CA2359445A1 - Universal narrow-band emi filter - Google Patents

Abstract

A new method of elimination of periodic or quasi-periodic noise is presented.
Present method employs, as its main building block, a recently developed signal processing algo-rithm capable of extracting a specified component of a signal and tracking its variations over time. Performance of the present method is exemplified by application of the present EMI filter to elimination of power line noise potentially present on electrocardiogram and telephone cables. Superior performance of the method in terms of effective elimination of noise under frequency varying condition of power line signal is observed.
Present method offers a simple and robust structure which complies with practical constraints involved in the problem such as low computational resources available and low sampling frequency.

Description

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 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 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 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

~(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.

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

Filter Characteristics t o°
c A tU

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.

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 ~~0 20 40 BO 80 100 120 140 t60 t80 Fraquency(Hz) 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.

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.

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 O
a _, _2 0 0.2 0.4 0.6 D.8 1 7.2 1.4 1.8 7 nT-0.5 ... ~~..

~ -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 Input/output in Frequency Domain y-50~ ~~
r, ~ , Original n, ii - - - . Retrieved i 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 Time-Varying Interference (p.u.) t _.
m C 0.5 m C -0.5 _1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 i.6 t w a o.5 E
a 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, 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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