CN103886199A - Harmonic wavelet analysis method for modulating spectral signals - Google Patents
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Abstract
The invention discloses a harmonic wavelet analysis method for modulating spectral signals. The harmonic wavelet analysis method is based on the wavelength of a TDLAS, and includes the implementation steps of (1) building a harmonic wavelet equation of the modulated spectral signals of the TDLAS, (2) computing the harmonic wavelet expansion coefficients of the signals with a decomposition algorithm, (3) determining decomposition layer numbers required by signal analysis according to the corresponding relation between wavelet decomposition layer numbers and analysis frequency bands, (4) retaining the harmonic wavelet coefficients of the required frequency bands, and obtaining the signals of the frequency bands through Fourier transformation, (5) constructing an envelope function of the frequency bands, and (6) carrying out an envelope taking process on the signals of the frequency bands to obtain frequency doubling signals of the modulated signals of the TDLAS.
Description
Technical field
The invention belongs to field of optical measuring technologies, a nearlyer step relates to a kind of tunable semiconductor laser absorption spectrum (TDLAS) modulated signal analysis method based on harmonic wavelet principle, can be used for the measurement of gas temperature, concentration and gas velocity aspect based on TDLAS technology.
Background technology
Tunable semiconductor laser absorption spectrum (TDLAS) technology because it is subject to that gas environmental impact is little, fast response time, reliability be high, can not cause test environment the outstanding advantages such as disturbance to show one's talent in numerous novel measuring techniques, in widespread attention.Wavelength-modulated spectral technology in TDLAS technology carries out the modulation of high frequency to laser intensity, can be applied in the environment that noise is larger, thereby application is very extensive.Wavelength-modulated spectral technology has adopted high-frequency modulation signal, and its metrical information is included among harmonic signal, by harmonic signal analysis being obtained to the measurement result of gas temperature, concentration and gas velocity aspect.Existing TDLAS modulated signal analysis method has following one.
TDLAS modulation signal digital phase-locking Phase Analysis Method.For example, Li Hejie is at PhD dissertation " NEAR-INFRARED DIODE LASER ABSORPTION SPECTROSCOPY WITH APPLICATIONS TO REACTIVE SYSTEMS AND COMBUSTION CONTROL ": in 46-50, propose to utilize the phase-locked method of numeral to carry out harmonic signal detection to TDLAS modulation signal, but the signal that the method detects comprises more impurity signal, result is not very accurate, affects the accuracy of detection of TDLAS technology.
Summary of the invention
The object of the invention is to overcome the deficiencies in the prior art, according to the feature of TDLAS modulation signal, adopt harmonic wavelet principle to decompose modulation signal, according to the frequency range of frequency-doubled signal, obtain the needed decomposition number of plies of analytic signal.On this basis, propose a kind of Harmonic Wavelet Analysis method of the TDLAS of being applicable to modulation signal, realized comparatively accurate frequency-doubled signal and extract.
Specific embodiment of the invention step is as follows:
1) set up harmonic wavelet expression formula: utilize classical harmonic wavelet formula, and enable to reflect that compression and the translation of small echo in dimension obtains being applicable to the harmonic wavelet equation that frequency range is analyzed:
h(2
jt-k)＝[exp(i4π(2
jt-k))-exp(i2π(2
jt-k))]/i2π(2
jt-k)
Wherein j, k ∈ Z;
2) calculate harmonic wavelet expansion coefficient
2a) real signal is carried out to discrete Fourier transformation, obtain corresponding Fourier coefficient;
2b) based on harmonic wavelet fast algorithm, harmonic wavelet coefficient is by step 2a) in Fourier coefficient segmentation, each section of Fourier coefficient carried out to IFFT conversion and obtains corresponding harmonic wavelet coefficient;
3) determine the signal decomposition number of plies
3a) get the frequency multiplication of TDLAS modulation signal;
3b) according to the analysis frequency f of discrete signal
ndivide the frequency range of frequency-doubled signal;
3c) this frequency range is brought into the corresponding relation that harmonic wavelet decomposes the number of plies and signal analysis frequency band division, obtain the needed decomposition number of plies of analytic signal;
4) get frequency band signals
4a) the decomposition number of plies corresponding according to required frequency range, takes out harmonic wavelet coefficient in this layer;
4b) according to harmonic wavelet fast algorithm, this layer of harmonic wavelet coefficient carried out to a series of Fourier transforms and obtains the Fourier coefficient of signal;
4c) Fourier coefficient is carried out to inverse Fourier transform and obtains step 3b) discrete signal that Mid Frequency is corresponding;
5) structure envelope function;
5a) the frequency multiplication of the TDLAS modulation signal based in 3 (a), sets up sine and the cosine discrete signal of respective frequencies;
5b) be multiplied by respectively with cosine signal the signal that need to get envelope by sinusoidal, obtain two paths of signals;
5c) build low-pass filter, and by 5b) in the two paths of signals that obtains respectively by this wave filter;
5d) the two paths of signals pointwise by wave filter carried out square, be added and open radical sign computing;
6) get frequency-doubled signal: by 4c) in discrete signal bring in envelope function and carry out computing, obtain the frequency-doubled signal of TDLAS modulation signal.
Brief description of the drawings
Fig. 1 is process flow diagram of the present invention;
Fig. 2 is the modulated spectrum signal graph of emulation;
Fig. 3 is for utilizing digital filtering method, and it is 6 that Butterworth filter exponent number is set, and low-pass cut-off frequencies is respectively 28kHz, 38kHz, 48kHz and 62kHz, the 2 frequency-doubled signal figure that obtain;
Fig. 4 is for utilizing digital filtering method, and it is 48kHz that Butterworth filter low-pass cut-off frequencies is set, and filter order is respectively 2 rank, 3 rank, 4 rank and 6 rank, the 2 frequency-doubled signal figure that obtain;
Fig. 5 is frequency band signals and 2 frequency-doubled signals that Harmonic Wavelet Analysis method of the present invention obtains;
Fig. 6 is the comparison diagram of 2 frequency-doubled signals of 2 frequency-doubled signals that obtain of Harmonic Wavelet Analysis method of the present invention and emulation.
Embodiment
Below in conjunction with accompanying drawing, the present invention will be further described.
With reference to Fig. 1, specific embodiment of the invention step is as follows:
Step 1. is set up harmonic wavelet expression formula.
Classical harmonic wavelet expression formula is as follows:
With variable (2
jt-k) substitute the variable t in above formula, can obtain
h(2
jt-k)＝[exp(i4π(2
jt-k))-exp(i2π(2
jt-k))]/i2π(2
jt-k)
Wherein, j, k ∈ Z.Small echo has compressed 2 in dimension
jdoubly, and its position in new dimension translation k unit.
Step 2. is calculated harmonic wavelet expansion coefficient.
Harmonic wavelet forms L
2(R) orthonormal basis in space, therefore any real function signal x (t) can be expressed as the linear combination of harmonic wavelet, is also that signal can be decomposed into:
The harmonic wavelet of Here it is signal launches, because harmonic wavelet is for multiple small echo, therefore expansion coefficient a
j, kfor plural number, have
a
j,k＝<x(t),h(2
jt-k)> (j,k∈Z)
2a) establish the discrete-time series of a given real signal x (t):
x(n) n＝0,1,...,N-1
N=2 in formula
m.By discrete Fourier transformation (DFT), corresponding Fourier coefficient is:
2b) Fourier coefficient has relational expression:
F
N-k＝F
k k＝1,2,...N/2 (0.1)
In N Fourier coefficient, except F
0with F
n/
2total is outside real number, and all the other are generally plural number.
The harmonic wavelet coefficient of now supposing discrete-time series x (n) is
a
r r＝0,1,...,N-1 (0.2)
A
rby F
ksegmentation, obtains each section of IFFT conversion, can be obtained by following expression:
F
N-k＝F
k k＝1,2,...N/2 (0.3)
In N Fourier coefficient, except F
0with F
n/2total is outside real number, and all the other are generally plural number.
The harmonic wavelet coefficient of now supposing discrete-time series x (n) is
a
r r＝0,1,...,N-1 (0.4)
A
rby F
ksegmentation, obtains each section of IFFT conversion, can be obtained by following expression:
Step 3. is determined the signal decomposition number of plies.
3a) frequency-doubled signal is determined frequency according to TDLAS modulation signal, and if modulation signal is 1kHz, the frequency of 2 frequency-doubled signals is 2kHz;
3b) according to the analysis frequency f of discrete signal
ndivide the frequency range of frequency-doubled signal.
The sample frequency that is provided with arbitrary discrete signal x (t) is f
s, its analysis frequency is f
n=f
s/ 2, the analysis frequency band of harmonic wavelet relation with 1/2 from high frequency to low frequency is successively decreased gradually, can be expressed as:
By the frequency substitution above formula of frequency-doubled signal, calculate n value, thereby obtain the frequency range of frequency-doubled signal.
3c) solve the needed decomposition number of plies of analytic signal.
The corresponding relation that harmonic wavelet decomposes the number of plies and signal analysis frequency band division is:
j＝log
2(N/4)-n
Wherein, j is that harmonic wavelet decomposes the number of plies, and N is counting of signal x (n), n is step 3b) n value in Mid Frequency scope.Can calculate harmonic wavelet by this corresponding relation and decompose number of plies j.
Step 4. is got frequency band signals.
4a) harmonic wavelet coefficient extracts.
The number of plies of harmonic wavelet and harmonic wave wavelet coefficient have following corresponding relation
According to step 3c) in the harmonic wavelet of trying to achieve decompose the number of plies, in substitution above formula relation, can obtain the harmonic wavelet coefficient that frequency-doubled signal is corresponding.
4b) according to harmonic wavelet fast algorithm, by step 4a) the harmonic wavelet coefficient that obtains carries out Fourier transform;
4c) adopt remainder certificate, the data extending after Fourier transform is become to the signal of N point, N is counting of signal x (n).Signal after expanding is carried out to Fourier inversion, obtains step 3b) discrete signal x that Mid Frequency is corresponding
frequency range(n).
Step 5. is constructed envelope function
5a) the frequency multiplication f of the TDLAS modulation signal based in 3 (a), sets up sine and cosine discrete signal: sin (2 π fn) and the cos (2 π fn) of respective frequencies.
5b) by sine and cosine signal respectively with discrete signal x
frequency range(n) pointwise is multiplied each other, and obtains signal X
fand Y
f;
5c) build Butterworth LPF, and by 5b) in signal obtain X ' by Butterworth filter respectively
fand Y '
f;
5d) by X '
fand Y '
fcarry out following computing:
Step 6. is got frequency-doubled signal: by 4c) in discrete signal x
frequency range(n) bring in envelope function and carry out computing, obtain the frequency-doubled signal R of TDLAS modulation signal
f.
Effect of the present invention can be illustrated by following emulation experiment:
Simulated conditions
One group of modulated spectrum data of emulation, adopt Gaussian curve as absorption curve; On this basis, utilize digital filtering method and harmonic wave wavelet method to carry out 2 frequency-doubled signal extractions; Finally, the 2 frequency multiplication data that two kinds of methods are extracted compare, and determine the relative merits of two kinds of methods.Simulation parameter arranges as shown in the table.
Simulation result
According to the setting of simulated conditions, calculate modulated spectrum signal as shown in Figure 2.First investigate 2 frequency-doubled signals that digital phase-locking method extracts.It is 6 that Butterworth filter exponent number is set, and low-pass cut-off frequencies is respectively 28kHz, 38kHz, 48kHz and 62kHz, obtains four kinds of results, as shown in Figure 3.
It is 48kHz that Butterworth filter low-pass cut-off frequencies is set again, and filter order is respectively 2 rank, 3 rank, 4 rank and 6 rank, obtains four kinds of results, as shown in Figure 4.
From two groups of results, can see: change cutoff frequency, signal center's peak value changes, and signal location changes; Change filter order, signal center's peak value changes, and flashlight slippery changes, and signal location changes; Can know, digital phase-locking method is difficult to find accurate central peak.
Original modulated spectrum signal is analyzed according to harmonic wavelet principle, obtained following result, as shown in Figure 5.Fig. 5 (a) is frequency band signals, and Fig. 5 (b) is 2 frequency-doubled signals.The frequency band signals of Fig. 5 (a) is definite unique, and has kept preferably the original appearance of 2 frequency-doubled signals; Frequency-doubled signal in Fig. 5 (b) is comparatively symmetrical, and peak value center is very clear and definite, is easy to identification.
Original signal is asked for to 2 frequency-doubled signals and compare with 2 frequency-doubled signals that harmonic wavelet method obtains, as shown in figure (6).In figure, solid line is 2 frequency-doubled signals that harmonic wavelet method obtains, 2 frequency-doubled signals that dotted line is emulation, and both coincide better; Peak point place, A
empty=0.0247, A reality=0.02445, e
error=1.01%.
In sum, compared with harmonic wavelet method is phase-locked with numeral, there is following characteristics: the phase-locked result of numeral is subject to the impact of cutoff frequency and filter order, is difficult to find accurate signal; The result of harmonic wavelet method has determinacy, is not subject to the impact of cutoff frequency and filter order; The central peak of frequency-doubled signal is comparatively accurate, and error is very little.Visible, the present invention can realize the Accurate Analysis of tunable semiconductor laser absorption spectrum (TDLAS) modulation signal.
In the present invention, all operations is all completed by data dot product and Fast Fourier Transform (FFT), there is higher efficiency, be applicable to Project Realization, the frequency-doubled signal of the TDLAS modulation signal that its method obtains can be widely used in the measurement of the aspect such as gas temperature, concentration based on TDLAS technology.
Claims (5)
1. a Harmonic Wavelet Analysis method for modulated spectrum signal, comprises the steps:
1) set up harmonic wavelet expression formula: utilize classical harmonic wavelet formula, and enable to reflect that compression and the translation of small echo in dimension obtains being applicable to the harmonic wavelet equation that frequency range is analyzed:
h(2
jt-k)＝[exp(i4π(2
jt-k))-exp(i2π(2
jt-k))]/i2π(2
jt-k)
Wherein j, k ∈ Z;
2) calculate harmonic wavelet expansion coefficient;
2a) real signal is carried out to discrete Fourier transformation, obtain corresponding Fourier coefficient;
2b) based on harmonic wavelet fast algorithm, harmonic wavelet coefficient is by step 2a) in Fourier coefficient segmentation, each section of Fourier coefficient carried out to IFFT conversion and obtains corresponding harmonic wavelet coefficient;
3) determine the signal decomposition number of plies
3a) get the frequency multiplication of TDLAS modulation signal;
3b) according to the analysis frequency f of discrete signal
ndivide the frequency range of frequency-doubled signal;
3c) this frequency range is brought into the corresponding relation that harmonic wavelet decomposes the number of plies and signal analysis frequency band division, obtain the needed decomposition number of plies of analytic signal;
4) get frequency band signals
4a) the decomposition number of plies corresponding according to required frequency range, takes out harmonic wavelet coefficient in this layer;
4b) according to harmonic wavelet fast algorithm, this layer of harmonic wavelet coefficient carried out to a series of Fourier transforms and obtains the Fourier coefficient of signal;
4c) Fourier coefficient is carried out to inverse Fourier transform and obtains step 3b) discrete signal that Mid Frequency is corresponding;
5) structure envelope function
5a) based on 3a) in the frequency multiplication of TDLAS modulation signal, set up sine and the cosine discrete signal of respective frequencies;
5b) be multiplied by respectively with cosine signal the signal that need to get envelope by sinusoidal, obtain two paths of signals;
5c) build low-pass filter, and by 5b) in the two paths of signals that obtains respectively by this wave filter;
5d) the two paths of signals pointwise by wave filter carried out square, be added and open radical sign computing;
6) get frequency-doubled signal: by 4c) in discrete signal bring in envelope function and carry out computing, obtain the frequency-doubled signal of TDLAS modulation signal.
2. the Harmonic Wavelet Analysis method of modulated spectrum signal according to claim 1, is characterized in that: described step 3a) in frequency multiplication determined by TDLAS modulation signal.
3. the Harmonic Wavelet Analysis method of modulated spectrum signal according to claim 1, is characterized in that: described step 5a) in sine identical with the frequency multiplication of TDLAS modulation signal with the frequency of cosine discrete signal.
4. the Harmonic Wavelet Analysis method of modulated spectrum signal according to claim 1, is characterized in that: described step 5b) in need to get envelope signal be the discrete signal obtaining by step 1,2,3,4.
5. the Harmonic Wavelet Analysis method of modulated spectrum signal according to claim 1, is characterized in that: described step 5c) in low-pass filter be Butterworth LPF.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104062264A (en) * | 2014-07-11 | 2014-09-24 | 刘颖东 | Spectral analysis type high-precision on-line detector for gas and liquid detection |
| CN104615846A (en) * | 2014-12-14 | 2015-05-13 | 励春亚 | Wavelet recognition method for landslide deformation sudden change abnormity |
| CN105223906A (en) * | 2015-09-15 | 2016-01-06 | 华中科技大学 | A kind of auto-correction method of digital control system servo drive signal harmonic frequency |
| CN105989240A (en) * | 2015-03-06 | 2016-10-05 | 中国石油天然气股份有限公司 | Sand layer prediction method and device |
| CN110865042A (en) * | 2019-11-26 | 2020-03-06 | 东北石油大学 | Gas concentration detection method, device and system |
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| CN102590138A (en) * | 2012-01-16 | 2012-07-18 | 清华大学 | Gas concentration on-line measurement method based on laser absorption spectrum |
| US20120188550A1 (en) * | 2010-07-27 | 2012-07-26 | Shimadzu Corporation | Gas Concentration Measurement Device |
| CN102680428A (en) * | 2012-05-16 | 2012-09-19 | 清华大学 | Gas temperature and concentration online measuring method based on first harmonic signal |
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2014
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| US20120188550A1 (en) * | 2010-07-27 | 2012-07-26 | Shimadzu Corporation | Gas Concentration Measurement Device |
| CN102590138A (en) * | 2012-01-16 | 2012-07-18 | 清华大学 | Gas concentration on-line measurement method based on laser absorption spectrum |
| CN102680428A (en) * | 2012-05-16 | 2012-09-19 | 清华大学 | Gas temperature and concentration online measuring method based on first harmonic signal |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104062264A (en) * | 2014-07-11 | 2014-09-24 | 刘颖东 | Spectral analysis type high-precision on-line detector for gas and liquid detection |
| CN104615846A (en) * | 2014-12-14 | 2015-05-13 | 励春亚 | Wavelet recognition method for landslide deformation sudden change abnormity |
| CN105989240A (en) * | 2015-03-06 | 2016-10-05 | 中国石油天然气股份有限公司 | Sand layer prediction method and device |
| CN105989240B (en) * | 2015-03-06 | 2018-09-04 | 中国石油天然气股份有限公司 | Sand layer prediction method and device |
| CN105223906A (en) * | 2015-09-15 | 2016-01-06 | 华中科技大学 | A kind of auto-correction method of digital control system servo drive signal harmonic frequency |
| CN110865042A (en) * | 2019-11-26 | 2020-03-06 | 东北石油大学 | Gas concentration detection method, device and system |
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