CN104007312B - Signal frequency real-time measuring method based on low-frequency square signal frequency prediction - Google Patents

Abstract

A signal frequency real-time measuring method based on low-frequency square signal frequency prediction comprises the steps that (1) tested square signals are obtained; (2) the initial moment and the time width of the square signals are measured and recorded; (3) a linear fitting prediction method or a quadratic fitting prediction method is used, and a frequency linear fitting formula or a frequency quadratic fitting formula of tested signals is obtained; (4) prediction frequency is computed in real time and output; and (5) whether new signals are obtained is judged, if yes, the step (2) is carried out, and otherwise the step (4) is carried out. Prediction values are used for replacing measuring values to be used as output values, the prediction values can compensate the hysteresis errors existing in the measuring values, accordingly, the accuracy of real-time frequency measuring is improved, the measuring accuracy of steady state frequency is not lowered, an extra timer is not occupied, computing quantity is small, and meanwhile the hardware cost of frequency testing equipment cannot be increased.

Description

Signal frequency method for real-time measurement based on low-frequency square-wave signal frequency predication

Technical field

The present invention relates to signal testing technical field, particularly a kind of signal frequency method for real-time measurement.

Background technology

In frequency measuring equipment, signal is through rings such as sensor senses, modulate circuit shaping, processor collection and calculating Section obtains measured value, because each link is required for the time, measured value lags behind actual value in time, works as actual frequency When being continually changing, measured value will produce hysteresis error because of time lag.The frequency such as current Frequency tester and tachoscope Measuring apparatus are all using measured value as output valve, therefore there is also hysteresis error.

The timer clock frequency of current single-chip microcomputer data capture card generally in tens mhz, in addition to the communications field, In most of control systems, measured signal is less than the square-wave signal of 100khz, compared with timer frequency, measured signal for frequency For low frequency signal, typically measurement frequency is come using cycle test method.For cycle test method, in each square wave rising edge (or decline) along measurement Square wave time width, updates and outputting measurement value, and average lag-time is half square wave time width, rises next Before arriving along (or trailing edge), holding output valve is constant, and the curve of therefore output valve is stepped, does not accurately reflect reality The variation tendency of frequency.

The purpose of the present invention is exactly to propose a kind of more real-time, accurately measurement low-frequency square-wave signal frequency method, mends Repay the hysteresis error that existing cycle test method exists, can be used for frequency recorder and tachoscope etc. and there is frequency Measurement of LF function Equipment.

Content of the invention

It is an object of the invention to provide a kind of side of measurement in real time of the signal frequency based on low-frequency square-wave signal frequency predication Method, it compensates the hysteresis error that existing cycle test method exists, and significantly improves the real-time recording signal frequency and accuracy.

The purpose of the present invention is realized by such technical scheme, specifically comprises the following steps that

1) obtain tested square-wave signal；

2) measure and record initial time and the time width of tested each square wave of square-wave signal；

3) initial time and the time width of square wave have been surveyed according to tested square-wave signal, using linear fit predicted method or two Secondary matching predicted method, obtains frequency linearity fitting formula or the frequency quadratic fit formula of tested square-wave signal；

4) according to frequency linearity fitting formula or frequency quadratic fit formula, calculate and export next square-wave signal in real time Signal estimation frequency before arrival；Or be changed to: before new square-wave signal arrives, calculate in real time and the pre- frequency measurement of output signal Rate；

5) judge whether to get new signal, if getting new signal, return to step 2), otherwise return to step 4).

Further, step 3) described in linear fit predicted method concrete grammar as follows:

Initial time t in n-th square wave_n, obtain the initial time t having surveyed nearest 2 square waves_n-1、t_n-2During with square wave Between width t_n-t_n-1And t_n-1-t_n-2If the linear fit formula for pre- measured frequency is

F (t)=at+b (1)

In formula, a and b is coefficient；

In t_n-1In the moment, [t can be calculated_n-2, t_n-1] average frequency of time period isAnd be considered asMoment Frequency, that is, $f\left(\frac{t_{n-1}+t_{n-2}}{2}\right)=\frac{1}{t_{n-1}-t_{n-2}};$

In t_nIn the moment, [t can be calculated_n-1, t_n] average frequency of time period isAnd be considered asThe frequency in moment Rate, that is, $f\left(\frac{t_n+t_{n-1}}{2}\right)=\frac{1}{t_n-t_{n-1}};$

Will $f\left(\frac{t_{n-1}+t_{n-2}}{2}\right)=\frac{1}{t_{n-1}-t_{n-2}}$ With $f\left(\frac{t_n+t_{n-1}}{2}\right)=\frac{1}{t_n-t_{n-1}}$ Substitute into formula (1), obtain equation group:

$\left\{\begin{array}{c}a\frac{t_{n-1}+t_{n-2}}{2}+b=\frac{1}{t_{n-1}-t_{n-2}}\\ a\frac{t_n+t_{n-1}}{2}+b=\frac{1}{t_n-t_{n-1}}\end{array}\right.---\left(2\right)$

Solve equation group, obtain a and b coefficient, a and b is substituted into formula (1), the linear fit obtaining pre- measured frequency is public Formula, before calculating next square wave rising edge arrival, that is, in t_n+1[t before moment_n, t_n+1] time period frequency.

Further, step 3) described in quadratic fit predicted method concrete grammar as follows:

Initial time t in n-th square wave_n, obtain the initial time t having surveyed nearest 3 square waves_n-1、t_n-2、t_n-3And side Ripple time width t_n-t_n-1、t_n-1-t_n-2And t_n-2-t_n-3If the quadratic fit formula for pre- measured frequency is

F (t)=at²+bt+c (3)

In formula, a, b and c are coefficient；

Nearest 3 square-wave signals are taken to be analyzed, f (t) meets relationship below in each square width:

${\&integral;}_{t_i}^{t_{i+1}}f\left(t\right)\mathrm{dt}=1---\left(4\right)$

In formula, t_iFor square wave start time, the i.e. rising edge of square wave, t_i+1For the finish time of square wave, formula (3) is substituted into (4) formula obtains

${\&integral;}_{t_i}^{t_{i+1}}({\mathrm{at}}^2+\mathrm{bt}+c)\mathrm{dt}=1---\left(5\right)$

Formula (5) integration expansion can obtain

$\frac{{t_{i+1}}^3-{t_i}^3}{3}a+\frac{{t_{i+1}}^2-{t_i}^2}{2}b+(t_{i+1}-t_i)c=1---\left(6\right)$

The start and end time of nearest 3 square waves is substituted into formula (6) respectively, obtains ternary linear function group:

$\left\{\begin{array}{c}\frac{{t_{n-2}}^3-{t_{n-3}}^3}{3}a+\frac{{t_{n-2}}^2-{t_{n-3}}^2}{2}b+(t_{n-2}-t_{n-3})c=1\\ \frac{{t_{n-1}}^3-{t_{n-2}}^3}{3}a+\frac{{t_{n-1}}^2-{t_{n-2}}^2}{2}b+(t_{n-1}-t_{n-2})c=1\\ \frac{{t_n}^3-{t_{n-1}}^3}{3}a+\frac{{t_n}^2-{t_{n-1}}^2}{2}b+(t_n-t_{n-1})c=1\end{array}\right.---\left(7\right)$

Solve equation group, obtain coefficient a, b and c, substitute into formula (3), obtain the quadratic fit formula of pre- measured frequency, use Before calculating next square wave rising edge arrival, that is, in t_n+1[t before moment_n, t_n+1] time period frequency.

Due to employing technique scheme, the present invention has the advantage that:

The present invention adopts predictive value to replace measured value as output valve, and predictive value can compensate for the delayed mistake of measured value presence Difference, thus improving real time frequency measurement precision, and not reducing the certainty of measurement of steady frequency, being not take up extra intervalometer, Amount of calculation is little, will not increase the hardware cost of Frequency tester equipment simultaneously.

Other advantages of the present invention, target and feature will be illustrated to a certain extent in the following description, and And to a certain extent, will be apparent to those skilled in the art based on to investigating hereafter, or can To be instructed from the practice of the present invention.The target of the present invention and other advantages can be wanted by description below and right Book is asked to realize and to obtain.

Brief description

The brief description of the present invention is as follows.

Fig. 1 is the signal schematic representation of linear fit predicted method；

Fig. 2 is the signal schematic representation of quadratic fit predicted method；

Fig. 3 is the signal comparison schematic diagram after cycle test method, linear fit predicted method and quadratic fit predicted method are processed；

Fig. 4 is the schematic flow sheet of the present invention.

Specific embodiment

The invention will be further described with reference to the accompanying drawings and examples.

Linear fit predicted method:

Linear fit predicted method is the method predicting following frequency according to the time width of 2 nearest square waves.If using Linear fit formula in pre- measured frequency is

F (t)=at+b (1)

In formula, a and b is coefficient, solves this 2 coefficients, you can according to following frequency of this formula prediction.

As shown in Fig. 1 (a), take up-to-date 2 square wave, the process solving a and b is as follows:

In t_n-1In the moment, [t can be calculated_n-2, t_n-1] average frequency of time period isAnd be considered asMoment Frequency, that is, $f\left(\frac{t_{n-1}+t_{n-2}}{2}\right)=\frac{1}{t_{n-1}-t_{n-2}};$

In t_nIn the moment, [t can be calculated_n-1, t_n] average frequency of time period isAnd be considered asThe frequency in moment Rate, that is, $f\left(\frac{t_n+t_{n-1}}{2}\right)=\frac{1}{t_n-t_{n-1}};$

Will $f\left(\frac{t_{n-1}+t_{n-2}}{2}\right)=\frac{1}{t_{n-1}-t_{n-2}}$ With $f\left(\frac{t_n+t_{n-1}}{2}\right)=\frac{1}{t_n-t_{n-1}}$ Substitute into formula (1), obtain equation below group

$\left\{\begin{array}{c}a\frac{t_{n-1}+t_{n-2}}{2}+b=\frac{1}{t_{n-1}-t_{n-2}}\\ a\frac{t_n+t_{n-1}}{2}+b=\frac{1}{t_n-t_{n-1}}\end{array}\right.---\left(2\right)$

Solving equation group (2), obtains the value of a and b, substitutes into formula (1), obtains the linear fit formula of pre- measured frequency, Before next square wave rising edge arrives, i.e. t_n+1Before moment, calculate frequency values and as output valve with this fitting formula.

As shown in Fig. 1 (b), in t_n+1In the moment, collect square wave rising edge, need again to take up-to-date 2 square-wave signal, And design factor a and b again, calculate [t first_n, t_n+1] average frequency of time period isAnd be considered asWhen The frequency carved, that is, $f\left(\frac{t_n+t_{n+1}}{2}\right)=\frac{1}{t_{n+1}-t_n},$ In conjunction with $f\left(\frac{t_n+t_{n-1}}{2}\right)=\frac{1}{t_n-t_{n-1}},$ Obtain equation group (3), solve a and b, substitute into Formula (1), obtains the linear fit formula of pre- measured frequency, before next square wave rising edge arrives, i.e. t_n+2Before moment, Calculate frequency values with this fitting formula and as output valve

$\left\{\begin{array}{c}a\frac{t_n+t_{n-1}}{2}+b=\frac{1}{t_n-t_{n-1}}\\ a\frac{t_{n+1}+t_{n-1}}{2}+b=\frac{1}{t_{n+1}-t_n}\end{array}\right.$

The like, when each square wave rising edge arrives, according to 2 up-to-date square-wave signals come renewal equation group, weight New solution coefficient a and b, obtains the linear fit formula of new pre- measured frequency, before next square wave rising edge arrives, is used for Calculate frequency values and as output valve.

Quadratic fit predicted method:

Quadratic fit predicted method is the method predicting following frequency according to the width of 3 nearest measured signal square waves. If the quadratic fit formula for pre- measured frequency is

F (t)=at²+bt+c (3)

In formula, a, b and c are coefficient, solve this 3 coefficients, you can according to following frequency of this formula prediction.

Coefficient a is described below, the solution procedure of b and c:

As shown in Fig. 2 (a), up-to-date 3 square-wave signal is taken to be analyzed, f (t) is full in each signal square width Sufficient relational expression

${\&integral;}_{t_i}^{t_{i+1}}f\left(t\right)\mathrm{dt}=1---\left(4\right)$

In formula, t_iFor square wave start time, i.e. square wave rising edge, t_i+1Finish time for square wave.

Wushu (3) substitutes into formula (4) and obtains

${\&integral;}_{t_i}^{t_{i+1}}({\mathrm{at}}^2+\mathrm{bt}+c)\mathrm{dt}=1---\left(5\right)$

Integration expansion can obtain

$\frac{{t_{i+1}}^3-{t_i}^3}{3}a+\frac{{t_{i+1}}^2-{t_i}^2}{2}b+(t_{i+1}-t_i)c=1---\left(6\right)$

The start and end time of 3 up-to-date square waves is substituted into formula (6) respectively, obtains ternary linear function group

$\left\{\begin{array}{c}\frac{{t_{n-2}}^3-{t_{n-3}}^3}{3}a+\frac{{t_{n-2}}^2-{t_{n-3}}^2}{2}b+(t_{n-2}-t_{n-3})c=1\\ \frac{{t_{n-1}}^3-{t_{n-2}}^3}{3}a+\frac{{t_{n-1}}^2-{t_{n-2}}^2}{2}b+(t_{n-1}-t_{n-2})c=1\\ \frac{{t_n}^3-{t_{n-1}}^3}{3}a+\frac{{t_n}^2-{t_{n-1}}^2}{2}b+(t_n-t_{n-1})c=1\end{array}\right.---\left(7\right)$

Solve equation group and obtain coefficient a, b and c, substitute into formula (3) and obtain predicting the quadratic fit formula of frequency.

As shown in Fig. 2 (b), in t_n+1In the moment, collect square-wave signal rising edge, again take up-to-date 3 square wave, obtain New ternary linear function group, such as formula (8), solve equation group and obtain coefficient a, b and c, substitute into formula (3) and obtain prediction frequency The quadratic fit formula of rate.

$\left\{\begin{array}{c}\frac{{t_{n-1}}^3-{t_{n-2}}^3}{3}a+\frac{{t_{n-1}}^2-{t_{n-2}}^2}{2}b+(t_{n-1}-t_{n-2})c=1\\ \frac{{t_n}^3-{t_{n-1}}^3}{3}a+\frac{{t_n}^2-{t_{n-1}}^2}{2}b+(t_n-t_{n-1})c=1\\ \frac{{t_{n+1}}^3-{t_n}^3}{3}a+\frac{{t_{n+1}}^2-{t_n}^2}{2}b+(t_{n+1}-t_n)c=1\end{array}\right.---\left(8\right)$

The like, when each new square wave arrives, update ternary first power according to 3 up-to-date square-wave signal width Journey group, solves coefficient a, b and c, obtains new frequency fitting formula, for pre- measured frequency.

Below the calculating process of cycle test method, linear fit predicted method and quadratic fit predicted method is illustrated, as Fig. 3 institute Show:

The calculating process of cycle test method

Cycle test method calculates frequency and updates output valve in the rising edge of each square wave.Calculating process is as follows:

During time t=1.30s, frequency can be calculated

During time t=1.48s, frequency can be calculated

During time t=1.64s, frequency can be calculated

During time t=1.78s, frequency can be calculated

During time t=1.90s, frequency can be calculated

During time t=2.00s, frequency can be calculated

The calculating process of linear fit predicted method

Linear fit predicted method lists equation group in the rising edge of each square wave according to 2 up-to-date square waves, solve a and B, obtains the linear fit formula of pre- measured frequency, calculates output valve according to predictor formula.The process of digital simulation formula is as follows:

Calculate the fitting formula of t ∈ [1.48,1.64] time period: t_n-2=1.10；t_n-1=1.30；t_n=1.48；Generation Enter formula (2), the equation group obtaining solving coefficient a and b is $\left\{\begin{array}{c}a\×1.20+b=5.000\\ a\×1.39+b=5.556\end{array}\right.,$ Solve a=2.926, b=1.488, then line Property fitting formula be f (t)=2.926t+1.488.

Calculate the fitting formula of t ∈ [1.64,1.78] time period: t_n-2=1.30；t_n-1=1.48；t_n=1.64；Generation Enter formula (2), the equation group obtaining solving coefficient a and b is $\left\{\begin{array}{c}a\×1.39+b=5.556\\ a\×1.56+b=6.250\end{array}\right.,$ Solve a=4.082, b=-0.1185, then Linear fit formula is f (t)=4.082t-0.1185.

Calculate the fitting formula of t ∈ [1.78,1.90] time period: t_n-2=1.48；t_n-1=1.64；t_n=1.78；Generation Enter formula (2), the equation group obtaining solving coefficient a and b is $\left\{\begin{array}{c}a\×1.56+b=6.250\\ a\×1.71+b=7.143\end{array}\right.,$ Solve a=5.953, b=-3.037, then line Property fitting formula be f (t)=5.953t-3.037.

Calculate the fitting formula of t ∈ [1.90,2.00] time period: t_n-2=1.64；t_n-1=1.78；t_n=1.90；Generation Enter formula (2), the equation group obtaining solving coefficient a and b is $\left\{\begin{array}{c}a\×1.71+b=7.143\\ a\×1.84+b=8.333\end{array}\right.,$ Solve a=9.154, b=-8.510, then line Property fitting formula be f (t)=9.154t-8.510.

Calculate the fitting formula of t ∈ [2.00, next square wave rising edge time] time period: t_n-2=1.78；t_n-1= 1.90；t_n=2.00；Substitution formula (2), obtain solve coefficient a and b equation group be $\left\{\begin{array}{c}a\×1.84+b=8.333\\ a\×1.95+b=10.00\end{array}\right.,$ Solve a= 15.15, b=-19.55, then linear fit formula is f (t)=15.15t-19.55.

The calculating process of quadratic fit predicted method

Calculate the fitting formula of t ∈ [1.64,1.78] time period: t_n-3=1.10；t_n-2=1.30；t_n-1=1.48；t_n =1.64；Substitution formula (7), obtains solving coefficient a, the equation group of b and c is $\left\{\begin{array}{c}0.2887a+0.2400b+0.2000c=1\\ 0.3483a+0.2502b+0.1800c=1\\ 0.3897a+0.2496b+0.1600c=1\end{array}\right.,$ Solve a= 3.243, b=-5.465, c=6.877, then linear fit formula is f (t)=3.243t²-5.465t+6.877.

Calculate the fitting formula of t ∈ [1.78,1.90] time period: t_n-3=1.30；t_n-2=1.48；t_n-1=1.64；t_n =1.78；Substitution formula (7), obtains solving coefficient a, the equation group of b and c is $\left\{\begin{array}{c}0.3483a+0.2502b+0.1800c=1\\ 0.3897a+0.2496b+0.1600c=1\\ 0.4096a+0.2394b+0.1400c=1\end{array}\right.,$ Solve a= 5.792, b=-12.97, c=12.38, then linear fit formula is f (t)=5.792t²-12.97t+12.38.

Calculate the fitting formula of t ∈ [1.90,2.00] time period: t_n-3=1.48；t_n-2=1.64；t_n-1=1.78；t_n =1.90；Substitution formula (7), obtains solving coefficient a, the equation group of b and c is $\left\{\begin{array}{c}0.3897a+0.2496b+0.1600c=1\\ 0.4096a+0.2394b+0.1400c=1\\ 0.4064a+0.2208b+0.1200c=1\end{array}\right.,$ Solve a= 11.51, b=-31.65, c=27.59, then linear fit formula is f (t)=11.51t²-31.65t+27.59.

Calculate the fitting formula of t ∈ [2.00, next square wave rising edge time] time period: t_n-3=1.64；t_n-2= 1.78；t_n-1=1.90；t_n=2.00；Substitution formula (7), obtains solving coefficient a, the equation group of b and c is $\left\{\begin{array}{c}0.4096a+0.2394b+0.1400c=1\\ 0.4064a+0.2208b+0.1200c=1\\ 0.3803a+0.1950b+0.1000c=1\end{array}\right.,$ Solve a=25.07, b=-79.75, c=70.15, then linear fit formula is f (t) =25.07t²-79.75t+70.15.

Finally illustrate, above example only in order to technical scheme to be described and unrestricted, although with reference to relatively Good embodiment has been described in detail to the present invention, it will be understood by those within the art that, can be to the skill of the present invention Art scheme is modified or equivalent, the objective without deviating from the technical program and scope, and it all should be covered in the present invention Right in the middle of.

Claims (3)

1. the signal frequency method for real-time measurement based on low-frequency square-wave signal frequency predication is it is characterised in that specifically comprise the following steps that

1) obtain tested square-wave signal；

2) measure and record initial time and the time width of tested each square wave of square-wave signal；

3) initial time and the time width of square wave have been surveyed according to tested square-wave signal, using linear fit predicted method or secondary plan Close predicted method, obtain frequency linearity fitting formula or the frequency quadratic fit formula of tested square-wave signal；

4) according to frequency linearity fitting formula or frequency quadratic fit formula, calculate and export next square-wave signal in real time and arrive Signal estimation frequency before；

5) judge whether to get new signal, if getting new signal, return to step 2), otherwise return to step 4).

2. the signal frequency method for real-time measurement based on low-frequency square-wave signal frequency predication as claimed in claim 1, its feature Be, step 3) described in linear fit predicted method concrete grammar as follows:

Initial time t in n-th square wave_n, obtain the initial time t having surveyed nearest 2 square waves_n-1、t_n-2With square wave time width t_n-t_n-1And t_n-1-t_n-2If the linear fit formula for pre- measured frequency is

F (t)=at+b (1)

In formula, a and b is coefficient；

In t_n-1In the moment, [t can be calculated_n-2, t_n-1] average frequency of time period isAnd be considered asThe frequency in moment Rate, that is, $f\left(\frac{t_{n-1}+t_{n-2}}{2}\right)=\frac{1}{t_{n-1}-t_{n-2}};$

In t_nIn the moment, [t can be calculated_n-1, t_n] average frequency of time period isAnd be considered asThe frequency in moment, I.e.

$f\left(\frac{t_n+t_{n-1}}{2}\right)=\frac{1}{t_n-t_{n-1}};$

Will $f\left(\frac{t_{n-1}+t_{n-2}}{2}\right)=\frac{1}{t_{n-1}-t_{n-2}}$ With $f\left(\frac{t_n+t_{n-1}}{2}\right)=\frac{1}{t_n-t_{n-1}}$ Substitute into formula (1), obtain equation group:

$\left\{\begin{array}{c}a\frac{t_{n-1}+t_{n-2}}{2}+b=\frac{1}{t_{n-1}-t_{n-2}}\\ a\frac{t_n+t_{n-1}}{2}+b=\frac{1}{t_n-t_{n-1}}\end{array}\right.---\left(2\right)$

Solve equation group, obtain a and b coefficient, a and b is substituted into formula (1), obtains the linear fit formula of pre- measured frequency, use Before calculating next square wave rising edge arrival, that is, in t_n+1[t before moment_n, t_n+1] time period frequency.

3. the signal frequency method for real-time measurement based on low-frequency square-wave signal frequency predication as claimed in claim 1, its feature Be, step 3) described in quadratic fit predicted method concrete grammar as follows:

Initial time t in n-th square wave_n, obtain the initial time t having surveyed nearest 3 square waves_n-1、t_n-2、t_n-3With the square wave time Width t_n-t_n-1、t_n-1-t_n-2And t_n-2-t_n-3If the quadratic fit formula for pre- measured frequency is

F (t)=at²+bt+c (3)

In formula, a, b and c are coefficient；

Nearest 3 square waves are taken to be analyzed, f (t) meets relationship below in each square width:

${\&integral;}_{t_i}^{t_{i+1}}f\left(t\right)\mathrm{dt}=1---\left(4\right)$

In formula, t_iFor square wave start time, the i.e. rising edge of square wave, t_i+1For the finish time of square wave, formula (3) is substituted into (4) formula ?

${\&integral;}_{t_i}^{t_{i+1}}({\mathrm{at}}^2+\mathrm{bt}+c)\mathrm{dt}=1---\left(5\right)$

Formula (5) integration expansion can obtain

$\frac{{t_{i+1}}^3-{t_i}^3}{3}a+\frac{{t_{i+1}}^2-{t_i}^2}{2}b+(t_{i+1}-t_i)c=1---\left(6\right)$

The start and end time of nearest 3 square waves is substituted into formula (6) respectively, obtains ternary linear function group:

$\left\{\begin{array}{c}\frac{{t_{n-2}}^3-{t_{n-3}}^3}{3}a+\frac{{t_{n-2}}^2-{t_{n-3}}^2}{2}b+(t_{n-2}-t_{n-3})c=1\\ \frac{{t_{n-1}}^3-{t_{n-2}}^3}{3}a+\frac{{t_{n-1}}^2-{t_{n-2}}^2}{2}b+(t_{n-1}-t_{n-2})c=1\\ \frac{{t_n}^3-{t_{n-1}}^3}{3}a+\frac{{t_n}^2-{t_{n-1}}^2}{2}b+(t_n-t_{n-1})c=1\end{array}\right.---\left(7\right)$

Solve equation group, obtain coefficient a, b and c, substitute into formula (3), obtain the quadratic fit formula of pre- measured frequency, by based on Before calculating next square wave rising edge arrival, that is, in t_n+1[t before moment_n, t_n+1] time period frequency.