CN107271002A - A kind of Spectrum Correction interpolation algorithm of quick high accuracy - Google Patents
A kind of Spectrum Correction interpolation algorithm of quick high accuracy Download PDFInfo
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- CN107271002A CN107271002A CN201710463003.2A CN201710463003A CN107271002A CN 107271002 A CN107271002 A CN 107271002A CN 201710463003 A CN201710463003 A CN 201710463003A CN 107271002 A CN107271002 A CN 107271002A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
- G01F23/00—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm
- G01F23/22—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm by measuring physical variables, other than linear dimensions, pressure or weight, dependent on the level to be measured, e.g. by difference of heat transfer of steam or water
- G01F23/28—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm by measuring physical variables, other than linear dimensions, pressure or weight, dependent on the level to be measured, e.g. by difference of heat transfer of steam or water by measuring the variations of parameters of electromagnetic or acoustic waves applied directly to the liquid or fluent solid material
- G01F23/296—Acoustic waves
- G01F23/2966—Acoustic waves making use of acoustical resonance or standing waves
Abstract
A kind of Spectrum Correction interpolation algorithm of quick high accuracy is claimed in the present invention, comprises the following steps：With signal picker to signal sampling.Signal adding window pretreatment to collecting；The null value of equal length is added after signal after the pre-treatment；Calculate the coefficient of the Taylor series relevant with institute windowed function；Amplitude Ration is tried to achieve by Fourier transformation, the smart estimate after frequency rough estimate and iteration 1 time is further obtained.The invention has the advantages that：1, this method has broken the limitation that interpolation method depends on window function, i.e., for arbitrary window function, and the method is applicable.2, to different window functions, the systematic error of this algorithm is respectively less than 10‑7Even if, can be close to Cram é r Rao lower bound (CRLB), when especially adding rectangular window, with very strong noise robustness in the case that signal is disturbed by white Gaussian noise (signal to noise ratio changes from 5dB to 100dB).
Description
Technical field
The invention belongs to field of measuring technique, a kind of estimating for signal frequency in well fluid level e measurement technology is particularly belonged to
Meter.
Background technology
The well fluid level detection method based on tubing string sound field characteristic having pointed out at present, using acoustic theory to single-ended
The impedance of closed conduct is analyzed, and by the resonance principle of air column in tube and casing in downhole, establishes fluid level depth of oil well
With the mathematical modeling of inner air tube resonant frequency
fnFor the n-th order resonant frequency of air column in oil jacket annular space, v is the spread speed of Acoustic, and D is downhole tubular
The diameter in road.Therefore, in the case of known to spread speed, if the n-th rank resonant frequency of underground air post can be measured accurately
fn, that dynamic oil level can obtain.From the foregoing, it will be observed that how the resonant frequency for estimating underground air post of precise and high efficiency is
Measurement dynamic oil level wants the problem that emphasis is solved.
In actually measurement, the true resonant frequency of acoustic signals can not be learnt by other method, it is difficult to select suitable
Sample frequency with reach it is integer-period sampled eliminate spectrum leakage and fence effect that aperiodic sample strip comes, therefore, how profit
Sampled obtained signal message with aperiodic and obtained the popular class that more accurate frequency values are field of signal processing in recent years
Topic, but still suffer from following deficiency currently with the Spectrum Correction algorithm of interpolation method：1st, for different window functions, correspondence is not
Same interpolation algorithm, and only having specific window function at present has its to correct expression formula, such as rectangular window, Hanning window, and it is right
In Gaussian window, its expression formula of Caesar Bel window derives complexity, and difficulty is very big.2nd, the noise immunity for the difference arithmetic that presently, there are
Growing requirement of engineering can be also insufficient for.
The content of the invention
Present invention seek to address that above problem of the prior art.Propose that a kind of error is small, be adapted to arbitrary window letter
The Spectrum Correction interpolation algorithm of the strong quick high accuracy of number, noise robustness.Technical scheme is as follows：
A kind of Spectrum Correction interpolation algorithm of quick high accuracy, it comprises the following steps：
1), measured signal is sampled with signal picker；2), the signal adding window collected is pre-processed, after the pre-treatment
Signal after add the null value of equal length；3) coefficient of the Taylor series relevant with institute windowed function, is calculated；4), by right
Signal Fourier transformation, obtains time amplitude and maximum amplitude, tries to achieve Amplitude Ration, frequency is obtained using frequency domain amplitude search method
Smart estimate after rough estimate evaluation and iteration 1 time.Further, the step 1) in measured signal is adopted with signal picker
Sample, introduces signal
In formula, N is the points of collection signal, f0For the actual frequency of signal,For the true initial phase of signal, fsTo adopt
Collect sample frequency during signal, fsWith f0Meet Nyquist conditions, i.e. fs＞ 2f0, andλ0For f0After normalization
Signal frequency.
Further, step 2) in the signal adding window that collects is pre-processed, added after signal after the pre-treatment identical
The null value of length includes：
The window function of N points is constructed for w (n), n=0,1 ... N-1, i.e., it is identical with gathering the length of signal,
Then the signal after adding window is expressed as xw(n)=x (n) w (n), now, in xw(n) zero sequence that length is N is added after
Row, then to data progress discrete Fourier transform of the length after adding window zero padding for 2N, obtainAnd l ∈ Z+, A represents amplitude,
W represents the window function after Fourier transformation.
Further, the step 3) calculate the Coefficient ms of the Taylor series relevant with institute windowed function1It is calculated as follows；
The modular function of window function is represented by
Wherein
H ' (0.5) represents H (0.5) single order local derviation.
(11)
Then m1It is represented by
Wherein
Further, step 4) frequency domain amplitude search method is utilized, it is l to obtain corresponding spectral line number at amplitude maximum, can be obtained
Time amplitude and maximum amplitude are obtained by Fourier transformation, Amplitude Ration is tried to achieve
It then can obtain frequency rough estimate
Further, alternative manner is utilized to frequency rough estimate, obtains accurate frequency estimation, redefine width
Value ratio etc.
The then smart estimate of frequency
f2=f1+τ2 (19)。
Advantages of the present invention and have the beneficial effect that：
The invention has the advantages that the interpolation method proposed is applied to any window function, and for different window functions, estimation
Precision is higher, and next is to solve the coefficient relevant with window function, and proposes its corresponding fast algorithm, greatlys save calculation
Method run time, emulation experiment shows that this algorithm is applied to Practical Project field.
Brief description of the drawings
Fig. 1 is the system absolute value error that the present invention is adapted to conventional window function；
Fig. 2 is the root-mean-square error of algorithm when adding different window functions；
Fig. 3 is the preferred embodiments of the present invention flow chart.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, detailed
Carefully describe.Described embodiment is only a part of embodiment of the present invention.
The present invention solve above-mentioned technical problem technical scheme be：
1st, a kind of frequence estimation new method, it comprises the following steps：
1) by analog-digital converter with sample frequency fsSampling is digitized to measured signal, length adopting for N is obtained
Sample data.
2) any window function of length N points is constructed, adding window pretreatment first is carried out to sampled data, then data are being obtained
Tail end adds the null value that length is N, finally carries out discrete Fourier transform (DFT) computing, obtains the frequency after signal adding window zero padding
Numeric field data Xw(k), k=0,1 ... N-1.Frequency domain data X (k), the k=0,1 of the windowing signal of non-zero padding ... N-1.
3) coefficient of the relevant Taylor series of institute's windowed function is calculated, m is set to.
4) utilize frequency domain spectrum search method, find corresponding spectral line l at maximum amplitude, i.e. l=max (| Xw(k) |),
Then spectral line l ± 1 of maximum amplitude both sides can be obtained.
If 5) setIt then can obtain frequency rough estimate
6) it is iterated, nowThe then smart estimate f of frequency2=f1+τ2。
2nd, in order to preferably describe the method, step 1) in introduce signal
In formula, N is the points of collection signal, f0For the actual frequency of signal,For the true initial phase of signal, fsTo adopt
Collect sample frequency during signal, fsWith f0Nyquist conditions are met, with the error for avoiding signal aliasing from bringing, i.e. fs＞
2f0, andλ0For f0Signal frequency after normalization.
3rd, step 2) in construction N points window function be w (n), n=0,1 ... N-1, i.e., with collection signal length phase
Together, then the signal after adding window is represented by xw(n)=x (n) w (n) (2)
Now, in xw(n) added after length be N null sequence, then to length after adding window zero padding for 2N data carry out from
Fourier transformation is dissipated, is obtained
4th, step 3) in window coefficient correlation be calculated as follows：Due to during actual samples, it is impossible to accomplish that complete cycle adopts
Sample, so the actual signal frequency after normalization is always located between two spectral lines, i.e.,
λ0=l+ τ (4)
L represents λ0Integer part, τ represents λ0Fractional part.If Amplitude Ration
If
Then
By h (τ), Taylor series expansion can be obtained at τ=0
H (τ)=m can be obtained by omitting high-order term1τ (9)
Further we can obtain, if knowing m1, then correcting value τ is that can obtain.
m1It is calculated as follows：
The modular function of window function is represented by
Wherein
Then m1It is represented by
Wherein
5th, step 5) frequency domain amplitude search method is utilized, it is l to obtain corresponding spectral line number at amplitude maximum, can be obtained
It then can obtain frequency rough estimate
6th, step 6) alternative manner is utilized, accurate frequency estimation is obtained, Amplitude Ration etc. is redefined
The then smart estimate of frequency
f2=f1+τ2 (19)
Proof of algorithm example one：
The discrete-time series of checking is produced by formula (1).Sample frequency is set to fs=1024, sampling number is N=1024,
That is frequency resolutionFrequency is with step pitch 0.025 from 255.5 to 256.5 changes, and phase is become with step pitch 1/36 from-π to π
Change, during the phase value for taking correspondence different, system worst error is as evaluation criterion, and Fig. 1 is exhausted for the system of different window function algorithm
To value error；
Fig. 1 is shown (is followed successively by rectangular window, Hanning window, hamming window, Blackman window, Kai Sabei using different window functions
That window, Gaussian window) when, the system absolute error of new method.According to shown in Fig. 1, for all window functions, maximum frequency error is about
For 10-7, this is sufficient for most engineering applications, while showing that the algorithm is applicable to different window functions.
Proof of algorithm example two：
In actual engineer applied, the signal collected causes discrete spectrum to correct inevitably by noise pollution
Arithmetic accuracy greatly reduce, the present invention have studied when signal is disturbed by different degrees of white Gaussian noise, the calculation of proposition
The ability of the antinoise influence of method, the discrete-time series of checking is produced by formula (1).Sample frequency is set to fs=1024, sampling
Count as N=1024, i.e. frequency resolutionFrequency is randomly selected from 255.5 to 256.5, and phase is selected at random from-π to π
Take, produce 10000 examples disturbed with white Gaussian noise, investigate the root-mean-square error of various window functions.Fig. 2 is compared
The effect of algorithm during different window functions, while also show the carat Metro lower limit (CRLB) of Frequency Estimation.
From figure 2 it can be seen that for different window functions, with SNR change, new algorithm all has smaller
Error, and for rectangular window, the root-mean-square error of algorithm is in close proximity to CRLB, and therefore, new algorithm has preferable antinoise
Performance.
The above embodiment is interpreted as being merely to illustrate the present invention rather than limited the scope of the invention.
After the content of record of the present invention has been read, technical staff can make various changes or modifications to the present invention, and these are equivalent
Change and modification equally fall into the scope of the claims in the present invention.
Claims (6)
1. the Spectrum Correction interpolation algorithm of a kind of quick high accuracy, it is characterised in that comprise the following steps：
1), measured signal is sampled with signal picker；2), the signal adding window collected is pre-processed, letter after the pre-treatment
The null value of equal length is added after number；3) coefficient of the Taylor series relevant with institute windowed function, is calculated；4), by signal
Fourier transformation, obtains time amplitude and maximum amplitude, tries to achieve Amplitude Ration, frequency rough estimate is obtained using frequency domain amplitude search method
Smart estimate after value and iteration 1 time.
2. the Spectrum Correction interpolation algorithm of quick high accuracy according to claim 1, it is characterised in that the step 1) in
Measured signal is sampled with signal picker, signal is introduced
In formula, N is the points of collection signal, f0For the actual frequency of signal,For the true initial phase of signal, fsFor collection letter
Number when sample frequency, fsWith f0Meet Nyquist conditions, i.e. fs＞ 2f0, andλ0For f0Signal after normalization
Frequency.
3. the Spectrum Correction interpolation algorithm of quick high accuracy according to claim 2, it is characterised in that step 2) in adopting
The null value of equal length is added after the signal adding window pretreatment collected, signal after the pre-treatment to be included：
The window function for constructing N points is w (n), n=0,1 ... N-1, i.e., then signal adding window after identical with the length of collection signal
It is expressed as xw(n)=x (n) w (n), now, in xw(n) null sequence that length is N is added after, then is 2N to length after adding window zero padding
Data carry out discrete Fourier transform, obtain
And l ∈ Z+, A represents the window function after amplitude, W Fourier transformations.
4. the Spectrum Correction interpolation algorithm of quick high accuracy according to claim 3, it is characterised in that
The step 3) calculate the Coefficient ms of the Taylor series relevant with institute windowed function1It is calculated as follows；
The modular function of window function is represented by
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Cited By (3)
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| CN109540545A (en) * | 2018-11-30 | 2019-03-29 | 厦门大学 | Used with tractor power output assembly abnormal sound diagnostic signal acquisition device and processing method |
| CN111580188A (en) * | 2020-07-06 | 2020-08-25 | 吉林大学 | Magnetotelluric time domain calibration method and system |
| CN115857013A (en) * | 2022-12-09 | 2023-03-28 | 中国科学院地质与地球物理研究所 | Method for calculating self-noise of seismometer by using improved welch method |
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