Signal processing algorithm based on differential cross multiplication algorithm

Abstract

The invention provides a signal processing algorithm based on a differential cross multiplication algorithm. The method is characterized in that after an interference signal is subjected to frequency mixing low-pass filtering with single frequency multiplication and double frequency multiplication respectively, a pair of cosine term and sine term which are orthogonal to each other is obtained, and then demodulation of a signal to be measured is achieved after differential cross multiplication, subtraction, integration and high-pass filtering. The interference signal is subjected to carrier frequency mixing and low-pass filtering to obtain two paths of signals, the two paths of signals are subjected to differential cross multiplication, subtraction and integration processing and then pass through a high-pass filter to obtain a to-be-measured signal, the amplitude of the demodulated to-be-measured signal is only changed by a coefficient, and in order to reduce the dependency relationship of an output result on a function, the demodulated to-be-measured signal is subjected to differential cross multiplication, subtraction and integration; by selecting a proper carrier signal amplitude, namely a phase modulation degree C, the two paths of signals obtain a maximum value, and when the C value is slightly changed, the system demodulation output amplitude is slightly changed, so that the complete demodulation of the to-be-detected signal can be realized through amplitude compensation.

Description

(I) Technical field

[0001] The present invention relates to a signal processing algorithm based on a differential cross-multiplication algorithm, which can perform differential operation processing on a signal and belongs to the technical field of signal processing. (II) Background technology

[0002] The signal demodulation algorithms for orthogonal phase demodulation technology mainly include the differential cross multiplication algorithm (DCM) and the inverse tangent algorithm (ARCTAN). The differential cross multiplication method has the characteristics of simple demodulation and low hardware requirements. DCM originally used analog circuits. With the development of modern electronic technology, that is, the advantages of signal processing shown by digital circuits, DCM schemes generally adopt digital demodulation schemes. The ARCTAN scheme is similar to the DCM scheme in that both of them first use the first and second times of the modulated signal for mixing, and then filter out the DC value. The ARCTAN scheme directly calculates the tangent of the DC value after mixing the first and second times of the frequency. The process is simple, but the amount of calculation for the tangent operation is large.

[0003] The inverse tangent algorithm cannot eliminate the influence of the initial phase on the demodulated signal. In addition, the inverse tangent algorithm involves relatively complex tangent nonlinear operations and is affected by phase entanglement. The differential operation of the differential cross-multiplication algorithm is relatively simple, there is no phase entanglement, and the demodulation efficiency is high. Moreover, in the signal processing module, there is no direct method to solve the inverse tangent function value, and it can only be replaced by an approximate method, resulting in a high computational complexity of the inverse tangent algorithm, and its failure process is transient. (III) Summary of the invention

[0004] The object of the present invention is to provide a signal processing algorithm based on a differential cross-multiplication algorithm.

[0005] The present invention is achieved in that:

[0006] A signal processing algorithm based on a differential cross-multiplication algorithm comprises the following steps:

[0007] Step 1: First, in order to meet the application premise of the orthogonal demodulation algorithm, it is necessary to eliminate the bias term and amplitude term in the signal, and use the ellipse fitting algorithm to solve the corresponding parameters;

[0008] Step 2: Establish the general equation of the ellipse using two orthogonal signals;

[0009] Step 3: Use the least square method to perform ellipse fitting on the two signals and solve the ellipse coefficient;

[0010] Step 4: Calculate the optimal parameters of the ellipse fitting, and further calculate the bias term and amplitude term in the two signals according to the parameters;

[0011] Step 5: Calculate the signal-to-noise ratio of the optical fiber vibration signal according to the signal-to-noise ratio formula, that is, obtain the signal-to-noise ratio of the detection signal at each optical fiber sampling point.

[0012] Step 6: After the interference signal is mixed with the single frequency and double frequency and low-pass filtered, a pair of mutually orthogonal cosine terms and sine terms are obtained, and then the demodulation of the signal to be measured is realized after differential cross-multiplication and subtraction, integration, and high-pass filtering.

[0013] Step 7: The demodulated signal to be tested has only its amplitude changed by a coefficient. In order to reduce the dependence of the output result on the function, the two signals can achieve maximum values ​​by selecting an appropriate carrier signal amplitude, i.e., phase modulation index C. The amplitude compensation can be used to achieve complete demodulation of the signal to be tested. (IV) Description of the drawings

[0014] Figure 1 The following is a summary of the present invention.

[0015] Figure 2 The figure is a flow chart of a signal processing algorithm based on a differential cross-multiplication algorithm according to an embodiment of the present invention.

[0016] Figure 3 The schematic diagram of the signal processing algorithm based on the differential cross multiplication algorithm according to the embodiment of the present invention. (V) Specific implementation methods

[0017] The present invention is further described below.

[0018] like Figure 1 As shown, a signal processing algorithm based on a differential cross-multiplication algorithm specifically includes the following steps:

[0019] Step 1: In order to meet the application premise of the differential cross-multiplication algorithm, it is necessary to eliminate the bias term and amplitude term composed of the average light intensity, photoelectric conversion coefficient, and contrast in the output signal. When the sensor coefficient is fixed, the parameters in the formula will also be fixed, and the ellipse fitting algorithm can be used to solve the corresponding parameters. The ellipse equation is established as follows:

[0020]

[0021] Among them, V1 and V2 are voltage signals output after the two light intensity signals are photoelectrically converted.

[0022] Step 2: To find the best ellipse coefficient, the least square method is used to perform ellipse fitting on the two signals, and the ellipse coefficient equations are established as follows:

[0023]

[0024] Where N is the number of input data points.

[0025] Step 3: To solve the elliptic coefficient equations, it is necessary to set constraints on the equations so that the solved elliptic parameters can achieve the optimal effect. The constraints introduced are as follows:

[0026]

[0027] According to the above conditions, the elliptic coefficient equations are expressed in a new form:

[0028]

[0029] In the above equations, a is the coefficient matrix of the ellipse, a=[1,a1,a2,a 3, a4,a5] T D is the data matrix of the two collected signals. H is the intermediate matrix.

[0030]

[0031]

[0032] Step 4: Solve the eigenvector of the above equations to obtain the optimal parameters of the ellipse fitting. According to the solved parameters, further calculate the average light intensity bias term and AC signal amplitude term in the two collected signals as follows:

[0033]

[0034] Step 5: Express the two orthogonal signals as:

[0035]

[0036] The above signal expression is differentiated with respect to time:

[0037]

[0038] Multiplying the signal expression by the differential term and then subtracting it gives:

[0039]

[0040] Integrating both sides of the above equation gives:

[0041]

[0042] The present invention provides a signal processing algorithm based on a differential cross-multiplication algorithm, which has relatively simple differential operations, no phase entanglement, and high demodulation efficiency. It should be noted that although the embodiments described in the present invention are illustrative, they are not limitations of the present invention, and therefore the present invention is not limited to the above-mentioned specific implementations. Without departing from the principles of the present invention, any other implementations obtained by those skilled in the art under the enlightenment of the present invention are within the protection of the present invention.

Claims

1. A signal processing algorithm based on a differential cross-multiplication algorithm, characterized in that: The steps include: Step 1: After the interference signal is mixed with the single frequency and double frequency and low-pass filtered, a pair of mutually orthogonal cosine and sine terms are obtained. The two signals can be expressed as: Step 2: After differential cross-multiplication and subtraction, integration, and high-pass filtering, the sine term and cosine term are demodulated to achieve the signal to be measured. The two signals are differentiated with respect to time to obtain: Step 3: The interference signal is mixed with the carrier and low-pass filtered to obtain two signals. The two signals are processed by differential cross-multiplication, subtraction and integration, and then passed through a high-pass filter to obtain the signal to be measured. The cosine term, sine term and differential term are cross-multiplied and then subtracted to obtain: Integrating both sides simultaneously gives: Step 4: Select an appropriate carrier signal amplitude, i.e., phase modulation index C, so that the two signals reach maximum values.

Images