EP-4740862-A1 - AN IMPROVED PROCEDURE FOR REDUCTION OF QUASI-PERIODIC INTERFERENCES

EP4740862A1EP 4740862 A1EP4740862 A1EP 4740862A1EP-4740862-A1

Abstract

The procedure is focused on the cancellation of the QPI frequency drift, in order to minimize the spectral width of the interference harmonics and, therefore, to efficiently reduce this interference (i.e. reduction of the QPI components with minimum distortion of the signal of interest). The procedure selects QPI harmonics suitable for the estimation of a time drift associated to the frequency drift; estimates the time drift; transforms the signal to a time-scale where the time drift (and therefore also the frequency drift) is cancelled; efficiently reduces the QPI components with minimal distortion of the signal; and transforms the signal back to the original time-scale, obtaining a signal substantially free of QPI.

Inventors

DE LA TORRE VEGA, Ángel
ÁLVAREZ RUIZ, Isaac Manuel
MUÑOZ ORELLANA, Juan Antonio

Assignees

Universidad de Granada

Dates

Publication Date: 20260513
Application Date: 20250327

Claims (15)

A method to reduce a quasi-periodic interference (QPI) of nominal fundamental frequency f 0 from an input digital signal y[n] digitized at a sampling rate f s , comprising: A) Estimating a time drift dt[n] of the QPI; B) Compensating the estimated time drift dt[n] by transforming the time scale of the digital input signal from its original time scale to a corrected time scale based on the estimated time drift dt[n], obtaining a signal y c [n] in the corrected time scale; C) Cancelling harmonics of the QPI from the signal in the corrected time scale y c [n], either by applying notch filters tuned at f 0 and its harmonics in the time domain, or by cancelling frequency components corresponding to f 0 and its harmonics in the frequency domain, obtaining a signal x c [n] in the corrected time scale; D) Transforming the signal x c [n] from the corrected time scale to the original time scale obtaining a signal x[n] in the original time scale.
The method of claim 1, where the estimation of the time drift dt[n] in step A comprises: 1) Selecting one or more harmonics, k sel , to be used for the estimation of the phase drift of the QPI, being the selected harmonics the harmonics with the highest signal-to-noise ratio SNR, where k sel = k sel1 k sel2... k selH are the indexes of the selected harmonics and H>=1 is the number of harmonics selected; 2) For each selected harmonic h, h=1... H, estimating the phase drift, φ h [n], of the QPI with respect to the nominal frequency, k selh ·f 0 , by applying a digital phase demodulation procedure applied to the band around the nominal frequency; 3) Calculating the time drift, dt h [n], associated to the phase drift estimated for each selected harmonic h, h=1... H as: dt h n = φ h n / 2 ⋅ π ⋅ k selh ⋅ f 0 and determining the estimated time drift, dt[n], of the QPI as the average or the weighted average of the calculated time drifts for the selected harmonics.
The method of claim 2, wherein the selection of one or more harmonics to be used for the phase drift estimation of step 1, comprises: 1.a) Computing the Discrete Fourier Transform (DFT) Y[m] of the input digital signal y[n]; 1.b) For each harmonic k, defining a maximum expected frequency excursion B k of the harmonic with respect to its nominal frequency k·f 0 ; 1.c) For each harmonic k, estimating the energy of the harmonic E k from the frequency components in the interval [k·f 0 ± B k ], and to estimate the energy of the noise affecting the harmonic E nk from the frequency components in the intervals [k·f 0 - 2·B k , k·f 0 - B k ] and [k·f 0 + B k , k·f 0 + 2·B k ]; 1.d) For each harmonic k, estimating the signal-to-noise ratio, SNR as the ratio of the harmonic energy to the noise energy, SNR k = E k /E nk ; 1.e) Selecting the harmonics with the highest SNR k .
The procedure according to any of the previous claims 2-3, wherein the phase drift estimation for each selected harmonic h, h=1... H, is based on a quadrature phase demodulation of the signal y[n] around the carrier k selh ·f 0 , using a pair of carriers of frequency k selh ·f 0 in quadrature, comprising the following steps: 2.a) Obtaining the base-band in-phase component y i [n] by multiplying the digital signal y[n] with the in-phase carrier cos(2·π·k selh ·f 0 ·n/f s ) and obtaining the base-band quadrature component y q [n] by multiplying the digital signal y[n] with the quadrature carrier -sin(2·π·k selh ·f 0 ·n/f s ); 2.b) Combining the in-phase and quadrature base-band components into the complex base-band signal y cbb [n]=y i [n] + j·y q [n], being j the imaginary unit of the complex numbers; 2.c) Filtering the complex base-band signal using a low-pass filter with an appropriate cut-off frequency equal to the maximum expected frequency excursion for said harmonic, therefore obtaining the filtered complex base-band signal y fcbb [n]; 2.d) Estimating the phase drift φ h [n] for said harmonic as the phase (or argument) of the filtered complex base-band signal y fcbb [n] as: φ h n = atan imag y fcbb n / real y fcbb n or φ h n = angle y fcbb n 2.e) Unwrapping the phase drift φ h [n] in order to provide continuity to the estimated phase and avoid phase jumps.
The method according to any of the previous claims 2-4, wherein the time drift dt[n] is estimated as the weighted average of the time drift estimations from each selected harmonic, with weights proportional to the SNR of each selected harmonic, preferably, proportional to the SNR of each selected harmonic and to the square of the harmonic index.
The method according to any of the previous claims, wherein the compensation of the estimated time drift in step B, comprises the following steps: B.a) For each sample n of the signal, estimating the original time t[n] and the corrected time t c [n], respectively, as: t[n] = n/f s and t c [n] = t[n]-dt[n]; B.b) From the pairs (t[n],y[n]) and using the corrected time t c [n], estimating the signal in the corrected time scale y c [n] by interpolation.
The method according to any of the previous claims, wherein the cancellation of the harmonics of the QPI from the signal y c [n] in the corrected time scale in step C, comprises the following steps: C.a) Obtaining the spectrum of the signal in the corrected time scale Y c [m] by applying a DFT to the signal in the corrected time scale y c [n]. C.b) Defining a spectral threshold df as the maximum expected semi-width of the harmonics after the cancellation of the time drift, the spectral threshold df being at least half of the inverse of the duration of the signal y[n], and removing the harmonics of the QPI by making null those spectral components in the spectrum Y c [m] at a spectral distance to the frequency of each harmonic k, k·f 0 , smaller than the threshold df, providing a spectrum in the corrected time scale X c [m];. C.c) Obtaining the signal in the corrected time scale x c [n] by applying an inverse discrete Fourier transform, iDFT, to the spectrum X c [m].
The method according to any of the previous claims, wherein the transformation of the signal from the corrected time scale x c [n] to the original time scale x[n] in step D is obtained by interpolation from the pairs (t c [n],x c [n]) and using the original time values t[n], where, t[n] = n/f s and t c [n] = t[n]-dt[n].
The method according to any of the previous claims, wherein the compensation of the estimated time drift in step B and/or the transformation of the signal from the corrected time scale to the original time scale in step D is based on cubic spline interpolation.
The method according to any of the previous claims, wherein the method is performed as an off-line algorithm, that is, each step of the method is performed after the previous step is completed for the complete signal to be processed.
The method according to any of the previous claims, wherein the method is performed as an on-line algorithm, that is each step is applied up to the current available samples of its input signal with some delay depending on the cumulated delay caused in each step.
The method according to claim 11, wherein the on-line version is implemented by segmentation of the input signal into portions and by applying the off-line version of the procedure to each portion of the input signal.
Computer program comprising instructions for making a computer or any other information processing system carry out the method according to any of the claims 1 to 12.
Computer-readable storage medium comprising program instructions capable of making a computer to carry out the method according to any of the claims 1 to 12.
System for acquisition of an electrical signal including the means to carry out the procedure for QPI reduction of the invention, the system comprising: means for acquiring electrical signals; means for analog-to-digital conversion of the acquired electrical signal obtaining digital input signal y[n]; processing means capable to carry out the procedure for QPI reduction of the invention according to any of the claims 1 to 12; and means for storage, transmission, processing and/or displaying the output signal of the method.

Description

FIELD OF THE INVENTION The present invention belongs to the field of noise reduction techniques in electronic instrumentation for acquisition of electrical signals (like electrocardiograms -ECG-, electroencephalograms -EEG-, other biopotentials or any other electrical signals) and more particularly to a method and a system for removing or reducing, from electrical signals, quasi-periodic interference (QPI) such as the power line interference (PLI). STATE OF THE ART Electrical signals are usually affected by quasi periodic interferences (QPI). For example, power line interference (PLI) often degrades low amplitude electrical signals acquired by recording instruments, in spite of different amplifier and shielding designs or proper grounding methods. PLI is a quasi-periodic interference associated to power line (or mains), with nominal fundamental frequency at either 50 Hz or 60 Hz depending on the geographical area. The PLI is observed as a 50 or 60 Hz periodic oscillation superimposed to the signal of interest when the signal is represented as a function of the time. The PLI can also be observed with spectral analysis, as a series of harmonics at the frequencies k·f0 (with k=1, 2, 3, etc.) being f0 the fundamental frequency of the power line (either 50 or 60 Hz). The problem of QPI and specifically of PLI is relevant in the acquisition of biopotentials (such as electrocardiogram -ECG-, electroencephalogram -EEG-, electromyogram - EMG-, etc.) or other low amplitude electrical signals, because usually the PLI severely degrades those signals. For this reason, several digital solutions are known in the art, aimed to remove or at least to reduce the PLI components from the digital recorded signal. For example, notch filters are applied to attenuate the frequency components around the nominal frequency (f0) and/or several harmonics (2·f0, 3·f0, etc.) of the PLI (for example document US9247911B2). However, notch filters can cause significant distortion to the recovered signals. Adaptive filters are also applied to adapt to fluctuations in the fundamental frequency and therefore to improve the cancelation of the PLI while reducing the distortion in the recovered signal (for example documents US8761867B2; WO2020197490A). Another group of methods include procedures for the estimation of the amplitude, frequency and phase of the PLI at one or several harmonics of the PLI, combined with digital subtraction procedures (for example documents US5278777A; US7894885B2). The efficiency of the methods for PLI reduction is mainly limited due to the fluctuation of the PLI frequency with respect to its nominal frequency. The fundamental frequency of the PLI fluctuates slowly (with typical frequency drifts in the range of tens to hundreds of milli-Hertz) and this causes an expansion of the frequency peaks in the spectrum. It is important to note that the frequency expansion of the harmonics associated to this frequency drift is proportional to the index of the harmonic (for example, a frequency drift of 80 mHz at f0=50 Hz, causes a drift of 1.6 Hz in the 20th harmonic at 1000 Hz). When methods based on notch filters are applied, the expansion of the harmonics constrains the design of the notch filters and causes important distortion in the signal of interest (if the removed bandwidth is wide) or inefficient PLI reduction (if the removed bandwidth is narrow). On the other hand, in digital subtraction methods, the frequency fluctuation makes the estimation of the PLI components inaccurate (because PLI cancellation is based on a fixed average frequency but PLI frequency fluctuates). Finally, methods based on adaptive filters are able to provide appropriate PLI reduction under fluctuating power line frequency, but only if frequency fluctuations are very slow (because if frequency fluctuation is fast, the frequency bands to be removed are wide and this causes important distortions in the filtered signal). Hence, there is a need for a robust and adaptive solution which effectively and precisely reduces QPI even under conditions of fluctuating frequency, without compromising the integrity of the original signal (signal of interest). SUMMARY OF THE INVENTION The present invention proposes a method and system which efficiently reduce the QPI with minimal distortion of the signal of interest, solving the above stated problems of the prior art techniques. In order to do it, the time drift associated with the frequency and phase drift of the QPI is estimated. Then the time scale is transformed in order to compensate the time drift (and consequently cancel the frequency and phase drift). After the compensation of the time drift, the harmonics of the QPI concentrate the energy at their respective nominal frequency (because in the compensated time scale the interference is not quasi-periodic but periodic), which enables an efficient QPI reduction either by using very narrow notch filters in the time domain or by canceling a few frequency compone