Patent Application
20190138572
The technical field of the invention is that of signal processing and more specifically that of reducing the noise level in an electrical signal.
A characteristic problem of the measurement of an electrical signal concerns the presence of noise, notably coming from the source of the signal itself, or instead intrinsic to the amplifiers, present for example in the signal transmission paths. Noise is particularly bothersome when the signal to measure is of low amplitude, of the order of magnitude of the noise. This problem is encountered very widely for measurements having high sensitivity, as in measurements of turbulence with a sensor (Pitot tube or other) with capacitive, piezoresistive or optical reading, or for the transmission of data through paths comprising noise.
Different noise level reduction methods exist, a first method is that of averaging in the time domain, known as “time averaging”. This method consists in sampling the signal to measure a large number of times. The start of a sampling sequence is triggered by a reference signal synchronised with the signal to measure. The samples of a sequence form a sampled signal, or “piece”, of the original signal.
The sampled signals, and thus the noise that they contain, are next averaged. The power of the noise decreases proportionally to the inverse of the number of averaged pieces; on the other hand the signal is not affected by averaging. However, this first method requires repeated excitations of the system to measure and a well-defined reference signal.
A second noise level reduction method is that of averaging in the frequency domain, known as “spectrum averaging”. In the same way as described previously, the signal to measure is sampled a large number of times. Next, a spectrum of each sampled signal is calculated by transformation in the frequency domain. It is generally a discrete Fourier transform, also called DFT. Finally, the set of spectra is averaged.
These operations are carried out a first time with the signal to measure and a second time without the signal. Two average spectra are then obtained, the difference between these two spectra corresponding to the spectrum of the signal to measure. This second method thus requires the possibility of carrying out the measurements with and without the signal, that is to say being able to activate and de-activate the signal in a controlled manner. In theory, an average calculated over a long duration enables measurements having good resolution. However, the resolution is in reality limited by drift, notably of the levels of noise and gains of the amplifiers, when the signal is activated and when the signal is de-activated.
A third method consists in carrying out a cross-correlation between the outputs of different amplification paths connected to the source of the signal. Indeed, the noise coming from the amplifiers comprises a non-correlated part, including voltage noise which is specific to each amplifier and invisible for the other amplifiers, and a correlated part, including current noise applied to the source by the counter-reaction of the amplifier and thus visible by all the amplifiers.
Cross-correlation makes it possible to reduce the noise level by cancelling the non-correlated part of the noise, which only provides a partial solution. Furthermore, when current noise is preponderant, cross-correlation can in fact reduce the signal to noise ratio since the current noises of several amplifiers contribute to the result. In addition, if the source of the signal is a sensor, this method is not useful either against the intrinsic noise of the sensor, which is also seen by all the paths.
The method according to the invention aims to resolve the problems that have been described by proposing a method for reducing the noise level in an electrical signal, and in particular in a modulated electrical signal, which is not necessarily synchronised with a reference signal. The present invention also aims to reduce the current noise coming from the counter-reaction of an amplifier as well as the intrinsic noise of a sensor, such as thermal noise.
A first aspect of the invention thus relates to a method for reducing noise in a modulated electrical signal having a carrier frequency, the method comprising the following steps:
The modulated signal comprises a signal component, which corresponds to the signal of interest, and a noise component, which is generally not desired. These signal and noise components are located in the spectrum of the modulated signal, that is to say in the upper sideband and in the lower sideband. The signal component in the upper sideband and the signal component in the lower sideband are perfectly correlated. On the other hand, the noise components in these sidebands are generally not correlated. By calculating the power spectra from the values of the spectrum of the modulated signal taken in the upper sideband and in the lower sideband, then by averaging these power spectra, the non-correlated noise components are eliminated. It is thereby possible to reduce the noise level while conserving the signal of interest.
In a preferential embodiment, the power spectrum of each piece of the modulated signal comprises a set of values, each value of the power spectrum being calculated by multiplication of a first value of the upper sideband and a second value of the lower sideband situated at equal distance from the carrier frequency. In other words, for a carrier frequency f0, the value that the power spectrum takes at any frequency δf is calculated by multiplying the values taken by the spectrum at the frequency f0+δf and at the frequency f0−δf.
In an alternative embodiment, the step of calculating the power spectrum of each piece of the modulated signal comprises the following operations:
Preferably, the method for reducing noise according to the first aspect of the invention comprises a step of synchronous detection of the modulated signal.
Advantageously, the modulated signal has a plurality of carrier frequencies, the spectrum of each piece of the modulated signal comprising an upper sideband and a lower sideband for each carrier frequency of the modulated signal, a plurality of power spectra being calculated for each piece of the modulated signal from the values belonging to two distinct sidebands of the spectrum of said each piece of the modulated signal. Thus, at equal number of pieces of the modulated signal, it is possible to improve the signal to noise ratio by calculating a larger number of power spectra.
For example, for a modulated signal having two carrier frequencies, the spectrum of the modulated signal comprises four sidebands. Two different sidebands being able to be correlated, the number of power spectra to average is multiplied by 6. Thus the signal to noise ratio is substantially improved.
The modulated signal results for example from an amplitude modulation, a frequency modulation or a phase modulation.
A second aspect of the invention relates to a device for reducing noise in a modulated electrical signal having a carrier frequency, the device comprising:
Preferably, the noise reduction device according to the second aspect of the invention comprises means for synchronous detection of the modulated signal.
Advantageously, the acquisition means comprise several acquisition paths, each acquisition path being dedicated to a carrier frequency of the modulated signal.
The invention and its different applications will be better understood on reading the description that follows and by examining the figures that accompany it.
The invention and its different applications will be better understood on reading the description that follows and by examining the figures that accompany it, among which:
The figures are only presented for indicative purposes and in no way limit the invention.
For greater clarity, identical or similar elements are marked by identical reference signs in all of the figures.
The aim of the present invention is to propose a method intended to reduce the noise level in an electrical signal. This method applies particularly to situations in which a useful signal modulates a carrier signal. The present invention is also particularly efficient for unpredictable signals, that is to say signals that are not synchronised with a reference signal.
A basic diagram of a preferential embodiment of the method of the invention is illustrated in
Indeed, the variations in the physical quantity modify a capacitance, resistance, inductance, position, pressure, or light intensity value of the sensor, according to the type of sensor chosen, which produces the modulated signal a(t) at the output of the sensor C (represented by a variable capacitance in
Signal modulation is also frequently used in telecommunications, notably for transmitting information, initially contained in the useful signal u(t), inside the carrier signal c(t), which may be more easily transmitted physically.
The modulated signal a(t), which lies in the time domain, is digitized during an acquisition step E1. To do so, the modulated signal a(t) is sampled, preferably at constant pitch, that is to say with a fixed sampling frequency. The sampling of the modulated signal a(t) is carried out on a finite number, noted N in the remainder of the description, of time intervals. The latter generally have identical durations. The samples acquired in each time interval form a numerical representation k, also called piece k, of the modulated signal a(t), k being an integer comprised between 1 and N.
A spectrum Ak of each piece k of the modulated signal a(t) is next calculated, during a step E2, by transformation in the frequency domain. The pieces of the modulated signal a(t) are not continuous signals but successions of discrete values. Hence, the transformation in the frequency domain is for example a discrete Fourier transform, also called DFT. The discrete Fourier transform may be implemented using an FFT (fast Fourier transform) algorithm.
The carrier signal c(t) has a carrier frequency f0. The spectrum Ak of the modulated signal a(t) comprises an upper sideband BLS and a lower sideband BLI arranged on either side of the carrier frequency f0. The upper sideband BLS extends over a range of frequencies greater than or equal to the carrier frequency f0, and the lower sideband BLI extends over a range of frequencies less than or equal to the carrier frequency f0. The upper sideband BLS and the lower sideband BLI are symmetrical with respect to the carrier frequency f0.
The modulation of the carrier signal c(t) by the useful signal u(t) may be an amplitude modulation, a frequency modulation, a phase modulation or any other type of modulation producing two sidebands in the frequency domain.
For example, the amplitude modulation of a monochromatic sinusoidal carrier signal c(t) of carrier frequency f0 by a useful signal u(t) of frequency fs, creates, in theory, an upper sideband BLS at the frequency f0+fs and a lower sideband BLI at the frequency f0−fs. In this theoretical case, the sidebands BLS, BLI are peaks, each being situated at a single frequency.
The spectrum Ak of the modulated signal a(t) comprises a first set of values, which are hereafter called “first values”, belonging to the upper sideband BLS and a second set of values, which are hereafter called “second values”, belonging to the lower sideband BLI.
After the step E2 of calculating the spectra Ak of the pieces of the modulated signal a(t), a power spectrum is calculated, during a step E3, for each piece of the modulated signal a(t).
In this preferential embodiment, the values of the power spectrum of a piece k of the modulated signal a(t) are calculated by multiplying two by two the first values of the upper sideband BLS by the second values of the lower sideband BLI of the spectrum Ak of this piece k. These multiplications are carried out in a symmetrical manner with respect to the carrier frequency f0, that is to say that the value of the power spectrum at a given frequency δf is the result of the multiplication of the value of the spectrum at the frequency f0+δf by the value of the spectrum at the frequency f0−δf. This type of calculation is also called cross-correlation between the upper sideband and the lower sideband.
An average of the power spectra is next calculated during a step E4. An average power spectrum is thereby obtained. From a mathematical viewpoint, the average power spectrum PM is calculated according to the following equation:
P
M(δf)=(Ak(f0−δf)·Ak(f0+δf)ei.arg(A (1)
where f0 is the carrier frequency, δf is any frequency, Ak is the Fourier transform of a piece k of the modulated signal a(t), k being an integer comprised between 1 and N, N being the number of pieces of the modulated signal a(t) acquired, and the chevrons symbolise the calculation of the arithmetic average of the power spectra of the N pieces of the modulated signal a(t).
The phase of the Fourier transform of the modulated signal a(t) is random and depends on the moment at which the acquisition starts. To compensate this, the term e−i.arg(F(f
The modulated signal a(t) comprises a signal part s(t) and a noise part b(t) such that:
a(t)=s(t)+b(t) (2)
In this case, the spectra Ak of the modulated signal a(t) each comprise a signal part Sk and a noise part Bk such that:
A
k
=S
k
+B
k (3)
The signal parts Sk of the sidebands BLS, BLI of a same spectrum Ak are perfectly correlated whereas the noise parts Bk of these same sidebands BLS, BLI are generally not correlated. This applies to all additive noise sources such as current and voltage noise sources of amplifiers, present notably in the acquisition or transmission paths of the signals, or instead the additive noise of the sensor C.
Thus, thanks to the invention, the signal part s(t) of the modulated signal a(t) is preserved and the noise part b(t) is eliminated, with the exception of noise coming from non-linear noise sources. Consequently, by averaging over a sufficiently long duration, it is theoretically possible to lower the noise level down to a desired value. However, in practice, cross-correlation of the noise part b(t) of the modulated signal a(t) decreases with the number of pieces N used for the calculation of the average of the power spectra, and does so until reaching a noise level that corresponds to a portion of the initial noise, the noise of this portion being correlated.
For a resistance, it involves what is known as excess noise of the resistance, which is proportional to the voltage applied to the terminals of the resistance and which increases with frequency. The excess noise value, which essentially depends on the technology used to manufacture the resistance, is typically comprised between 1 and 10−4 μV per volt applied per decade. On the other hand, the capacitances and the inductances do not have known limits, the noise level being able to be continually reduced.
Furthermore, it should be noted that the method according to the invention does not require any reference or triggering signal.
Advantageously, before the acquisition step E2, the modulated signal is subjected to a step E5 of synchronous detection of the modulated signal a(t). Thus, the spectra Ak of the pieces of the modulated signal a(t) are not centred either on the carrier frequency f0 but on the zero frequency. The spectra Ak are shifted from the carrier frequency f0 to 0. In this case, the upper sideband BLS corresponds to positive frequencies and the lower sideband BLI corresponds to negative frequencies.
At the output of the synchronous detection, a signal in phase i(t) with the carrier signal c(t), also called “in-phase signal”, and a signal in phase quadrature q(t) with the carrier signal c(t), that is to say turned by 90°, also called “quadrature signal” are obtained. To be able to calculate a spectrum at negative frequencies, it is important to conserve these two signals in phase and in quadrature.
The step E5 of synchronous detection is for example carried out by multiplying the modulated signal a(t) by cos(2πf0t) to obtain the signal in phase, and by sin(2πf0t) to obtain the signal in phase quadrature, these two signals next being subjected to a low frequency filtering.
Synchronous detection makes it possible to fix the phase of the Fourier transform of the modulated signal a(t), which facilitates the calculation of the average power spectrum PM. When synchronous detection is used, one works with the complex signal z(t) of the modulated signal a(t) obtained from the following equation:
z(t)=i(t)+j·q(t) (4)
The average power spectrum PM is then calculated according to the following equation, a variant of equation (1):
P
M(δf)=Zk(−δf)·Zk(+δf)
(1′)
where Zk is the Fourier transform of a piece k of the complex signal z(t). It is to be noted that, due to the synchronous detection, the frequencies f0−δf and f0+δf of the equation (1) become −δf and +δf because the spectra Zk of the complex signal z(t) are displaced from the carrier frequency f0 to 0.
In addition, synchronous detection makes it possible to facilitate the calculation of averages, for example carried out by filtering. Indeed, it is very difficult to realise a band pass filter with a narrow band around a high carrier frequency. Conversely, it is very easy to realise a band pass filter with a narrow band around 0.
In an alternative embodiment, the modulated signal a(t) has several carrier frequencies. In this case, the spectra Ak of the pieces of the modulated signal a(t) comprise an upper sideband BLS and a lower sideband BLI with respect to each carrier frequency. Advantageously, several power spectra are calculated for a piece k of the modulated signal a(t) from two distinct sidebands of the spectrum Ak of this piece k. Thus, the reduction in noise is accelerated because for a same number of pieces N of the modulated signal a(t), the number of power spectra to average is increased.
For example, the amplitude modulation of a sinusoidal carrier signal c(t) having two carrier frequencies f1 and f2 by a useful signal u(t) of frequency fs creates two upper sidebands respectively at the frequencies f1+fs and f2+fs, and two lower sidebands respectively at the frequencies f1−fs and f2−fs. These sidebands may be correlated two by two according to equation (1).
However, when the upper sideband situated at the frequency f1+fs is correlated with the upper sideband situated at the frequency f2+fs, or when the lower sideband situated at the frequency f1−fs is correlated with the lower sideband situated at the frequency f2−fs, it is necessary to consider the complex conjugated value of one of the two sidebands. For each piece k of the modulated signal a(t), it is then possible to obtain up to 6 power spectra by carrying out the following products:
A
k(f1−fS)·Ak(f1+fS) (a)
A
k(f1−fS)·Ak(f2+fS) (c)
A
k(f1−fS)·Ak(f2−fS) (b)
A
k(f2−fS)·Ak(f2+fS) (d)
A
k(f2−fS)·Ak(f1+fS) (e)
A
k(f1+fS)·Ak*(f2+fS) (f)
where A is the conjugated spectrum of the spectrum Ak.
Indeed, it is sought to obtain the square of a complex value, which is normally calculated by the multiplication of the complex value and its conjugated value (or in mathematical terms: X.X*, where X is a complex value and X* is its conjugated value).
However, the Fourier transform of the modulated signal, for example in amplitude modulation, has the following property:
A
k(f1−fS)=Ak(f1+fS)
The products (a) and (d) are thus deduced therefrom. Similarly, by considering the two carriers, and by correcting the phase difference between the carriers, this gives:
A
k(f1−fS)=Ak*(f2+fS)
The products (c) and (e) are thus deduced therefrom. Conversely, in order to correlate together the sidebands situated on the same side of the carriers (i.e. the upper sideband sets or the lower sideband sets), it is necessary to take the conjugated value of one of the two complex values to obtain a squaring. The products (b) and (f) are thus deduced therefrom.
A first embodiment of a noise reduction device 340 according to the invention, able to implement the method described previously, is illustrated in
In this first example, the modulated signal a(t) is sampled with a sampling frequency of 500 kHz, then cut into pieces of a duration equal to is.
Advantageously, the noise reduction device 330 comprises means for synchronous detection 345 arranged on an acquisition path CH of the acquisition means 341. The synchronous detection means comprise a first output for the signal in phase i(t) with the carrier signal c(t) and a second output for the signal in phase quadrature q(t) with the carrier signal c(t).
It is to be noted that, for low frequencies, the values of the average power spectrum PM do not change with the number of averaged pieces N (100 or 14000). The white noise value is not modified either by the number of pieces N for the highest frequencies (greater than 5 kHz) when the average power spectrum PM is calculated with the method of averaging in the frequency domain. However, the noise level of the average power spectrum PM calculated with the method of the invention continues to decrease while revealing a structure with erroneous amplitude peaks. These peaks are probably due to non-linearities of the acquisition path CH. The noise level decreases with the number of averaged pieces N.
The spectral density of the noise DSPB as a function of the number of averaged pieces N is illustrated in
An excitation is applied in antiphase to the electrodes 612 in such a way that when the membrane 611 is at rest, the modulated signal a(t) coming from the membrane 611 is approximately equal to zero. The displacements of the membrane 611 change the amplitude of the modulated signal a(t). It is thus an amplitude modulation.
In this example, two carrier frequencies f1 and f2, as well as two amplifiers 620 are used, in order to calculate the power spectra from 4 sidebands.
Similarly to the first example described, the spectral density of the noise DSPB as a function of the number of averaged pieces N is illustrated in
Naturally the invention is not limited to the embodiment described with reference to the figures and alternatives could be envisaged without going beyond the scope of the invention. To calculate the power spectrum of a piece of the modulated signal a(t), instead of multiplying the first values of the upper sideband by the second values of the lower sideband of the spectrum Ak of this piece, it is notably possible to calculate a unilateral spectrum by adding together the first values of the upper sideband BLS and the second values of the lower sideband BLI of the spectrum Ak of this piece then squaring the unilateral spectrum. From a mathematical viewpoint, the average power spectrum PM is then calculated according to the following equation:
P
M(δf)=(Ak(f0−δf)+Ak(f0+δf))2
(5)
where f0 is the carrier frequency, δf is any frequency, Ak is the Fourier transform of a piece k of the modulated signal a(t), k being an integer comprised between 1 and N, N being the number of pieces of the modulated signal a(t) acquired, and the chevrons symbolise the calculation of the average of the power spectra of the N pieces of the modulated signal a(t).
In another alternative embodiment, the means of synchronous detection are adjusted so as to obtain at the output two signals g(t) and h(t) having a phase difference of 45° with the carrier signal c(t), these two signals g(t) and h(t) being defined by the following equations:
where i(t) and q(t) are respectively the signals in phase and in phase quadrature with the carrier signal c(t). The average power spectrum PM is then calculated by averaging the product of the spectra of the signals g(t) and h(t), according to the following equation:
P
M(δf)=Gk(δf)·Hk(δf)
(6)
where δf is any frequency, Gk and Hk are the Fourier transforms of the signals g(t) and h(t), k being an integer comprised between 1 and N, N being the number of pieces of the signals g(t) and h(t) acquired, and the chevrons symbolise the calculation of the average of the power spectra of the N pieces of the signals g(t) and h(t).
| Number | Date | Country | Kind |
|---|---|---|---|
| 1653787 | Apr 2016 | FR | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/EP2017/060087 | 4/27/2017 | WO | 00 |
