Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
  • G06F17/10—Complex mathematical operations
  • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
  • H04B1/06—Receivers
  • H04B1/10—Means associated with receiver for limiting or suppressing noise or interference
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L27/00—Modulated-carrier systems
  • H04L27/10—Frequency-modulated carrier systems, i.e. using frequency-shift keying
  • H04L27/14—Demodulator circuits; Receiver circuits
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L27/00—Modulated-carrier systems
  • H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
  • H04L27/22—Demodulator circuits; Receiver circuits
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L27/00—Modulated-carrier systems
  • H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
  • H04L27/22—Demodulator circuits; Receiver circuits
  • H04L27/233—Demodulator circuits; Receiver circuits using non-coherent demodulation
  • H04L27/2334—Demodulator circuits; Receiver circuits using non-coherent demodulation using filters

Definitions

• the technical field of the invention is that of the signal processing, and more particularly that of the reduction of the noise level in an electrical signal.
• a characteristic problem of the measurement of an electrical signal concerns the presence of noise, originating in particular from the source of the signal itself, or intrinsic to the amplifiers, present for example in the signal transmission paths.
• the noise is particularly troublesome when the signal to be measured is of low amplitude, of the order of magnitude of the noise. This problem is very widely encountered for measurements with high sensitivity, such as in turbulence measurements with a sensor (pitot tube or other) with capacitive, piezoresistive or optical readout, or for data transmission through channels with noise.
• a first method is that of averaging in the time domain, called "time averaging" in English. This method involves sampling a large number of times the signal to be measured. The beginning of a sampling sequence is triggered by a reference signal synchronized with the signal to be measured. The samples of a sequence form a sampled signal, or "piece,” of the original signal.
• the sampled signals, and therefore the noise they contain, are then averaged.
• the power of the noise decreases proportionally to the inverse of the number of averaged pieces; however, the signal is not affected by averaging.
• this first method requires repeated excitations of the system to be measured and a well-defined reference signal.
• a second method of reducing the noise level is that of averaging in the frequency domain, called spectrum averaging.
• the signal to be measured is sampled a large number of times.
• a spectrum of each sampled signal is calculated by transformation in the frequency domain. This is usually a discrete Fourier transform, also called DFT for "Discrete Fourier Transform" in English.
• DFT discrete Fourier Transform
• a third method consists in performing a cross-correlation, in English, between the outputs of different amplification channels connected to the source of the signal.
• the noise coming from the amplifiers comprises a non-correlated part, comprising voltage noise which is specific to each amplifier and invisible to the other amplifiers, and a correlated part, comprising noise current applied to the source by the counter-current. amplifier reaction and therefore visible by all amplifiers.
• Cross-correlation reduces the noise level by canceling the uncorrelated part of the noise, providing only a partial solution.
• cross-correlation can actually reduce the signal-to-noise ratio since the current noise of several amplifiers contributes to the result.
• this method is also not useful against the intrinsic noise of the sensor, which is also seen by all channels.
• the method according to the invention aims to solve the problems that have just been exposed by proposing a method of reducing the noise level in an electrical signal, and in particular in a modulated electrical signal, which is not necessarily synchronized with a reference signal.
• the present invention also aims to reduce the current noise from the feedback of an amplifier and the intrinsic noise of a sensor, such as thermal noise.
• a first aspect of the invention therefore relates to a noise reduction method in a modulated electrical signal having a carrier frequency, the method comprising the following steps:
• the modulated signal includes a signal component, which corresponds to the signal of interest, and a noise component, which is generally not desired.
• signal and noise components are found in the spectrum of the modulated signal, i.e. in the upper and lower sideband.
• the signal component in the upper sideband and the signal component in the lower sideband are perfectly correlated.
• the noise components in these sidebands are generally not correlated.
• the power spectrum of each piece of the modulated signal comprises a set of values, each value of the power spectrum being calculated by multiplying a first value of the upper sideband and a second value. value of the lower sideband equidistant from the carrier frequency.
• the value assumed by the power spectrum at any frequency ⁇ f is calculated by multiplying the values taken by the spectrum at the frequency f 0 + ⁇ f and at the frequency f 0 - ⁇ f.
• the step of calculating the power spectrum of each piece of the modulated signal comprises the following operations:
• the value assumed by the power spectrum at any frequency ⁇ f is calculated by squaring the result of the sum of the values taken by the spectrum at the frequency f 0 + ⁇ f and at the frequency f 0 - ⁇ f.
• the noise reduction method according to the first aspect of the invention comprises a synchronous detection step of the modulated signal.
• 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.
• signal modulated from the values belonging to two distinct sidebands of the spectrum of said each piece of the modulated signal it is possible to improve the signal-to-noise ratio by calculating a larger number of power spectra.
• the spectrum of the modulated signal has four sidebands. Since two different sidebands can be correlated, the number of power spectra to be averaged 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 noise reduction device in a modulated electrical signal having a carrier frequency, the device comprising: means of acquisition in the time domain of the modulated signal so as to obtain a plurality of pieces of the modulated signal;
• the noise reduction device comprises synchronous detection means of the modulated signal.
• the acquisition means comprise several acquisition channels, each acquisition channel being dedicated to a carrier frequency of the modulated signal.
• FIG. 1 shows a block diagram of a noise reduction method in a modulated signal, according to a preferred embodiment of the invention
• FIG. 2 represents a functional diagram of the preferred mode of implementation of the method of FIG. 1;
• FIG. 3 diagrammatically represents a first exemplary implementation context of the method of FIG. 1 for reducing the noise in a modulated signal simulated by a signal generator;
• FIG. 4 represents the spectral power of the signal of FIG. 3, measured with the method of the invention and with the averaging method in the spectral domain of the prior art;
• FIG. 5 represents, as a function of the number of pieces used in the calculation of the average, the power of the noise contained in the signal of FIG. 3 measured with the method of the invention
• FIG. 6 diagrammatically represents a second exemplary implementation context of the method of FIG. 1 for reducing the noise in a modulated signal originating from a capacitive sensor installed in a Pitot tube;
• FIG. 7 represents, as a function of the number of pieces used in the calculation of the average, the variation of the noise level in the spectral power of the signal of FIG.
• the present invention is intended to provide a method for reducing the noise level in an electrical signal. This method is particularly applicable to situations in which a useful signal modulates a carrier signal. The present invention is also particularly effective for unpredictable signals, i.e., signals that are not synchronized with a reference signal.
• FIG. 1 A schematic diagram of a preferred mode of implementation of the method of the invention is illustrated in FIG. A functional diagram of this preferred embodiment is shown in Figure 2. Figures 1 and 2 are described together.
• FIG. 1 shows a modulated electrical signal a (t) resulting from a modulation of a carrier signal c (t) by a useful signal u (t), also called a modulating signal u (t).
• a useful signal u (t) also called a modulating signal u (t).
• the useful signal u (t) represents variations of the measured physical quantity.
• the variations of the physical quantity modify a value of capacitance, resistance, inductance, position, pressure, or light intensity of the sensor, depending on 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 FIG. 1).
• a variation of position, a variation of pressure or a variation of light intensity is easily convertible into a variation of capacitance, resistance or inductance.
• Signal modulation is also frequently used in telecommunication, in particular for transmitting information, initially contained in the useful signal u (t), inside the carrier signal c (t) which can be more easily transmitted physically.
• the modulated signal a (t), which is in the time domain, is digitized during an acquisition step E1.
• 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 performed on a finite number, denoted 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 digital representation k, also called piece k, of the modulated signal a (t), where k is an integer between 1 and N.
• a spectrum A k of each piece k of the modulated signal a (t) is then 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.
• the transformation in the frequency domain is for example a discrete Fourier transform, also called DFT for "Discrete Fourier Transform" in English.
• the discrete Fourier transform can be implemented using a Fast Fourier Transform algorithm, called FFT for "Fast Fourier Transform" in English.
• the carrier signal c (t) has a carrier frequency f 0 .
• the spectrum A k of the modulated signal a (t) comprises an upper lateral band BLS and a lower lateral band BLI disposed on either side of the carrier frequency f 0 .
• the upper sideband BLS extends over a frequency range greater than or equal to the carrier frequency f 0
• the lower sideband BLI extends over a frequency range less than or equal to the carrier frequency f 0
• the band upper BLS and the lower lateral band BLI are symmetrical with respect to the carrier frequency f 0 .
• 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.
• the amplitude modulation of a monochromatic sinusoidal carrier signal c (t) of carrier frequency f 0 by a useful signal u (t) of frequency f s created, in theory, an upper sideband BLS at the frequency f 0 + f s and a lower sideband BLI at the frequency f 0 - f s -
• the sidebands BLS, BLI are peaks, each being located at a single frequency.
• the spectrum A k of the modulated signal a (t) comprises a first set of values, which are hereinafter called “first values”, belonging to the upper lateral band BLS and a second set of values, which are subsequently called “ second values "belonging to the lower lateral band BLI.
• a power spectrum is calculated, during a step E3, for each piece of the modulated signal a (t).
• the values of the power spectrum of a piece k of the modulated signal a (t) are calculated by multiplying the first values of the upper sideband BLS in pairs by the second values of the band. lower side BLI of the spectrum A k of this piece k.
• These multiplications are effected symmetrically with respect to the carrier frequency f 0 , that is to say that the value of the power spectrum at a given frequency ⁇ f is the result of the multiplication of the value of the spectrum at the frequency f 0 + ⁇ f by the value of the spectrum at the frequency f 0 - ⁇ f.
• This type of calculation is also called cross-correlation between the upper sideband and the lower sideband.
• P M W (A k (f 0 ⁇ ⁇ f) A k (f Q + ⁇ f). (1 ) where f 0 is the carrier frequency, ⁇ f is any frequency, A k is the Fourier transform of a piece k of the modulated signal a (t), where k is an integer between 1 and N, where N is the number of pieces of the modulated signal a (t) acquired, and the chevrons (> symbolize the calculation of the arithmetic mean of the power spectra of the N pieces of the modulated signal a (t).
• phase of the Fourier transform of the modulated signal a (t) is random and depends on the moment when the acquisition begins.
• arg (F f Q ) is the phase of the carrier signal c (t), is introduced in equation (1).
• the parties signal S k sidebands BLS, BLI same spectrum A k are perfectly correlated noise while the portions B k of these side bands BLS, BLI are generally uncorrelated. This applies to all sources of additive noise such as sources of noise current and voltage amplifiers, present in particular in the acquisition or transmission channels of the signals, or the additive noise of the sensor C.
• 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 the noise coming from non-linear noise sources. Therefore, by averaging over a sufficiently long duration, it is theoretically possible to lower the noise level to a desired value.
• the cross-correlation of the noise part b (t) of the modulated signal a (t) decreases with the number of pieces N used for calculating the average of the power spectra, and until a level is reached. noise corresponding to a portion of the initial noise, the noise of this portion being correlated.
• excess noise For resistance, this is called excess noise, or "excess noise” in English, the resistance that is proportional to the voltage applied across the resistance and increases with frequency.
• the value of the excess noise which depends essentially on the technology used to manufacture the resistance, is typically between 1 and 10 -4 ⁇ per volt applied per decade, whereas the capacitances and inductances have no known limit, the noise level can be continuously reduced.
• the modulated signal is subjected to a synchronous detection step E5 of the modulated signal a (t).
• the spectra A k of the pieces of the modulated signal a (t) are no longer centered on the carrier frequency f 0 but on the zero frequency.
• the spectra A k are shifted from the carrier frequency f 0 to 0.
• the upper sideband BLS corresponds to the positive frequencies
• the lower sideband BLI corresponds to the negative frequencies.
• a signal in phase i (t) is obtained with the carrier signal c (t), also called “in-phase signal” in English, and a signal in phase quadrature q (t) with the carrier signal c (t), that is to say turned 90 °, also called “quadrature signal” in English.
• the step E5 of synchronous detection is for example carried out by multiplying the modulated signal a (t) by ⁇ (2 ⁇ 0 ⁇ ) to obtain the signal in phase, and by ⁇ (2 ⁇ 0 ⁇ ) to obtain the signal in quadrature phase these two signals are then subjected to low frequency filtering.
• the 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 P M.
• synchronous detection we work with the complex signal z (t) of the modulated signal a (t) obtained from the following equation:
• the average power spectrum P M is then calculated according to the following equation, variant of equation (1):
• the synchronous detection facilitates the calculation of averages, for example by filtering. Indeed, it is very difficult to achieve a bandpass filter with a narrow band around a high carrier frequency. By cons it is very easy to achieve a bandpass filter with a narrow band around 0.
• the modulated signal a (t) has several carrier frequencies.
• the spectra A k of the pieces of the modulated signal a (t) comprise an upper lateral band BLS and a lower lateral band BLI with respect to each carrier frequency.
• several power spectra are calculated for a piece k of the modulated signal a (t) from two distinct sidebands of the spectrum A k of this piece k.
• the noise reduction is accelerated because for the same number of pieces N of the modulated signal a (t), the number of power spectra to be averaged is increased.
• the amplitude modulation of a sinusoidal carrier signal c (t) having two carrier frequencies f 1 and f 2 by a useful signal u (t) of frequency f s creates two sidebands higher than the frequencies f + f s and f 2 + f s, and two lower sidebands respectively to the frequencies f - f s and f 2 - f s -
• These sidebands can be correlated pairs according to equation (1).
• FIG. 3 schematically represents a first exemplary context of implementation of the noise reduction method of the invention in the modulated signal a (t) whose signal part s (t) and the noise part b (t) are simulated respectively by a first signal generator 301 and a second signal generator 302.
• the first signal generator 301 produces a sinusoidal signal with a carrier frequency equal to 50 kHz amplitude modulated by a random noise signal having a bandwidth less than 50 kHz. 600 Hz.
• the second signal generator 302 produces a white noise signal b (t) which is added to the signal portion s (t) to form the noisy modulated signal a (t). Since the white noise signal b (t) is a random noise, the noisy modulated signal (t) thus obtained makes it possible to simulate a chaotic useful signal.
• FIG. 3 A first embodiment of a noise reduction device 340 according to the invention, capable of implementing the method described above, is illustrated in FIG. 3.
• the device comprises means 341 for acquiring the modulated signal a (FIG. t), such as an analog-to-digital converter, calculation means 342 of the spectra A k of the pieces of the modulated signal a (t) by transformation in the frequency domain, calculation means 343 of the power spectrum P k of each piece of the modulated signal a (t) and averaging means 344 of the average PM (ie the average power spectrum P M ) of the power spectra P k .
• the different calculation means 342, 343, 344 are for example implemented in the form of computer programs recorded on a memory medium.
• the modulated signal a (t) is sampled with a sampling frequency of 500 kHz, and then cut into pieces of a duration equal to 1 s.
• the noise reduction device 330 comprises synchronous detection means 345 arranged on an acquisition channel 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 quadrature phase q (t) with the carrier signal c (t).
• FIG. 4 graphically represents the average power spectrum P M of the modulated signal a (t), expressed in arbitrary unit, as a function of frequency.
• a first pair of curves P M n, PMI 2 is obtained with the method of the invention, the number of pieces N of the modulated signal a (t) used in the calculation of the average being respectively equal to 100 and 14000.
• a second pair PM21, PM22 is obtained with the averaging method in the frequency domain of the prior art, the number of pieces N of the modulated signal a (t) used in the calculation of the average being also respectively equal to 100 and 14000.
• the values of the average power spectrum P M do not change with the number of pieces N averaged (100 or 14000).
• the value of the white noise is also not modified by the number of pieces N for the higher frequencies (above 5 kHz) when the average power spectrum P M is calculated with the averaging method in the frequency domain.
• the level of noise in the average power spectrum P M calculated with the method of the invention continues to decrease revealing a structure with peaks of erroneous amplitudes. These peaks probably due to the nonlinearities of the CH acquisition channel.
• the noise level decreases with the number of averaged N pieces.
• the spectral density of the DSPB noise as a function of the number of averaged pieces N is illustrated in FIG. 5.
• the decreasing line 502 shows the theoretical decay of the noise level which is proportional to 1 / VN.
• FIG. 6 schematically represents a second exemplary context of implementation of the noise reduction method of the invention in the modulated signal a (t) coming from a pitot tube comprising a capacitive sensor 610 measuring the dynamic speed of flow of a fluid.
• the modulated signal a (t) is proportional to a pressure difference between two parts of the tube, one being perpendicular to the fluid flow and the other being parallel to the fluid flow. This pressure difference, or dynamic pressure, displaces a flexible membrane 61 1 of the capacitive sensor 610, thus varying a capacitance value between the membrane is a pair of electrodes 612 disposed on each side of the membrane 61 1.
• FIG. 6 shows a second embodiment of a noise reduction device 640 in which the acquisition means 341 comprise a first acquisition channel CH1 dedicated to the carrier frequency f- ⁇ , and to a second channel of acquisition CH2 acquisition dedicated to the carrier frequency f 2 .
• Each acquisition channel CH1, CH2 is equipped with synchronous detection means 345 at the output of which phase (t) and phase quadrature (q) signals are obtained with the modulated signal a (t) for the carrier frequency f - ⁇ , and the signals in phase i 2 (t) and in phase quadrature q 2 (t) with the modulated signal a (t) for the carrier frequency f 2 .
• the spectral density of the noise DSPB as a function of the number of averaged pieces N is illustrated in FIG. 7.
• the spectral density of the noise DSP B decreases by a ratio of about 40.
• decreasing right 702 shows the theoretical decay of the noise level which is proportional to 1 / VN.
• f 0 is the carrier frequency
• ⁇ f is any frequency
• a k is the Fourier transform of a piece k of the modulated signal a (t)
• k is an integer between 1 and N, N being the number of pieces of the modulated signal a (t) acquired
• the chevrons > symbolize the calculation of the average of the power spectra of the N pieces of the modulated signal a (t).
• the synchronous detection means are set to obtain 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: + g (t) i (t) - g (t) 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 P M is then calculated by averaging the product of the spectra of the signals g (t) and h (t), according to the following equation:
• 3 ⁇ 4 (5) (G fc (5) .3 ⁇ 4 (5)> (6)
• ⁇ f is any frequency
• G k and H k are the Fourier transforms of the signals g (t) and h (t), k being an integer between 1 and N, where N is the number of pieces of the signals g (t) and h (t) acquired, and the chevrons (> symbolize the calculation of the average of the power spectra of the N pieces of the signals g (t) and h (t).

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