CN114660359A - Third-order monotone fitting amplitude-frequency measurement method - Google Patents
Third-order monotone fitting amplitude-frequency measurement method Download PDFInfo
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- CN114660359A CN114660359A CN202210283442.6A CN202210283442A CN114660359A CN 114660359 A CN114660359 A CN 114660359A CN 202210283442 A CN202210283442 A CN 202210283442A CN 114660359 A CN114660359 A CN 114660359A
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Abstract
A three-order monotone fitting amplitude-frequency measurement method relates to the field of electronic measurement and control, and solves the problems that the existing method needs to measure a complete period of a signal to be measured, has large calculated amount, low measurement precision due to loss of characteristic point information, difficulty in realizing rapid measurement and the like; the method can measure and obtain the instantaneous frequency and the instantaneous amplitude of any signal; the method comprises the steps that any parameter of a signal does not need to be known in advance, a section of rising or falling half-cycle data in sampling quantization data of the signal to be detected is analyzed to serve as a monotonous calculation interval, then a third-order function is used for fitting, and finally the amplitude and the frequency of the signal are calculated by using a fitting system; for the frequency conversion signal, the required sampling frequency needs to be at least 8 times higher than the maximum frequency of the signal to be detected; only a half period of a signal to be measured needs to be measured, and the method has the advantage of high measurement speed; the sampling frequency is increased, so that possible noise in the signal to be measured can be suppressed, and the measurement precision is effectively improved.
Description
Technical Field
The invention relates to the technical field of measurement of electronic signal frequency, in particular to a third-order monotone fitting amplitude-frequency measurement method.
Background
For high-frequency signals, a counting method for measuring the occurrence frequency of the characteristic point of the signal within a fixed time period is generally adopted, for example, the frequency measurement is usually carried out after a sinusoidal signal is changed into a square wave by taking a zero crossing point as the characteristic point; for low frequency signals, a periodic method is usually adopted in which the frequency is obtained by taking the reciprocal after measuring the period of the signal; also using a Bo Li Yes method for analyzing frequency components of each signal after the Bo Li Yes level number expansion; for these methods, at least one complete cycle of the signal to be measured needs to be measured from the perspective of measuring speed, and particularly, the bort method not only needs to measure cycles of a plurality of signals to be measured, but also has the problem of huge calculation amount, and is more difficult to realize rapid measurement; from the view point of measurement accuracy, the counting method and the periodic method can only use some isolated characteristic point information in the signal to be measured, and other information is discarded and lost, so the accuracy is low in the process of rapid measurement.
For a signal to be measured mixed with noise, the bort leaf method needs to calculate all frequency components in a frequency band, and the frequency component with the maximum energy can be found after sequencing.
Disclosure of Invention
The invention aims to solve the problems that the prior method needs to measure a complete cycle of a signal to be measured, has large calculated amount, low measurement precision caused by loss of characteristic point information, difficult realization of quick measurement and the like; a third-order monotone fitting amplitude-frequency measurement method is provided.
The method is realized by calculating the monotonous interval of a signal to be measured, fitting the third order and calculating the amplitude frequency of the signal, and the specific process is as follows:
step one, calculating a monotone interval of a signal to be measured to obtain a calculated signal to be measured;
step A1, storing the signal to be measured in an array S [ i ], and taking data S [ P ] with the sequence number i being equal to the position P in the array S [ i ];
step A2, adopting a variable K as a cycle index serial number, wherein the initial value of K is equal to P;
step A3, comparing S [ K ] with S [ K-1], if S [ K-1] is larger than S [ K ], executing step A4, otherwise, executing step A5;
step A4, K is K-1, and step A3 is executed in a returning mode;
step A5, if the value of the variable K is smaller than P, the variable U is adopted to store the value of K at the moment, then the step A6 is executed, otherwise, the step A11 is executed;
step A6, setting the initial value of a variable K equal to P;
step A7, comparing S [ K ] with S [ K +1], if S [ K +1] is less than S [ K ], executing step A8, otherwise, executing step A9 by failure jump;
step a7 is executed after step A8, K + 1;
step A9, if the value of the variable K is larger than P, the variable E is adopted to store the value of K at the moment, then the step A10 is executed, otherwise, the step A11 is executed if the value fails;
step A10, storing the calculation information of the signal monotone interval in the variable U and the variable E at the moment, wherein the interval is a decreasing interval, and executing step II;
step A11, using a variable K as a cycle index sequence number, wherein the initial value of K is equal to P;
step A12, comparing the S [ K ] and the S [ K +1], if the S [ K +1] is larger than the S [ K ], executing step A13, otherwise, skipping to execute step A14;
step a13, K ═ K +1, execute step a 12;
step A14, saving the K value at the moment by using a variable U; adopting a variable K as a cycle index serial number, wherein the initial value of the K is equal to P;
step A15, comparing the size of S [ K ] and S [ K-1], if S [ K-1] is less than S [ K ], executing step A16, otherwise, executing step A17;
step a16, K-1, execute step a 15; storing the K value at the moment by adopting a variable E; at this time, the variable U and the variable E store the calculation information of a signal monotone interval, and the interval is an increasing interval, and the step II is executed;
step two, performing third-order fitting on the signal to be measured after the monotonic interval calculation is performed in the step one, wherein the specific process is as follows:
b1, defining a one-dimensional array Q, wherein the number of elements in the array is represented by Z, and the calculation method of Z is as follows;
Z＝4*(U-E)/5
defining a one-dimensional array R, wherein the number of elements in the array is also Z;
step B2, defining a variable j, enabling the value of j to be equal to E, and enabling the initial value of a variable K to be set to be zero;
step B3, using variable j as index sequence number of array S, saving the value of data Sj obtained from array S into Q K using K as index sequence number in array Q, then filling the value of R K using K as index sequence number in array R as the square of K;
step B4, accumulating the variable K, and after accumulating the variable j again, if the value of j is more than or equal to Z, executing step B5, otherwise executing step B3;
step B5, acquiring data from the array Q and the array R at the same time, constructing a third-order fitting equation set in a matrix form by taking j as a cyclic variable, and solving the equation set to calculate four unknown values of the variables a, B, c and d;
in the formula, a is a coefficient of a cubic term, b is a coefficient of a quadratic term, c is a coefficient of a primary term, and d is a constant term;
step three, calculating instantaneous frequency f and instantaneous amplitude Amp of the signal to be measured after the third-order fitting in the step two;
when the sampling frequency is F, calculating the instantaneous frequency F of the signal to be measured by adopting a, b and c solved by a third-order fitting equation set;
the instantaneous amplitude Amp of the signal to be measured in the corresponding monotone interval is expressed by the following formula:
the instantaneous frequency f is used for demodulation of FM broadcasting; the instantaneous amplitude Amp is used for am broadcast demodulation.
The invention has the beneficial effects that: the measuring method of the invention has the advantages of high measuring speed and high precision. Compared with the traditional frequency measurement method taking the zero crossing point as the characteristic point, the method provided by the invention has higher precision because the method utilizes the information of all sampling points; and because two frequency values are obtained by measurement in one signal period, the average can be taken again to further improve the measurement precision; compared with the traditional method such as the British leaf and the like, the method can solve the problem that the traditional technology cannot rapidly measure the signal frequency in less than one signal period to be measured; because the invention fully utilizes the information of all sampling points, the noise possibly existing in the signal to be measured can be inhibited, the measurement precision is effectively improved, and the higher the sampling frequency is, the more beneficial to inhibiting the noise is; the instantaneous amplitude and the DC voltage component can be synchronously measured while the signal frequency is measured.
Drawings
Fig. 1 is a schematic block diagram of a third-order monotonic fitting amplitude-frequency measurement method according to the present invention.
Detailed Description
In a first embodiment, the third-order monotonic fitting amplitude-frequency measurement method is described with reference to fig. 1, and the third-order monotonic fitting amplitude-frequency measurement method is implemented by a third-order monotonic fitting amplitude-frequency measurement system, where the system includes a data input terminal 1, a memory 2, a processor 3, and an output terminal 4;
the data input end 1 inputs a signal to be detected, and if the signal to be detected is an analog signal, the signal to be detected needs to be converted by an analog-to-digital converter and then is sent to the data input end 1; requiring signal data to be generated at fixed frequency fsamples; the signal to be detected is an original signal mixed with a random noise signal; the original signal is a cosine signal with single frequency, the instantaneous frequency is represented as an unknown value by f, and the instantaneous amplitude is represented as an unknown value by Amp; the maximum value of F is lower than the upper limit value H of frequency, and the sampling frequency F is ensured to be more than 8 times of the upper limit value H; the intensity of noise signals mixed in the signals to be detected at any time is required to be smaller than the signals to be detected;
the memory 2 stores the signal data to be measured obtained from the data input end; in each measurement process, a batch of data is required to have M numerical values, and the M numerical values are stored logically and continuously to form a one-dimensional array data structure which is expressed by Si; wherein S is an array name, and i is a subscript index sequence number; the minimum value of the subscript index serial number i is zero, and the maximum value N is equal to the number M of the signal data to be detected minus one; defining the decreasing direction of the subscript index serial numbers as the left direction and the increasing direction of the subscript index serial numbers as the right direction;
the processor 3 analyzes the data stored in the memory 2, and analyzes the instantaneous frequency and the instantaneous amplitude at the position with index number of i-P by calculating the signal monotone interval of the signal to be measured, fitting the third order and calculating the amplitude frequency of the signal.
The specific calculation process is as follows:
step one, calculating a signal monotone interval of a signal to be detected, wherein the signal monotone interval is obtained with the aim of obtaining the signal monotone interval stored in a variable E and a variable U;
a1, obtaining data S [ P ] with sequence number i ═ P in the array S [ i ];
a2, using a variable K as a cycle index sequence number, wherein the initial value of K is equal to P;
a3, comparing S [ K ] with S [ K-1], if S [ K-1] is larger than S [ K ], executing step A4, otherwise, jumping to execute step A5;
a4, after the variable K is reduced by 1, executing the step A3;
a5, if the value of the variable K is less than P, the variable U is used for saving the K value at the moment and then the step 6 is executed, otherwise the step A12 is executed;
a6, setting the initial value of a variable K equal to P;
a7, comparing the S [ K ] with the S [ K +1], if the S [ K +1] is less than the S [ K ], executing the step A8, otherwise, executing the step A9 by a failed jump;
a8, adding 1 to the variable K and then executing the step 7;
a9, if the value of the variable K is larger than P, the variable E is used for saving the value of K at the moment, and then the step A10 is executed, otherwise, the step A12 is executed in failure;
a10, storing signal monotone calculation interval information in the variable U and the variable E at the moment, wherein the interval is a subtraction interval, and executing a step II;
a12, using a variable K as a cycle index sequence number, wherein the initial value of K is equal to P;
a13, comparing the S [ K ] with the S [ K +1], if the S [ K +1] is larger than the S [ K ], executing the step A14, otherwise, jumping to execute the step A15;
a14, adding 1 to the variable K and then executing the step A13;
a15, saving the K value at the moment by using a variable U;
a16, setting the initial value of K equal to P;
a17, comparing S [ K ] with S [ K-1], if S [ K-1] is smaller than S [ K ], executing step A18, otherwise, jumping to execute step A19;
a18, after the variable K is reduced by 1, executing the step A17;
a19, using variable E to store the K value;
a20, storing signal monotone calculation interval information in the variable U and the variable E at the moment, wherein the interval is an increasing interval, and executing the step II;
step two, performing third-order fitting on the signal to be measured in the monotone interval obtained in the step one;
b1, defining a one-dimensional array Q, wherein the number of elements in the array is represented by Z, and the calculation method of Z is as follows;
Z＝4*(U-E)/5
that is, the value of Z is equal to the value of the variable U minus the variable E, and then four fifths of the value is taken;
defining a one-dimensional array R, wherein the number of elements in the array is also Z;
b2, defining a variable j, making the value of j equal to E and making the initial value of the variable K be zero;
b3, using variable j as index sequence number of array S, saving the value of data Sj obtained from array S into Q K using K as index sequence number in array Q, and filling the value in R K using K as index sequence number in array R as square of K;
b4, accumulating the variable K, and after accumulating the variable j again, if the value of j is more than or equal to Z, executing the step B5, otherwise executing the step B3;
b5, simultaneously acquiring data from the array Q and the array R, taking j as a cyclic variable, constructing a third-order fitting equation set in a matrix form, and solving the equation set to calculate four unknown values of a, B, c and d;
in the formula, a is a coefficient of a cubic term, b is a coefficient of a quadratic term, c is a coefficient of a primary term, and d is a constant term;
step three, calculating the amplitude frequency of the signal to be measured;
if the signal superposition noise component is too large, measurement errors can be caused, and the problem can be found by checking positive and negative signs in the solution of an equation set; if the calculation interval is a subtraction interval, the two values of b and d calculated by solving the equation set must be negative values, and c must be positive values, otherwise, the measurement is determined to be wrong; if the calculation interval is an increase interval, the two values of b and d calculated by solving the equation set must be positive values, and c must be negative values, otherwise, the measurement is determined to be wrong;
when the fixed sampling frequency is F, calculating the instantaneous frequency F of the signal to be measured at the moment by using a, b and c solved by the fitting equation set;
instantaneous amplitude Amp of the signal to be measured in the monotonous interval;
the direct current voltage component V in the monotone interval in the signal to be detected;
and outputting the measurement result from the output end.
As shown in fig. 1, the data input end can directly input data into the memory in two ways, one is that the data input end directly inputs data into the memory, and the other is that the data input end firstly sends data to the processor and then the data is transferred into the memory by the processor; the processor calculates the data in the memory and outputs the instantaneous frequency and the instantaneous amplitude through the output end.
According to the method, any parameter of the signal does not need to be known in advance, a section of rising or falling half-period data in the signal to be detected sampling quantization data is analyzed to serve as a monotone calculation interval, then a third-order function is used for fitting, and finally the amplitude and the frequency of the signal are calculated by using a fitting system; for the frequency conversion signal, the required sampling frequency needs to be at least 8 times higher than the maximum frequency of the signal to be detected; the invention has the advantage of high measurement speed because only a half cycle of a signal to be measured needs to be measured; because the information of all sampling points is utilized, the sampling frequency is improved, the noise possibly existing in the signal to be measured can be restrained, and the measurement precision is effectively improved.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that various changes and modifications can be made by those skilled in the art without departing from the spirit of the invention, and these changes and modifications are all within the scope of the invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (6)
1. The third-order monotone fitting amplitude-frequency measuring method is characterized by comprising the following steps: the method is realized by calculating the monotone interval of a signal to be measured, fitting in the third order and calculating the amplitude and frequency of the signal, and the specific process is as follows:
step one, calculating a monotone interval of a signal to be measured to obtain a calculated signal to be measured;
step A1, storing the signal to be measured in an array S [ i ], and taking data S [ P ] with the sequence number i being equal to the position P in the array S [ i ];
step A2, adopting a variable K as a cycle index sequence number, wherein the initial value of K is equal to P;
step A3, comparing S [ K ] with S [ K-1], if S [ K-1] is larger than S [ K ], executing step A4, otherwise, executing step A5;
step A4, K is K-1, and step A3 is executed in a returning mode;
step A5, if the value of the variable K is smaller than P, the variable U is adopted to store the value of K at the moment, then the step A6 is executed, otherwise, the step A11 is executed;
step A6, setting the initial value of a variable K equal to P;
step A7, comparing the S [ K ] and S [ K +1], if S [ K +1] is less than S [ K ], executing step A8, otherwise, executing step A9 by a failed jump;
step a7 is executed after step A8, K + 1;
step A9, if the value of the variable K is larger than P, the variable E is adopted to store the value of K at the moment, then the step A10 is executed, otherwise, the step A11 is executed if the value fails;
step A10, storing the calculation information of the signal monotone interval in the variable U and the variable E at the moment, wherein the interval is a decreasing interval, and executing step II;
step A11, using variable K as cycle index sequence number, the initial value of K is equal to P;
step A12, comparing the S [ K ] and the S [ K +1], if the S [ K +1] is larger than the S [ K ], executing step A13, otherwise, skipping to execute step A14;
step a13, K ═ K +1, execute step a 12;
step A14, saving the K value at the moment by using a variable U; adopting a variable K as a cycle index serial number, wherein the initial value of the K is equal to P;
step A15, comparing the size of S [ K ] and S [ K-1], if S [ K-1] is less than S [ K ], executing step A16, otherwise, executing step A17;
step a16, K-1, execute step a 15; storing the K value at the moment by adopting a variable E; at this time, the variable U and the variable E store the calculation information of a signal monotone interval, and the interval is an increasing interval, and the step II is executed;
step two, performing third-order fitting on the signal to be measured after the monotone interval calculation in the step one, wherein the specific process is as follows:
b1, defining a one-dimensional array Q, wherein the number of elements in the array is represented by Z, and the calculation method of Z is as follows;
Z＝4*(U-E)/5
defining a one-dimensional array R, wherein the number of elements in the array is also Z;
step B2, defining a variable j, making the value of j equal to E, and setting the initial value of the variable K to zero;
step B3, using variable j as index sequence number of array S, saving the value of data Sj obtained from array S into Q K using K as index sequence number in array Q, then filling the value of R K using K as index sequence number in array R as the square of K;
step B4, accumulating the variable K, and after accumulating the variable j again, if the value of j is more than or equal to Z, executing step B5, otherwise executing step B3;
b5, acquiring data from the array Q and the array R at the same time, constructing a third-order fitting equation set in a matrix form by taking j as a cyclic variable, and solving the equation set to calculate four unknown values of the variables a, B, c and d;
in the formula, a is a coefficient of a cubic term, b is a coefficient of a quadratic term, c is a coefficient of a primary term, and d is a constant term;
step three, calculating instantaneous frequency f and instantaneous amplitude Amp of the signal to be measured after the third-order fitting in the step two;
when the sampling frequency is F, calculating the instantaneous frequency F of the signal to be measured by adopting a, b and c solved by a third-order fitting equation set;
the instantaneous amplitude Amp of the signal to be measured in the corresponding monotone interval is expressed by the following formula:
the instantaneous frequency f is used for demodulation of frequency modulation broadcasting; the instantaneous amplitude Amp is used for am broadcast demodulation.
2. The third order monotonic fitting amplitude-frequency measurement method of claim 1, wherein: in the third step, when the monotonous interval is a decreasing interval, the numerical values of the calculated variables b and d are both negative values, the value of the variable c is a positive value, otherwise, the measurement is determined to be wrong, and all data are discarded;
and when the monotone interval is an increasing interval, the values of the calculated variables b and d are both positive values, the value of the variable c is a negative value, otherwise, the measurement is determined to be wrong, and all data are discarded.
3. The third order monotonic fitting amplitude-frequency measurement method of claim 1, wherein: in the third step, the dc voltage component V of the signal to be measured in the corresponding monotone interval is calculated by the following formula:
4. the third-order monotonic fitting amplitude-frequency measurement method according to claim 1, wherein the measurement method is implemented by a third-order monotonic fitting amplitude-frequency measurement system, the third-order monotonic fitting amplitude-frequency measurement system comprises a data input terminal 1, a memory 2, a processor 3 and an output terminal 4;
the data input end 1 inputs a signal to be detected, and the memory 2 stores the signal data to be detected obtained from the data input end; in each measurement process, a batch of data is required to have M numerical values, and the M numerical values are stored logically and continuously to form a one-dimensional array data structure which is expressed by Si; wherein S is an array name, and i is a subscript index sequence number; the minimum value of the index sequence number i of the subscript is zero, and the maximum value is N which is equal to the number M of the signal data to be detected minus 1; defining the decreasing direction of the subscript index serial numbers as the left direction and the increasing direction of the subscript index serial numbers as the right direction;
the processor 3 calculates instantaneous amplitude frequency at the position with index sequence number i equal to P through three steps of calculation of the monotone interval of the signal to be measured, third-order fitting and calculation of the amplitude frequency of the signal for the data in the memory 2.
5. The third order monotonic fitting amplitude-frequency measurement method of claim 4, wherein: requiring the signal to be detected to generate a fixed sampling frequency F;
the signal to be detected is an original signal mixed with a random noise signal; the original signal is a cosine signal with single frequency, and the instantaneous frequency f and the instantaneous amplitude Amp are unknown values; the maximum value of the instantaneous frequency F is lower than the upper limit value H of the frequency, and the fixed sampling frequency F is ensured to be larger than 8 times of the upper limit value H; and the intensity of the noise signal mixed in the signal to be detected is required to be smaller than the intensity of the signal to be detected.
6. The method according to claim 1, wherein when the signal to be measured input from the data input terminal is an analog signal, the analog signal is converted by an analog-to-digital converter and then is provided to the data input terminal.
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