Note: Descriptions are shown in the official language in which they were submitted.
CA 02359445 2001-10-03
Introduction
Power line interference coupled to signal carrying cables is particularly
troublesome in
medical equipment such as electrocardiograms (ECGs). Cables carrying ECG
signals from
the examination room to the monitoring equipment a,re susceptible to
electromagnetic
interference (EMI) of power frequency (50 Hz or 60 Hz) by ubiquitous supply
lines and
plugs so much so that sometimes the ECG signal is totally masked by this type
of noise.
Filtering such EMI signal is a challenging problem given that the frequency of
the time
varying power line signal lies within the frequency range of the ECG signal.
There a.re
some other technical difficulties involved, the most important of which is the
low sampling
frequency at which the ECG signals are taken a.nd low computational resources
available.
The history of attempts to mitigate powEer line EMI in ECG signals goes as far
back as
the ECG equipment itself. This problem wa.s one of the first to attract the
attention of
developers of adaptive filtering theory ~1~. Although classical adaptive
filtering provides a
partial solution to the problem, the problem is still considered open and
research continues
to find an ultimate solution (2, 3~.
Pollution of ECG signals presents a general problem with medical equipment.
This same
problem may occur in a variety of other scenarios. For example, telephone,
lines carrying
voice or data. are subject to induced EMI from bower lines both in the form of
differential
mode a,nd conmion mode interference. While elirnina.tion of common mode EMI is
trivial,
in practice some residual differential mode interference always persists to
exist. Presence of
such differential mode EMI, frequency content of which lies within the
frequency spectrum
of the signal of interest, degrades the duality of the communication channel.
The affected
signal ma.y be voice, or data. in the case of telephone line-haled data
communications.
The fact that cha,ra,c;teristics of the interfering signal including its
frequency may vary
over time renders the noise suppression task difficult. Various methods of
reduction of
2
CA 02359445 2001-10-03
power line interference have been proposed over the years each presenting
strengths and
weaknesses. No unique solution to this seemingly simple problem has been
proposed so far
(4~. Va.rious signal processing schemes have be.Pn proposed in recent years
for elimination
of power lice interference (3, 5~ .
A recently developed signal processing algorithm, introduced in (6~ wa.s found
promising
in construction of a universal EMI filter suitable for various applications in
which the
interference is a. time-varying periodic (i.e. quasi-periodic) signal. It
offers a robust
structure and is shown to have a high degree of irnnnmity with respect to
external noise.
This document presents structure and performance of such an adaptive EMI
filter for the
elimination of narrow-band interferences. Two examples of its application to
ECG signals
and signals carried by telephone lines a.re considered although the filter is
general and
may be applicable to other problems of similar nature.
Review of the Core Unit
This section reviews the rnatherna,tical structure and properties of the core
unit employed
to construct the EMI filter of this invention. Let. cc(t) denote a. signal
comprising a mzmber
of individual sinusoidal components and noise, expressed by
N
ic(t) _ ~ A~ sin ~k. + n(t) (1)
k=1
where ~~. = c.~h,t + ek is the total phase, and r~(t) denotes the total noise
imposed on the
signal. ThP objective is to find a scheme for estimating a. certain component
of such input
signal as fast a.nd accurate a,s possible; a scheme which should not be
sensitive to the noise
and the potential time variations of the input signal. Simplicity of the
structure, for the
sake of practical feasibility, is desirable.
3
CA 02359445 2001-10-03
Let .M be a. manifold containing all pure sinusoidal signals defined as
./~ _ ~y(y 8) = Br sln(BZf + ~3~1 ~i E ~Bi.min, ~i.ma.x~~
where B = ~9~ , B2, B3~T is the vector of parameters which belongs to the
parameters space
o = ~ fe~ , ez, e31 T I e; E ~e~.."~;,~, eZ,rnaxl ~
and T denotes matrix transposition. ~I'o extract a certain sinusoidal
component of i~,(t), the
solution has to be a.n orthogonal projection of r(t) onto the manifold ,/1~1,
or equivalently
has to be an optinrurn B which minimizes a distance function rl between y(t,
f3) and r,(t),
i.e.,
Bopr = argnunrl(y(t,,B), tc(t)).
eE~-~
In least squares method, d is the instantaneous distance function
cl2(t, f~) _ (or(t) - y(t, H))2 ~ e(t)2.
The parameter vector B is estimated using the gradient descent method,
at ~(t) - -~' ae OZ (t, e»
where the positive diagonal matrix E~ is the algorithm regulating constant. It
controls the
convergence rate as well as the stability of the algorithm.
Following the steps outlined above, a set of differential equations is
obtained. The gov-
erning set of equations of this algorithms can h written as
A ~~le sin ~, (2)
-
- uzeA cos ~, (3)
- ~l,3eA COs (h -f- W,
y(t)A sin ~, (5)
-
e(t)cc(t) - ~(t), (G)
-
4
CA 02359445 2001-10-03
u(t~ + ~ e(t)
X i t.,
CV" ~ ~ Sine
J ~TN. + ~ I
+ ~ Cosine
I ~~tl
Figure 1: Block diagram implementation o.f the core unit.
where y(t~ is the output.
It has been shown that the dynamic.al system represented by the above set of
differential
equations possesses a unique asymptotically stable periodic. orbit which lies
in a neighbor-
hood of the orbit associated with the desired component of the function m(t).
In terms of
the engineering performance of thE: system, this indicates that the output of
the system
y(t) = A sin ~ will approach a sinusoidal component of the input signal u(t).
Moreover,
time variations of parameters in v.(t) are tolerated by the system.
Figure 1 shows implementation of the algorithm in the form of composition of
simple
blocks suitable for schematic software development tools. Numerically, a
possible way of
writing the set. of equations governing the present algorithm in discrete
form, which can
be readily used in any progrannning language; is
A(n + 1) - A(rt~ + T,Ecxe(r~~ sin ~(ra~,
c,~(ra + l~ - c.~(ra~ -f-Tqy.Ze(~n~A(n~ cos~(n.,
J
CA 02359445 2001-10-03
~(rt ~- 1] - C~(17.] -f- 2'SCJ(7t] + TS ~t2Et3e(rt] A(rt] COS ~7(n],
y(n] - A('n] sin c~(n],
e(n] - r(n( - ~(n]
where a first order approximation for derivatives is assumed, Ts is the
sampling tune and
n is the index of iteration.
In the simulations presented in this document, Matlab SimulinkT~r
computational Soft-
ware is used as the main computational tool. Figure 2 shows an example of
performance
of the core algorithm in which the frequency of the input signal undergoes a
step change
of 10°~0. It is observed that the variations a.re effectively tracked
with a transient of few
cycles. Values of the parameters are chosen to be ~Ll = 100, ~L2 = 10000, N.;~
= 0.02, for
this simulation.
The dynamics of the core algorithm presents a notch filter in the sense that
it extracts
(i.e. lets pass through) one specific sinusoidal component and rejects a,11
other components
including noise. It is adaptive in the sense that the notch filter
accorrrrnoda,tes variations of
the characteristics of the desired output over time. The center frequency of
such adaptive
notch filter is specified by the initial condition of frequency W. In Figure 1
this initial
value is explicitly shown for easy visualization.
6
CA 02359445 2001-10-03
Structure of the Present EMI Filter
One single unit of the core algorithm ca.n be employed to extract the quasi-
periodic
interference mixed with the signal. This unit can effectively follow time
variations in
amplitude, phase and frequency of the interfering signal. Once it is
extracted, it can be
subtracted from the input signal to yield a clean signal.
In order to improve performance of the unit, the use of a band pass filter
(BPF) to filter
out non-interference signal components is proposed in Figure 3. This band pass
filter
does not need to be sophisticated and can be as simple as a. second order
filter. Its role
is to improve the signal to noise ratio (signal here meaning the interference.
and noise
meaning a,11 other components) a,t the input of the core unit. Whatever is not
removed
by this BPF will be effectively removed by the core unit so as to produce a
single pure
sinusoid which is the interference. This interference in then to be subtracted
from the
input to provide the clean signal. BPF characterized by its transfer function
H( f ) causes
an attenuation ~H( f ) ~ and phase delay LH( f ) which are functions of
frequency. Since
the core unit generates the value of the frequency in real-time, the
attenuation a.nd phase
delays a.re known and can be restored as depicted in Figure 3. In general, the
filter does
not have to be band pass and a. high pass filter may be sufficient. As a
concrete example,
the band-pass filter employed as the pre-filtering tool in Figures 3 and 4 is
chosen to be
a second order filter characterized by the following transfer function:
100s
H(5) -
s2 ~- 100s -i- cv~
Gain and phase characteristics of this filter are shown in Figure 5 in which
cvo is taken to
be 100 Hz for the ease of visualization.
Where the interfering signal is severely distorted, the harmonics may also be
present. In
such cases, desired signal is not polluted by a sinusoid, but, by a number of
sine waves. A
8
CA 02359445 2001-10-03
Filter Characteristics
t o°
c
A tU
L7
to
tt)
tUU ~T-
N
A
L
a
_5p
-t00 . .. ..
.. ..
t0 t0' to'
FrequencyiHz)
Figure 5: Gain and phrase diagrams of the pre-filter.
more general configuration in Figure 4 may then be employed to eliminate the
fundamental
and the harmonics of the EMI.
Application of the Present Filter to ECG Signals
ECG signal is basically an index of the functionality of heart. The physician
can detect
arrhythmia. by studying abnormalities in the ECG signal. Since delicacies
present in the
ECG signal convey important information, it is important to have the signal as
clean as
possible. Figure 6 shows a clean ECG signal recorded at Beth Israel Hospital
(BI I') in
Boston and made available by Massachuset Institute of rI'echnology MIT-BIH
~7~. The
recording was done using battery operated ECG equipment to minimize power line
EMI
although some such EMI still exists which is mostly coupled at the time of
recording
the signals on the tape. The frequency spectrum of this signal spans from near
DC
frequencies to about 100 Hz. The sampling frequency in most ECG devices are
240 Hz
or 360 Hz. In this case, the equipment wa.s operated at the sampling rate of
3fi0 Hz.
CA 02359445 2001-10-03
t.2
t
0.8
s
E
c
r'
U
W
0.5 1 t.5 2 2.5
time (s)
n
H
V
C
W
H
V
W
O
Figure 6: Recorded ECG signal and its frequency spectrum.
Therefore, the spectrum can theoretically include frequencies from zero to 180
Hz. The
data available from MIT-BIH contains a high DC offset which is eliminated it
simulations
of this document.
ECG signals can be easily polluted by power lin a noise of relatively large
amplitude. Were
the frequency of power line interference accuratf~ly at 50 Hz or 60 Hz, a
sharp notch filter
would be able to separate and eliminate the noise ~8~. The major difficulty is
that the
frequency ca.n vary about fractions of a Hertz, or even a. few Hertz in some
countries. The
11
~~0 20 40 BO 80 100 120 140 t60 t80
Fraquency(Hz)
CA 02359445 2001-10-03
sharper the notch filter is designed, the more inoperative, or rather
destructive, it becomes
if any change in the frequency of the power line occurs. Of course, turning
the notch
filter into a band stop filter by widening its rejcctiom band, and thereby
accommodating
frequency variations, does not offer any better solution since it will
undesirably distort
the ECG signal itself. The frequency of the power grid is usually taken as
being constant
when conventional EMI filters for ECGs are designed. In such arrangements, the
system
is very fragile with respect to power frequency variations and can become
completely
malfunctioned. Such adaptive or non-adaptive filters, those discussed in (9~
for instance,
greatly suffer from this shortcoming.
One of the possible alternatives to take frequency variations into account is
the use of
external reference power line signal (10~. This technique, available by the
use of adaptive
filters only, is reported practically difficult or rather impossible (~J~.
llor this reason, other
methods, usually very complex axed inflexible, are constantly being proposed
(2, 3~.
The ideal EMI filter for ECG is the one which acts as a sharp notch filter to
eliminate only
the undesirable power line interference while automatically adapting itself to
variations
in the frequency of the noise. Of course, this adaptation must be done very
quickly
so as to keep the signal clean all the time. It. is supposed to be able to
work in low
information background, namely that dictated by low sampling frequency, and
must be
robust with respect to variations in its internal a.s well as external
conditions. An example
of internal condition is its settings. External conditions can range from the
temperature
of the environment in which the equipment is supposed to function to the
superimposed
noise~distortion on the interfering power signal.
12
CA 02359445 2001-10-03
Performance of Present EMI Filter in the Case of ECG Signals
This section presents a number of simulations to demonstrate performance of an
EMI
filter constructed as in Figure 3. The filter a.t the input of the core unit
attenuates the
ECG signal by a factor of 10. Figures 7 and 8 show performance of the filter
in eliminating
a power line interference of 1 my constant level whose frequency is fixed at
60 Hz. This
is an elementary experiment. since a simple notch filter will easily eliminate
such a, fixed
frequency noise. In the simulation, only a. GO Hz component is added to the
clean ECG
signal obtained from MIT-BIH ~7~ whose presence is clear in the frequency
spectrum of
the input (Figure 8).
The values of the parameters fir, ~~~, arid ~C3 determine the convergence
speed versos error
compromise. Generally, the higher the values are chosen, the faster the
algorithm tracks
variations at the expense of larger steady state error. Therefore, it is
important to define
desirable balance of speeci/error. For the simulations in this document, a
moderate choice
of Eel = 200, Ec2 = 20000, a,nd ~C3 = 0.01 results in an EMI reduction of a
factor of about
20 while keeping the transient time short enough. All initial conditions of
integrators a,re
zero except for that of frequency which is taken to be 60.
To demonstrate the ability of the filter in adaptively tracking the variations
of the level
of noise, the level of the EMI is made to be changing with time in Figure 9.
Again, error
is confined to within about, 2~ of the maximum noise in the input.
Figure 10 shows performance of the filter in tracking the variations in
frequency of the
power line noise. The filter is adjusted -by virtue of its initial conditions-
to extract a
power line noise of frequency 60 Hz. The EMI in the input, however, is
oscillating at
55Hz. Effective tracking of unknown input frequency is observed.
18
CA 02359445 2001-10-03
Time Domain Representation (Normalized)
o.s ,. .
c
z o
~ -0.5
_1
0 0.2 0.6 0.6 0.6 1 112 1.4 7.8
2
7
0
O
a _,
_2
0 0.2 0.4 0.6 D.8 1 7.2 1.4 1.8
7 nT-
0.5 ... ~~..
C 0
0
~ -0.5
_1
0 0.2 0.4 0.6 0.8 1 112 1.4 1.8
Time (s)
Figure 12: Time-domain representation of the performance of the present EMI
eliminator
in suppression of a fixed frequency interference from an arbitrary input
signal.
Finally, Figure 11 shows performance of the filter when all characteristics of
the EMI
a,re changing with time. As before, the filter is adjusted to extract a power
line noise of
60 Hz. However, the incoming EMI has a frequency of 65 Hz. The level of the
EMI is
also cha,ngin g with time. Again, effective elimination of superimposed EMI is
observed.
Performance of Present EMI Eliminator in the Case of Telephone
Line Signals
Figure 12 shows performance of the EMI filter in suppression of an
interference of fixed
frequency of 60 Hz from an arbitrary input signal. The original input signal
is arbitrarily
taken as a recorded bird chirp sampled a.t FS = 8192 Hz. It goes without
saying that
the notch filter targets the pre-specified sinusoidal interference present in
its input, hence
frequency composition of the incoming signal is irrelevant as far as EMI
filter is concerned.
The level of interference added to the original signal is taken to be equal to
that of the
19
CA 02359445 2001-10-03
Input/output in Frequency Domain
y-50~ ~~
r, ~ ,
Original n,
ii
- - - . Retrieved
i
20 40 60 80 100 72
Frequency (Hz)
Figure 15: Magnified spectrum of the original and retrieved signals around the
frequency
of the interfering sinusoid (60 Hz).
original signal so that signal to noise ratio (SNR) is 0 dB in the following
simulations.
Figure 13 shows the incurred error in removing the EMI. It is basically the
difference
between the refined signal and the original signal not yet polluted by the
interference.
Frequency spectrums of the original, polluted and retrieved signals a,re shown
in Figure
14. Figure 15 shows the magnified portion of the frequency spectrum of the
original a,nd
the retrieved signals about the frequency of the interference. It is observed
that. the notch
filter effectively removes the interference and retains the original signal
almost untouched.
To show the adaptive nature of the present interference eliminator with
respect to vari-
ations in frequency of the interfering signal, performance of the present
method when a
step change in the frequency of interference occurs is shown in Figure 16. As
notc;d be-
fore, the rate of convergence in tracking time-variations such as that shown
in Figure 16
is totally controllable by means of adjustment of parameters. The tracking
capability of
the present method is a,dvamta,geous in devising a. universal power supply
noise eliminator
independent of the nominal frequency of the grid. Regardless of initial
frequency setting
(whether 50 Hz or 60 Hz), the filter finds the instantaneous frequency of the
power line
21
CA 02359445 2001-10-03
Time-Varying Interference (p.u.)
t _.
m
C 0.5
0
m
C -0.5
_1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 i.6
t
w
7
a o.5
E
a
0
0 o.z o.4 o.s 6~e t t.2 t.4 t.s
t
0.5
t 0
W
-0.5
_t
0 0.2 0.4 0.6 0.8 1 t.2 1.4 i.6
Time (s)
Figure 18: Performance of the present method in eliminating a sinusoidal
interference
of time-varying amplitude. rI'he top figure is the interference, the middle
figure is the
estimated value of the amplitude of the interference and the bottom figure is
the incurred
error in EMI suppression.
interference. Figure 17 shows an example in which the EMI filter expects a GO
Hz power
supply interference while the interference happens to be of 50 Hz frequency.
To demonstrate adaptive nature of the present method in tracking variations in
the level
of the interference, performance of the present method in eliminating an
interference of
time-varying amplitude is shown in Figure 18.
As noted before, power supply interference nlay be distorted by the presence
of harmonics.
Figure 19 shows an example of a highly distorted interference in which
harmonics of third
and seventh order are present. In such cases, a multiplicity of EMI filters,
connected in
parallel combination as suggested by Figure 4, may be used for EMI mitigation.
Figure 20
shows the frequency domain representation of the performance of an EMI filter
consisting
of three units connected in parallel. The fundamental frequency of the
interference is
made to slightly vary over time. An EMI reduction of about 40 dB is observed.
Again,
23
CA 02359445 2001-10-03
the level of desired EMI mitigation is controllable by the adjustment of
parameters and
at the expense of speed. Considering that the power supply noise is usually a.
slowly
time-varying signal, one can sacrifice speed for better interference
elimination.
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CA 02359445 2001-10-03
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