

1/22

1

1/22

1

ˆ( ) ( )_

( )

T

t

T

t

f t f trelative error

f t

: Estimator of spectral changeˆ ( )f t

: indicator of spectral change( )f t

: # of time points observedT

Results- Computer Synthesized Signals

100 steps linearly decreasing MNF

MNF(solid);Theoretical MNF(dotted)

Mean Values (±1 std) of MNF

Theoretical MNF(dotted)

A

B

A) Slop -22.97 (Hz/s) with 100 steps

B) Slop -46.40 (Hz/s) with 100 steps

Results- Linear Decreasing MNF

Results- Burst

#1:512ms, 72-160Hz

#2:512ms, 54-120Hz

#3:256ms, 72-160Hz

#4:256ms, 54-120Hz

512ms, 72-160Hz; MNF(solid);Theoretical MNF(dotted)

Results- MVC & RC with CWD

MVC RC

Results- RDC with CWD

Beginning Middle End

Results- MVC & RC with TFA

MVC RC

Results- RDC with TFA

Beginning Middle End

Discussion

STFT had larger relative errors when estimating the MNF for stronger nonstationary signals (bursts) than those of the PWVD and RWED methods.

PWVD method may overcome the problems associated with the cross-terms by removing them at the expense of smoothing the autoterms of the signal.

CWT has been found to be very reliable in the analysis of nonstationary biological signals and does not require any smoothing function like the STFT, PWVD, and RWED

Discussion

The increase in the MNF magnitudes are due to the recruitment of larger motor units.

The MNF values are decreased during the isokinetic test probably due to the decrease in muscle fiber conduction velocity and the decrease in the force.

The CWT method are more smoother than those obtained using the STFT, PWVD, and RWED methods.

Application

Wavelet of EMG in medical detection provides more details on time-frequency domain.

Study on Parkinson Disease patientProsthetic deviceSpeech recognition

Study on Parkinson Disease Patient

Effect of medication in Parkinson’s disease: a wavelet analysis of EMG signals.S.K. Strambi, B. Rossi, G. De Michele, and S. Sello. Medical Engineering and Physics, vol. 26, pp. 279-290, 2004.

Prosthetic Device

Classification of EMG signals through wavelet analysis and neural networks for controlling an active hand prosthesis.Matteo Arvetti, Giuseppina Gini, and Michele Folgheraiter. P531-536. 2007 IEEE 10th International Conference on Rehabilitation Robotics.

Speech Recognition

EMG-based speech recognition using hidden Markov models with global control variables.K.S Lee. P531-566. IEEE Transactions on Biomedical Engineering, vol. 55, pp. 930-940, 2008.

Conclusion

The CWT is a useful tool for the analysis of EMG signals in spite of the computational inefficiency.

The discrete wavelet transform (DWT) may provide more efficiency than CWT and keep the advantage of CWT.

The S transform with a drifting window may be used in time-frequency analysis of EMG.