A method for correcting timebase jitter of a high-speed sampling oscilloscope

Abstract

The application discloses a method for correcting time base jitter of a high-speed sampling oscilloscope, and the method comprises the following steps: constructing a function model of an oscilloscope waveform, processing an equation group of data by using a matrix, introducing a correction vector and a matrix, expressing a constraint matrix and solving; wherein the step of expressing the constraint matrix and solving comprises the following steps: calculating jitter errors generated by the oscilloscope by using an orthogonal distance regression algorithm; the calculation and solving step is to adopt different methods according to the number of solutions of the matrix, when the matrix is a single solution, a singular value decomposition method is adopted; when the matrix is a multiple solution, a gradient descent method is adopted. The technical scheme disclosed by the application corrects the time base jitter problem of the high-speed high-bandwidth sampling oscilloscope, and makes the measurement result more accurate.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of communication, and relates to an algorithm for correcting time base jitter of a high-speed sampling oscilloscope. BACKGROUND

[0002] As a precise measuring tool, the sampling oscilloscope must ensure its own precision. However, when measuring a signal, time base jitter may occur, and the waveform of the signal may deviate from the measurement. Time base jitter is caused by the mismatch between the actual sampling time and the ideal sampling time. In the time domain, the signal amplitude deviates, and periodic amplitude jumps occur. In the frequency domain, new frequency components appear.

[0003] Currently, existing methods for correcting time base jitter include zero-crossing detection time interval method and least squares estimation method. However, these methods have large measurement errors in the case of high-speed sampling. SUMMARY

[0004] The present application provides a method for correcting time base jitter of a high-speed sampling oscilloscope. The method aims to solve the problem of deviation between the actual sampling time and the ideal sampling time of a high-speed sampling oscilloscope, which causes time base jitter and measurement errors.

[0005] The present application provides a method for correcting time base jitter of a high-speed sampling oscilloscope based on the orthogonal distance regression algorithm and the gradient descent method, which comprises the following steps:

[0006] Step 1: Construct a function model of the oscilloscope waveform.

[0007] For any shaped waveform, we can use a high-order polynomial to represent it

[0008] f(x)=a0+a1x+a2x 2 +…+a n-1 x n-1

[0009] Step 2: Bring the observed results into the function and express them in the form of a matrix.

[0010] Bring the m groups of data received by the oscilloscope into the mathematical model, and express them in the form of a matrix

[0011] Ax=b

[0012] Where A is the set of data sampling times, x is the set of unknown waveform coefficients, and b is the set of data sampling values.

[0013] Step 3: Introduce an error correction matrix and an error correction vector.

[0014] A0 and b0 represent the unobservable error-free data matrix and error-free data vector respectively, and E and e represent the error data matrix and error data vector respectively.

[0015] The interference data vector b is compensated by the correction vector Δb, and the interference matrix data A is compensated by the correction matrix ΔA.

[0016]

[0017] The augmented data matrix [A, b] and the augmented correction matrix [ΔA, Δb] are represented by B and D, and [x, -1] T represented by z, wherein B and D are both m x (n+1) matrices, and z is an (n+1) x 1 column vector.

[0018] Step 4: Solve the solution of the constraint matrix.

[0019] Since the collected data m is much larger than the number n of unknown coefficients, the matrix is an overdetermined matrix, and there is no infinite solution.

[0020] Solving the minimum value of the objective function corresponds to ΔA, Δb, x, and the data jitter error and noise error are obtained to compensate the data.

[0021] The solution is divided into single solution and multiple solution cases. For the single solution case, the singular value decomposition algorithm is used, and for the multiple solution case, the gradient descent algorithm is used.

[0022] The singular value algorithm is to decompose the matrix B into orthogonal matrices U, V and a diagonal matrix Σ, and the diagonal elements are in order σ1≥σ2≥σ3≥…≥σ r >0, r=rank(B). Then the solution of z is the minimum singular value σ min corresponding to the right singular vector.

[0023] The gradient descent algorithm is to take the multiple solutions as the initial value respectively, and the error square sum of the sampling value and the sampling time is the loss function for gradient descent to obtain the minimum error value as the final solution.

[0024] The beneficial effects of the present application are:

[0025] The orthogonal distance regression theory, singular value decomposition algorithm and gradient descent algorithm are used for jitter compensation of a high-speed sampling oscilloscope, which is suitable for higher bandwidth, high-speed sampling of the oscilloscope, and the accuracy of the measured jitter is more accurate, and the problem of decrease in correction accuracy when the sampling speed increases in the traditional correction algorithm is avoided. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1Structure diagram for correcting time base jitter of high-speed sampling oscilloscope in embodiments of the present application

[0027] Figure 2 Flow chart for correcting time base jitter of high-speed sampling oscilloscope in embodiments of the present application

[0028] Figure 3 Original data waveform diagram for correcting time base jitter of high-speed sampling oscilloscope in embodiments of the present application

[0029] Figure 4 Corrected data waveform diagram for correcting time base jitter of high-speed sampling oscilloscope in embodiments of the present application DETAILED DESCRIPTION

[0030] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application is further described in detail below in combination with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0031] As shown in Figure 1 , the present application provides a method for correcting a high-speed sampling oscilloscope, which comprises a signal source, an oscilloscope, and a computer. The signal source is sampled by the high-speed sampling oscilloscope to obtain data, which is then transmitted into the computer for algorithm processing to obtain corrected waveform data. The algorithm steps are shown in Figure 2 .

[0032] Step 1: Construct a function model of the oscilloscope waveform.

[0033] For any shaped waveform, we can use a high-order polynomial to represent it.

[0034] f(x)≈p n (x)=a0+a1(x-x0)+a2(x-x0) 2 +…+a n-1 (x-x0) n-1

[0035] wherein x0=0 is set to obtain a fitting waveform function

[0036] f(x)=a0+a1x+a2x 2 +…+a n-1 x n-1

[0037] Step 2: Bring the observed results into the function and express them in the form of a matrix.

[0038] Suppose there are m observed results, then there are m equations:

[0039]

[0040] where i∈1,2,…,m, the equation set is expressed in matrix form as:

[0041] Ax = b

[0042] where

[0043] Step 3: Introducing error correction matrix and error correction vector.

[0044] Let A0 and b0 represent the unobservable error-free data matrix and error-free data vector, respectively, and the actually observed data matrix and data vector are:

[0045] A = A0 + E, b = b0 + e

[0046] where E and e represent the error data matrix and error data vector, respectively. We use the correction vector Δb to interfere with the data vector b, and use the correction matrix ΔA to interfere with the matrix data A to jointly compensate.

[0047] b + Δb = b + e + Δb→b0, A + ΔA = A0 + E + ΔA→A0

[0048] Suppress the influence of observation error or jitter noise on the solution of the matrix equation, and realize the conversion of the solution of the error matrix equation to the solution of the accurate matrix equation.

[0049] (A + ΔA)x = b + Δb→A0x = b0

[0050] To make the correction matrix and the correction data vector as small as possible, the problem is described as a constrained optimization problem:

[0051]

[0052] The constraint condition is:

[0053] subject to (A + ΔA)x = b + Δb

[0054] Rewrite the matrix equation Ax = b after adding the correction matrix and vector as:

[0055]

[0056] Or equivalently:

[0057] (B + D)z = 0

[0058] Where the augmented data matrix B = [A, b] and the augmented correction matrix D = [ΔA, Δb] are both m × (n + 1) matrices, and z is an (n + 1) × 1 column vector.

[0059] Step 4: Solve the constrained matrix.

[0060] Since the number of sampling data is much larger than the number of unknowns, the matrix is over-determined and there is no infinite solution.

[0061] When B+D is full rank, there is only one solution z=0, and the problem is reduced to finding a perturbation matrix D with the minimum norm, such that B+D is not full rank. The matrix B is singular value decomposition (SVD decomposition)

[0062] B=UΣV H

[0063] where U∈Rm×m and V∈Rn×n are orthogonal matrices, U is the left singular matrix of matrix B, V H is the conjugate transpose of V, V is the right singular matrix of matrix B, the column vectors ui and vj of U=[u1,u2,…,um] and V=[v1,v2,…,vn] are called the left singular vector and the right singular vector of matrix B respectively, and Σ is and Σ1=diag(σ1,σ2,σ3,…,σ r ), whose diagonal elements are in order σ1≥σ2≥σ3≥…≥σ r >0, r=rank(B).

[0064] When σ n is obviously larger than σ n+1 , the solution x exists uniquely. Then the solution of z is the right singular vector corresponding to the smallest singular value σ min .

[0065]

[0066] where u n+1 and v n+1 are the (n+1)th columns of U and V respectively, and Vi,j is the (i,j)th element of V.

[0067] When the minimum singular value of matrix B is multiple, multiple solutions will occur:

[0068] σ1≥σ2≥σ3≥…≥σ p =σ p+1 =…=σ n+1

[0069] That is, there are multiple singular values σ p ,σ p+1 ,…,σ n+1 and corresponding singular vectors, and vi is any column vector in {v p+1 ,v p+2 ,…,v n+1}, then any right vector v i gives a solution. Su

[0070]

[0071] wherein, alpha i is the first element of the vector v i , and the other elements form the vector y i .

[0072] Therefore, there are n+1-p solutions, we use the machine learning gradient descent method to obtain the final solution, and the n+1-p solutions obtained are the values of the coefficients a i , which are initialized into the waveform equation one by one, and the square sum of the difference between the actual sampling value and the sampling time and the sampling value and the sampling time of the waveform equation is used as the loss function.

[0073] The gradient descent method is used to iterate the loss function, a learning rate is set, and the solution corresponding to the minimum loss function obtained after iteration is used as the final solution.

[0074] The results of the present application are shown in Figure 3 and Figure 4 , Figure 4 is the corrected oscilloscope sampling waveform diagram.

[0075] The contents not described in detail in the specification belong to the prior art known to those skilled in the art.

[0076] Obviously, the above embodiments of the present application are only examples for clearly illustrating the present application, and are not intended to limit the embodiments of the present application, and for those skilled in the art, on the basis of the above description, other different forms of changes or variations can also be made, and it is impossible to enumerate all the embodiments here, and any changes or variations derived from the technical solutions of the present application still fall within the protection scope of the present application.

Claims

1. A method for correcting time base jitter in a high-speed sampling oscilloscope, characterized in that, Includes the following steps: Step S1: Using the sampling time of the oscilloscope as the independent variable of a function, and the sampled value as the dependent variable of the function along with the coefficients of the corresponding sampling time, a function is constructed. The characteristic feature is that a high-order polynomial equation is used to construct the waveform, and its representation is as follows: f(x)=a0+a1x+a2x 2 +…+a n-1 x n-1 ; Where a i Let x be the coefficient at the i-th sampling time, and x be the sampling time. Step S2: Substitute the sampled data from the oscilloscope into the function equation and represent it in matrix form. Its characteristics include: Substitute m sets of data into the constructed function equation, represented by matrix Ax = b. in Where matrix A is the set of sampling times, matrix x is the set of unknown parameters, and b is the set of sampled values. i For the i-th sampling time, y i Let be the sampled value at the i-th sampling time. Step S3: Based on the error model, introduce the error correction matrix and error correction vector to construct the constraint matrix equation. Its characteristics include: using the error correction vector Δb to disturb the data vector b, and using the error correction matrix ΔA to disturb the data matrix A for joint compensation. (A+ΔA)x=b+Δb→A0x=b0 Where A0 and b0 represent the unobservable error-free data matrix and error-free data vector, respectively; Δb is the error between the ideal sampled vector value and the actual sampled vector value; and ΔA is the error between the ideal sampling time and the actual sampling time. The constraint matrix equation is expressed according to the orthogonal distance regression algorithm. The constraints are: (A+ΔA)x=b+Δb; Step S4: Solve the constraint matrix equations using singular value decomposition and gradient descent to compensate for the time base jitter of the sampling oscilloscope. This step is characterized by the following steps: Step S41: When the solution to the constraint matrix is ​​a single solution, the singular vectors of the singular value decomposition are used as the final solution of the equation. Step S42: When there are multiple solutions to the constraint matrix, the solution with the smallest error after iteration using the machine learning gradient descent method is the final solution.

2. The method for correcting time base jitter in a high-speed sampling oscilloscope as described in claim 1, characterized in that: In step S3, the orthogonal distance regression algorithm is used to solve for the minimum sum of squared errors between the actual sampling time and the ideal sampling time, and between the actual sampled value and the ideal sampled value.

3. The method for correcting time base jitter in a high-speed sampling oscilloscope as described in claim 1, characterized in that: Let the augmented data matrix B = [A, b]. In step S41, the singular value decomposition involves decomposing the matrix into orthogonal matrices U and V and a diagonal matrix Σ. Therefore, the augmented matrix B can also be expressed as: B=UΣV H Where U∈Rm×m and V∈Rn×n are orthogonal matrices, U is the left singular matrix of matrix B, and V H Let V be the conjugate transpose of V, and V be the right singular matrix of B. The column vectors ui and vj of U = [u1, u2, ..., um] and V = [v1, v2, ..., vn] are called the left and right singular vectors of matrix B, respectively. Σ is... And Σ1=diag(σ1,σ2,σ3,…,σ r Its diagonal elements are in the order σ1≥σ2≥σ3≥…≥σ r If the value is greater than 0, r = rank(B), and the final solution is the minimum singular value σ. min The corresponding right singular vector.

4. The method for correcting time base jitter in a high-speed sampling oscilloscope as described in claim 1, characterized in that: In step S42, the loss function of gradient descent is the sum of the squares of the differences between the actual sampled value and the sampling time, and between the sampled value and the sampling time of the function equation. The initial value of gradient descent is a corresponding to the singular vector obtained through singular value decomposition. i .

Images