CN108983136B - Waveform calibration method and device - Google Patents
Waveform calibration method and device Download PDFInfo
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- CN108983136B CN108983136B CN201810728336.8A CN201810728336A CN108983136B CN 108983136 B CN108983136 B CN 108983136B CN 201810728336 A CN201810728336 A CN 201810728336A CN 108983136 B CN108983136 B CN 108983136B
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- G01R35/005—Calibrating; Standards or reference devices, e.g. voltage or resistance standards, "golden" references
Abstract
The invention discloses a waveform calibration method and a waveform calibration device, which solve the problems that the waveform calibration is inaccurate and the calibration process is not qualified in the existing method and device. The method comprises the following steps: calibrating the electric pulse signal by using a standard waveform display instrument to obtain a standard pulse signal; measuring the standard pulse signal by using a waveform display instrument to be calibrated to obtain a measured signal; according to a cyclic convolution theory, obtaining an indeterminate equation of a transmission characteristic function of a waveform display instrument to be corrected; and solving an optimal solution for the ill-defined equation by adopting a regularization method according to the compensation operator to obtain an optimal regularization parameter and a calibration result. The device includes: the device comprises an optical fiber femtosecond laser, a photoelectric detector and a waveform display instrument to be calibrated; the photoelectric detector receives an optical pulse signal generated by the fiber femtosecond laser to generate an electric pulse signal; and the waveform display instrument to be calibrated receives the electric pulse signal and measures. The invention objectively and accurately realizes the deconvolution of the signal in the time domain.
Description
Technical Field
The invention relates to the field of pulse measurement, in particular to a waveform calibration method and a waveform calibration device.
Background
In the waveform calibration process in the field of pulse measurement, due to the existence of signal noise, a stable solution cannot be directly obtained in a frequency domain division deconvolution mode, and the method has the disadvantage of being ill-qualified. This inadequacy is mainly manifested in two aspects, on one hand, due to the limitation of objective conditions, that is, part of the known information of a given solution is often underdetermined or overdetermined, which results in that the solution is not unique or does not exist, and on the other hand, the solution of the inverse problem often has no continuous dependency on the input data. The traditional waveform calibration solving method firstly utilizes a filter to filter signal noise and then carries out frequency domain deconvolution, but due to the unknown of the noise, the bandwidth of the filter cannot be accurately selected, and the manual attempt has great subjectivity and is not accurate enough.
Disclosure of Invention
The invention provides a waveform calibration method and a waveform calibration device, which solve the problems that the waveform calibration is inaccurate and the calibration process is not qualified in the conventional method and device.
A method of waveform calibration, comprising the steps of: calibrating the electric pulse signal by using a standard waveform display instrument to obtain a standard pulse signal; measuring the standard pulse signal by using a waveform display instrument to be corrected to obtain a measurement result as a measured signal, wherein the measured signal is the convolution of the standard pulse signal and the transmission characteristic function of the waveform display instrument to be corrected; according to the cyclic convolution theory, obtaining an indeterminate equation of the transmission characteristic function of the waveform display instrument to be corrected as follows:
y＝Acx
wherein y is the measured signal, AcGenerating a cyclic matrix for the standard pulse signal, wherein x is a transmission characteristic function of the waveform display instrument to be corrected; and solving an optimal solution for the ill-defined equation by adopting a Tikhonov regularization method according to a compensation operator to obtain an optimal regularization parameter and a calibration result of the waveform display instrument to be calibrated, wherein the calibration result is the transmission characteristic function corresponding to the optimal regularization parameter.
Preferably, the step of solving an optimal solution for the ill-defined equation by using a Tikhonov regularization method according to the compensation operator to obtain an optimal regularization parameter and a calibration result of the transmission characteristic of the waveform display instrument to be calibrated further includes: according to the Tikhonov regularization method, obtaining a Tikhonov functional of the ill-defined equation as the sum of the square of a residual two-norm and the square of a solution two-norm multiplied by the regularization parameter, solving the optimal solution of the ill-defined equation to be equivalent to solving the minimum value of the Tikhonov functional, wherein the process of solving the minimum value of the Tikhonov functional is a first process:
wherein λ is the regularization parameter, AcA circulant matrix generated for the standard pulse signal, x being a transfer characteristic function of the waveform display instrument to be calibrated, y being the measured signal, L being the compensation operator,
is the Tikhonov functional, | Acx-y||2Is a stand forResidual two-norm, | Lx | | non-woven phosphor2Is the solution two norm; according to the Tikhonov regularization method, the minimum value of the Tikhonov functional is a solution of a second equation:
wherein, x (λ)opt) Is the minimum value, λ, of the Tikhonov functionaloptFor the optimal regularization parameter, AcA circulant matrix generated for the standard pulse signal, L being the compensation operator, y being the measured signal; obtaining a curve of the residual error second norm and the solution second norm along with the change of the regularization parameter, which is an L curve, according to the first equation and the second equation; deriving the curvature of the L curve, wherein the regularization parameter corresponding to the position with the derivative being zero is the optimal regularization parameter; and substituting the optimal regularization parameter into the second equation to obtain a calibration result of the waveform display instrument to be calibrated.
Further, the compensation operator is a second order difference operator
Preferably, the standard waveform display instrument is an oscilloscope, and the model is 86100C of Agilent.
Preferably, the waveform display instrument to be calibrated is an oscilloscope, and the model is 86117A of Agilent.
A waveform calibration device, comprising: the device comprises an optical fiber femtosecond laser, a photoelectric detector and a waveform display instrument to be calibrated; the optical fiber femtosecond laser is used for generating an optical pulse signal and a synchronous trigger signal; the photoelectric detector is used for receiving the optical pulse signal and generating the electrical pulse signal; and the waveform display instrument to be calibrated is used for receiving the synchronous trigger signal and the electric pulse signal and measuring the electric pulse signal.
Further, the apparatus further comprises: an attenuator; the attenuator is used for receiving the optical pulse signal, attenuating the optical pulse signal and outputting the attenuated optical pulse signal to the photoelectric detector.
Further, the apparatus further comprises: a computer; the computer is used for receiving the measurement result of the waveform display instrument to be corrected, processing data and sending a control signal to the waveform display instrument to be corrected.
Preferably, the fiber femtosecond laser and the attenuator are connected through a single-mode polarization-maintaining fiber.
The beneficial effects of the invention include: compared with the traditional method for filtering noise by using a filter, the method and the device provided by the invention can objectively and accurately realize deconvolution of signals in a time domain, obtain a stable and unique solution and effectively solve the problem of waveform calibration instability caused by noise.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a flowchart of an embodiment of a waveform calibration method;
FIG. 2 is a flowchart of an embodiment of a waveform calibration method including a regularization process;
FIG. 3 is an embodiment of a waveform calibration device;
FIG. 4 is a diagram of an embodiment of a waveform calibration apparatus including an attenuator and a computer.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the specific embodiments of the present invention and the accompanying drawings. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Since the 60 s of the 20 th century, in a variety of scientific and technical fields such as signal processing, remote sensing technology, pattern recognition, physical life science, material science, hydromechanics, industrial control and even economic decision-making, the problem of 'solving the input by the output reversely', which is known as 'mathematical physics reverse problem', is provided, most of the reverse problems are ill-posed, this inadequacy is mainly manifested in two ways, on the one hand, due to limitations in objective conditions, input data in inverse problems, that is, part of the known information of a given solution is often underdetermined or overdetermined, which results in that the solution is not unique or the solution does not exist, on the other hand, the solution of the inverse problem often has no continuous dependency on the input data, and for the inevitable measurement error in the input data, a method for solving the inverse problem by using the disturbance data to approximate a stable solution in a certain sense must be provided.
The technical solutions provided by the embodiments of the present invention are described in detail below with reference to the accompanying drawings.
Fig. 1 is a flowchart of a waveform calibration method according to an embodiment of the present invention, which includes the following steps:
and 101, calibrating the electric pulse signal by using a standard waveform display instrument to obtain a standard pulse signal.
In step 101, the electrical pulse signal is a known signal for calibrating the standard waveform display instrument.
It should be noted that the standard waveform display instrument may be an oscilloscope, a pulse signal generator, or other time domain waveform display instrument, and is not limited herein. For example, the standard waveform display instrument is an oscilloscope, the model is an Agilent 86100C or 86118 module, the working frequency is 70GHz, and the calibrated result of the electric pulse signal is that the 3dB bandwidth is 70.81 GHz.
And step 102, measuring the standard pulse signal by using a waveform display instrument to be corrected to obtain a measurement result which is a measured signal, wherein the measured signal is the convolution of the standard pulse signal and the transmission characteristic function of the waveform display instrument to be corrected.
In step 102, it should be noted that the waveform display apparatus to be calibrated may be an oscilloscope, a pulse signal generator, or other time domain waveform display apparatus, and is not particularly limited herein. For example, the waveform display instrument to be calibrated is an oscilloscope, the model is 86117A of Agilent, the working frequency is 50GHz, and the 3dB bandwidth of the measurement result of the electric pulse signal is 60.55 GHz.
In step 102, the measured signal is a convolution of the standard pulse signal and the transfer characteristic function of the waveform display apparatus to be calibrated, so that the transfer characteristic function of the waveform display apparatus to be calibrated is a deconvolution of the measured signal and the standard pulse signal.
103, according to a cyclic convolution theory, obtaining an indeterminate equation of the transmission characteristic function of the waveform display instrument to be corrected as follows:
y＝Acx (1)
wherein y is the measured signal, AcAnd generating a cyclic matrix for the standard pulse signal, wherein x is a transmission characteristic function of the waveform display instrument to be corrected.
In step 103, the transmission characteristic function of the waveform display apparatus to be calibrated is a column vector, and the measured signal is a column vector.
And 104, solving an optimal solution for the ill-defined equation by adopting a Tikhonov regularization method according to a compensation operator to obtain an optimal regularization parameter and a calibration result of the waveform display instrument to be calibrated, wherein the calibration result is the transmission characteristic function corresponding to the optimal regularization parameter.
Further, the compensation operator is a second order difference operator
And obtaining an optimal regularization parameter of 595.20 by adopting a Tikhonov regularization method, wherein the calibration result is a 3dB bandwidth of 58.27 GHz.
The method provided by the embodiment of the invention solves the problem of inappropriate waveform calibration by using a regularization method, is not limited by noise unknown, can realize signal deconvolution in a time domain to obtain a stable and unique solution, and can be widely applied to the fields of image classification, image segmentation, image generation, edge detection and the like which need deconvolution.
Fig. 2 is a flowchart of a waveform calibration method including a regularization process, where the flowchart of the calibration method provided in the embodiment of the present invention includes the regularization process, and specifically includes the following steps:
and 101, calibrating the electric pulse signal by using a standard waveform display instrument to obtain a standard pulse signal.
And step 102, measuring the standard pulse signal by using a waveform display instrument to be corrected to obtain a measurement result which is a measured signal, wherein the measured signal is the convolution of the standard pulse signal and the transmission characteristic function of the waveform display instrument to be corrected.
103, according to a cyclic convolution theory, obtaining an indeterminate equation of the transmission characteristic function of the waveform display instrument to be corrected as follows:
y＝Acx
wherein y is the measured signal, AcAnd generating a cyclic matrix for the standard pulse signal, wherein x is a transmission characteristic function of the waveform display instrument to be corrected.
Step 105, according to the Tikhonov regularization method, obtaining a Tikhonov functional of the ill-defined equation, which is the sum of the square of a residual two-norm and the square of a solution two-norm multiplied by the square of regularization parameters, solving an optimal solution for the ill-defined equation equivalent to solving a minimum value for the Tikhonov functional, wherein the process of solving the minimum value for the Tikhonov functional is a first process:
wherein λ is the regularization parameter, AcA circulant matrix generated for the standard pulse signal, x being a transfer characteristic function of the waveform display instrument to be calibrated, y being the measured signal, L being the compensation operator,
is the Tikhonov functional, | Acx-y||2Is the residual two-norm, | Lx | | non-woven phosphor2Is the solution two norm.
It should be noted that, in the embodiment of the present invention, the compensation operator is a second-order difference operator
Other compensation operators may be used, and are not particularly limited herein.
wherein, x (λ)opt) Is the minimum value, λ, of the Tikhonov functionaloptFor the optimal regularization parameter, AcAnd a circulant matrix generated for the standard pulse signal, L being the compensation operator and y being the measured signal.
And 107, obtaining a curve of the residual error two-norm and the solution two-norm along with the change of the regularization parameter according to the first equation and the second equation, wherein the curve is an L curve.
And 108, deriving the curvature of the L curve, wherein the regularization parameter corresponding to the position where the derivative is zero is the optimal regularization parameter.
In step 108, derivation is performed on the curvature of the L curve, a position where the derivative is zero is a maximum curvature position of the curve, where a sum of the residual two-norm and the solution two-norm is minimum, and a corresponding regularization parameter is the optimal regularization parameter.
And step 109, substituting the optimal regularization parameter into the second equation to obtain a calibration result of the waveform display instrument to be calibrated.
In step 109, the optimal regularization parameter is substituted into the right side of the equation of the second equation, so as to obtain a calibration result of the waveform display apparatus to be calibrated, that is, a time domain transmission characteristic of the waveform display apparatus to be calibrated.
The method provided by the embodiment of the invention solves the problem of the waveform calibration which is not suitable, is not limited by noise unknown, can objectively and accurately realize the deconvolution of signals in a time domain compared with the traditional method of filtering noise by using a filter, obtains a stable and unique solution, and effectively solves the problem of the waveform calibration which is not suitable caused by the noise.
Fig. 3 is a diagram illustrating an embodiment of a waveform calibration apparatus, according to an embodiment of the present invention, the waveform calibration apparatus includes: the device comprises an optical fiber femtosecond laser 1, a photoelectric detector 2 and a waveform display instrument 3 to be calibrated.
The optical fiber femtosecond laser is used for generating an optical pulse signal and a synchronous trigger signal; the photoelectric detector is used for receiving the optical pulse signal and generating the electrical pulse signal; and the waveform display instrument to be calibrated is used for receiving the synchronous trigger signal and the electric pulse signal and measuring the electric pulse signal.
The device provided by the embodiment of the invention is applied to a waveform calibration method, can generate high-frequency electric pulse signals, can realize waveform calibration on a waveform display instrument to be calibrated with higher working frequency, and effectively solves the problem of waveform calibration instability caused by noise.
FIG. 4 is a diagram of an embodiment of a waveform calibration apparatus including an attenuator and a computer, the apparatus provided by the embodiment of the present invention including an attenuator and a computer, the apparatus including: the device comprises an optical fiber femtosecond laser 1, a photoelectric detector 2, a waveform display instrument 3 to be calibrated, an attenuator 4 and a computer 5.
The optical fiber femtosecond laser is used for generating an optical pulse signal and a synchronous trigger signal; the attenuator is used for receiving the optical pulse signal, attenuating the optical pulse signal and outputting the attenuated optical pulse signal to the photoelectric detector; the photoelectric detector is used for receiving the attenuated optical pulse signal and generating the electric pulse signal; the waveform display instrument to be calibrated is used for receiving the synchronous trigger signal and the electric pulse signal and measuring the electric pulse signal; the computer is used for receiving the measurement result of the waveform display instrument to be corrected, processing data and sending a control signal to the waveform display instrument to be corrected.
Preferably, the fiber femtosecond laser and the attenuator are connected through a single-mode polarization-maintaining fiber.
It should be noted that, the output signal of the femtosecond laser is attenuated by one attenuator, so as to effectively prevent the problem of excessive output signal power.
It should be noted that the computer may perform data acquisition and data processing on the signal output by the waveform display instrument to be calibrated, and may also transmit a control signal to the waveform display instrument to be calibrated to control the operating state of the waveform display instrument to be calibrated.
It is to be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above description is only an example of the present invention, and is not intended to limit the present invention. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (8)
1. A method of waveform calibration, comprising the steps of:
calibrating the electric pulse signal by using a standard waveform display instrument to obtain a standard pulse signal;
measuring the standard pulse signal by using a waveform display instrument to be corrected to obtain a measurement result as a measured signal, wherein the measured signal is the convolution of the standard pulse signal and the transmission characteristic function of the waveform display instrument to be corrected;
according to the cyclic convolution theory, obtaining an indeterminate equation of the transmission characteristic function of the waveform display instrument to be corrected as follows:
y＝Acx
wherein y is the measured signal, AcGenerating a cyclic matrix for the standard pulse signal, wherein x is a transmission characteristic function of the waveform display instrument to be corrected;
according to a Tikhonov regularization method, obtaining a Tikhonov functional of the ill-defined equation, namely the sum of the square of a residual two-norm and the square of a solution two-norm multiplied by the square of regularization parameters, solving the optimal solution of the ill-defined equation to be equivalent to solving the minimum value of the Tikhonov functional, wherein the process of solving the minimum value of the Tikhonov functional is a first process:
wherein λ is the regularization parameter, AcA circulant matrix generated for the standard pulse signal, x being a transfer characteristic function of the waveform display instrument to be calibrated, y being the measured signal, L being a compensation operator,
is the Tikhonov functional, | Acx-y||2Is the residual two-norm, | Lx | | non-woven phosphor2Is the solution two norm;
according to the Tikhonov regularization method, the minimum value of the Tikhonov functional is a solution of a second equation:
wherein, x (λ)opt) Is the minimum value, λ, of the Tikhonov functionaloptFor optimal regularization parameters, AcA circulant matrix generated for the standard pulse signal,l is the compensation operator and y is the measured signal;
obtaining a curve of the residual error second norm and the solution second norm along with the change of the regularization parameter, which is an L curve, according to the first equation and the second equation;
deriving the curvature of the L curve, wherein the regularization parameter corresponding to the position with the derivative being zero is the optimal regularization parameter;
substituting the optimal regularization parameter into the second equation to obtain a calibration result of the waveform display instrument to be calibrated;
the calibration result is the transmission characteristic function corresponding to the optimal regularization parameter.
2. The waveform calibration method of claim 1 wherein the compensation operator is a second order difference operator
3. The waveform calibration method according to claim 1, wherein the standard waveform display instrument is an oscilloscope having a model number of 86100C by Agilent.
4. The waveform calibration method according to claim 1, wherein the waveform display instrument to be calibrated is an oscilloscope having a model number of 86117A by Agilent.
5. A waveform calibration device applied to the method according to any one of claims 1 to 4, comprising: the device comprises an optical fiber femtosecond laser, a photoelectric detector and a waveform display instrument to be calibrated;
the optical fiber femtosecond laser is used for generating an optical pulse signal and a synchronous trigger signal;
the photoelectric detector is used for receiving the optical pulse signal and generating the electrical pulse signal;
and the waveform display instrument to be calibrated is used for receiving the synchronous trigger signal and the electric pulse signal and measuring the electric pulse signal.
6. The waveform calibration device of claim 5, further comprising: an attenuator;
the attenuator is used for receiving the optical pulse signal, attenuating the optical pulse signal and outputting the attenuated optical pulse signal to the photoelectric detector.
7. The waveform calibration device according to any one of claims 5 to 6, further comprising: a computer;
the computer is used for receiving the measurement result of the waveform display instrument to be corrected, processing data and sending a control signal to the waveform display instrument to be corrected.
8. The waveform calibration device of claim 6 wherein the fiber femtosecond laser and the attenuator are connected by a single-mode polarization-maintaining fiber.
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