CN105548711B - A kind of multifrequency information filter recursive demodulation method - Google Patents
A kind of multifrequency information filter recursive demodulation method Download PDFInfo
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Abstract
The present invention relates to a kind of multifrequency information filter recursive demodulation methods, it is characterised in that includes the following steps：(1) according to known to frequency multi-frequency excitation system m frequency component f1, f2..., fmAnd sample frequency fsEstablish recurrence equation；(2) it is risen in measuring signal initial time, the initial value of information matrix U (k) and recursion intermediary matrix K (k) is calculated according to 2m sample point data later；(3) initial value and newly-increased sample point data are substituted into recurrence equation, update U (k) and K (k)；(4) judge whether demodulation result meets system accuracy requirement, return to step (3) if being unsatisfactory for terminate recursive process if meeting, calculate data matrix Bk, and export the amplitude and phase data of m frequency component in measuring signal.Multifrequency information filter recursive demodulation method has the characteristics that in no initial value can to start, iteration is simple, conducive to hardware realization, take up less resources, the directions such as being imaged in impedance spectrometry, electricity has broad application prospects.
Description
Technical field
The present invention relates to a kind of multifrequency information filter recursive demodulation methods, belong to distribution parameter measurement field.
Background technology
It is typically relatively complex in fields, the electrology characteristic of measurand such as the detection of industrial multiphase stream and medicine detection.Such as
Biological tissue's impedance has the characteristic that changes with frequency, and different tissues impedance magnitude at different frequencies and phase are different
And its variation with driving frequency and change.Therefore, the spectral characteristic abundanter to obtain measurand inner electrical parameter,
More and more impedance measurement systems, electricity imaging system have been not only limited to a kind of frequency, often to measure simultaneously two or
Impedance value or boundary distribution of impedance under more than two driving frequencies.However, the mode of multi-frequency excitation is also brought to measurement
It is more difficult, it is especially embodied on multifrequency demodulation mode.Multifrequency demodulation refers to demodulate from the multiple-frequency signal of measurement each
The process of frequency component amplitude and phase information is the key link that the system hardwares such as impedance spectrometry, electricity imaging are realized, simple
The research of single, quick multifrequency demodulation method has great importance.
To realize multifrequency signal phase demodulation, usually each frequency component of measuring signal is demodulated to obtain respectively
Measuring signal amplitude and phase information under different frequency component.The mode of traditional simulation multifrequency phase demodulation is needed and is encouraged
The identical phase-sensitive demodulator of frequency component quantity, considerably increases hardware circuit scale and complexity, reduces the real-time of system
Property.Digital phase-sensitive demodulation method based on digital processing unit with its it is good measurement real-time and succinct hardware circuit and
Obtain extensive concern.
Digital phase-sensitive demodulation method samples measured signal first with high-speed AD converter, then utilizes high property
Energy digital signal processing device, such as FPGA, DSP are believed using the amplitude and phase of the method extraction measured signal of numerical computations
Breath.Presently the most common digital phase-sensitive demodulation method is demodulated for orthogonal sequence, is applied in multifrequency electricity chromatographic imaging system
When, it is required that sample sequence length must cover the integer period of mixing frequency excitation mode signal (by the signal week of lowest frequency components
Phase determines) amplitude and phase information of the measuring signal under all frequency components can be just demodulated, this is largely reduced
The flexibility of demodulation method, while also limit further improving for demodulation speed.
A kind of patent " recursive demodulation method for electricity chromatographic imaging system " (patent No.：ZL201210016831.9)
It is middle to propose a kind of demodulation method based on recursive least-squares method, a kind of patent " multifrequency for electricity chromatographic imaging system
The recursive demodulation method " (patent No.：ZL201210016461.9 a kind of multifrequency solution based on recursive least-squares method is proposed in)
Tune method.And both demodulation methods can not start when initial information is 0, and its recursive process is complicated, in the process of realization
In to occupy a large amount of hardware resource, which limits its application range.Patent is " a kind of for electricity chromatographic imaging system
Information filter the demodulation method " (patent No.：201310325488.0) the information filter demodulation method of single-frequency a kind of is proposed, it is used for
The demodulation of single frequency sine wave.
The present invention proposes a kind of multifrequency information filter recursive demodulation method, can be calculated with 2m initial sampled point
Initial multifrequency demodulation result with the increase for the sampling number for substituting into recursive process, can improve the noise immunity of demodulation result
Energy.Multifrequency information filter recursive demodulation method improves the flexibility of electricity chromatographic imaging system multifrequency demodulating process, and is conducive to
Hardware realization.The present invention is entirely different in mathematical meaning and implementation method with invention before, applied to impedance spectrometry, electricity
When learning tomography, application value is also different.The present invention has following two clear advantages：1) present invention can be without just
Start recursive process under beginning information state；2) recursive form of the present invention is simple, reduces one compared to recursive least-squares method
Half complex matrix multiplication, and without division.The occupancy of resource is considerably reduced during realizing, is had very real
The effect on border.
In conclusion a kind of multifrequency information filter recursive demodulation method proposed by the invention, is surveyed applied to impedance spectrum
Amount, in electricity chromatographic imaging system when, recursive form is simple, conducive to hardware realization, considerably reduces the occupancy resource of chip,
Cost is reduced for impedance spectrometry, electricity chromatographic imaging system, reduces power consumption, there is very practical meaning and value.
Invention content
The purpose of the present invention is to provide a kind of multifrequency information filter recursive demodulation methods, can be in less than one signal period
Time in obtain the higher demodulation result of precision, and with the increase for the sampling number for substituting into recursive process, demodulation knot can be improved
The noise robustness of fruit.
The present invention, i.e., a kind of multifrequency information filter recursive demodulation method, includes the following steps：
Step 1: the m frequency component f according to multi-frequency excitation system1, f2..., fmWith sample frequency fsEstablish solution by recursion formula
Adjust equation.
Assuming that the pumping signal of electricity imaging system contains m component, it is applied in measured zone, the multiple-frequency signal of measurement
Frequency component be respectively f1, f2..., fm, the amplitude components of respective frequencies component are respectively A1, A2..., Am.Turn by modulus
The uniform sampling of parallel operation, if sample frequency is fs, then measuring signal be represented by：
Wherein, k be sampled point ordinal number, θiThe phase of i-th of frequency component for measuring signal.According to Euler's formula, xkIt can
It is expressed as：
The form for being write as matrix is：
If being extended to multiple sampling dot matrixs, have：
X=[x0 x1 … xk …]T=VB (4)
Wherein：
Here, B is the data matrix containing measuring signal amplitude and phase information, and matrix V can pass through known frequency
Rate information is calculated.Therefore, our purpose is exactly calculating matrix B.
If it enables：
So equation (4) can be expressed as another form：
X (k)=V (k) B (10)
If V (k) is square formation and its inverse presence, can pass through
B=V (k)-1X(k) (11)
Data matrix B directly is calculated, and then demodulates the amplitude and phase of measuring signal.However, V (k) is a k+1
Row 2m row matrix, except k+1=2m in the case of cannot use equation (11) solve B.
The characteristics of in view of matrix V (k), reconfigures the formula for solving data matrix B with least square method, as k >=2m-
When 1, it is represented by：
Bk=[V (k)HV(k)]-1V(k)HX(k) (12)
As can be seen that with increasing for data is substituted into, the operand of matrix inversion is increasing.In work before,
The method that we employ recursive least-squares recursion solves, in order to hardware realization.Here, using another recursive form,
That is information filter algorithm.This method recursive form is simpler, more conducively hardware realization.
Enable information matrix：
U (k)=V (k)HV(k) (13)
Then
Equation (14) is first recursive expression of information filter algorithm.
In equation (12), if the relevant parameter of result update+1 calculating of kth calculated with kth time,：
Equation (15) can be deformed into：
U(k+1)Bk+1=U (k) Bk+Vk+1 Hxk+1 (16)
If recursion intermediate variable K (k)=U (k) Bk, equation (16) is substituted into, is had：
K (k+1)=K (k)+Vk+1 HVk+1 (17)
Equation (17) is second recursive expression of information filter algorithm.Pay attention to it being to recursion intermediate variable K here
(k)=U (k) BkRecursion is carried out as a whole.
By equation (14) and (17), it is known that the formula of recursion is：
Step 2: being risen in measuring signal initial time, information matrix U is calculated according to 2m sample point data later
(k) and the initial value of recursion intermediary matrix K (k), initial value can be by：
It is calculated.
Step 3: the initial value being calculated in step 2 and newly-increased sample point data are substituted into the recursion side in step 1
Cheng Zhong, update U (k) and K (k).
Step 4: judge whether demodulation result meets system accuracy requirement, return to step three if being unsatisfactory for；If meeting
Stop recursive process, and according to the following formula：
Bk=[U (k)]-1K(k) (20)
The final result of data matrix B is calculated, if b1, b2..., bmEach first prime component of respectively B, calculates survey
Measure the amplitude and phase of each frequency component of signal：
The advantages of the present invention over the prior art are that：It can be obtained first with 2m initial measuring signal sample point data
To preliminary demodulation result, suitably increase sampling number according to requirements such as the measurement accuracy of system and real-times later, by passing
The method that pushes away improves demodulation accuracy and noise resisting ability；Recursive process can be started in no initial information；Recursion shape
Formula is simple, compared to the complex matrix multiplication that recursive least-squares method reduces half, and without division, is realizing
The occupancy of resource is considerably reduced in journey, there is very practical effect.
Description of the drawings
Fig. 1 is signal waveform to be demodulated；
Fig. 2 is the simulation experiment result of demodulation method provided by the present invention.
Specific embodiment
The present invention, i.e., a kind of multifrequency information filter recursive demodulation method, includes the following steps：
Step 1: the m frequency component f according to multi-frequency excitation system1, f2..., fmWith sample frequency fsEstablish solution by recursion formula
Adjust equation：
Wherein, k be sampled point ordinal number, xkFor k-th of sample point data, VkIt is by m exciting signal frequency and systematic sampling
The constant vector that frequency uniquely determines：
And it defines：
U (k) is information matrix：
U (k)=V (k)HV(k) (26)
K (k)=U (k) BkFor recursion intermediary matrix, BkFor data matrix：
AiFor the amplitude of i-th of frequency component of measuring signal, θiThe phase of i-th of frequency component for measuring signal；
Step 2: being risen in measuring signal initial time, information matrix U is calculated according to 2m sample point data later
(k) and the initial value of recursion intermediary matrix K (k), initial value by：
It calculates；
Step 3: the initial value being calculated in step 2 and newly-increased sample point data are substituted into the recursion side in step 1
Cheng Zhong, update U (k) and K (k)；
Step 4: judge whether demodulation result meets system accuracy requirement, return to step three if being unsatisfactory for；If meeting
Stop recursive process, and according to the following formula：
Bk=[U (k)]-1K(k) (29)
The final result of data matrix B is calculated, if b1, b2..., bmEach first prime component of respectively B, calculates survey
Measure the amplitude and phase of each frequency component of signal：
Son is described in further details the present invention in the following with reference to the drawings and specific embodiments.
Emulation experiment is carried out to information filter demodulating algorithm in Matlab software for calculation：Measuring signal is believed for ideal sinusoidal
Number：
A. amplitude is 2048, phase is 30 °, frequency 10kHz；
B. amplitude is 2040, phase is 45 °, frequency 20kHz；
C. amplitude is 2030, phase is 60 °, frequency 30kHz；
The superposition of three kinds of signals, as shown in Figure 2.Sample frequency to measuring signal is 1MHz, then for low-limit frequency point
For amount, there are 100 sampled points in each signal period.In one cycle, the recursive demodulation result of amplitude and phase is distinguished
(a), (b) are shown in Fig. 2.Then, 0.1% random noise (on the basis of amplitude 2048) is added in the signal, is demodulated
Amplitude and phase angle result such as Fig. 2 (c), (d) shown in.
The above results are once to calculate as a result, without statistical significance.0.1% different random noise is added in, repeats 100
Secondary above-mentioned calculating obtains measuring relationship such as Fig. 2 (e), (f) of amplitude average value/signal-to-noise ratio and recursion number.Wherein, signal-to-noise ratio
It is defined as：
Wherein, C (i),The average value of respectively i-th of demodulation value, demodulation result.
It can be seen from the simulation experiment result in the case of preferable sinusoidal signal, by taking three kinds of frequency compounding waveforms as an example,
Recursive demodulation method provided by the present invention can calculate the agonic amplitude of standard and phase using 6 initial sampled points
Demodulation result, and with sampling number to increase demodulation result unchanged；Contain the situation of 0.1% random noise in measuring signal
Under, multifrequency information filter demodulation method first obtains initial magnitude and phase demodulating as a result, in recursion using 6 initial sampled points
Signal-to-noise ratio is close to 60dB after half period；Signal-to-noise ratio is close to 70dB after 2/3 period of recursion.With increasing for sampling number,
Method enhances the rejection ability of random noise, and ascendant trend is presented in demodulation signal-to-noise ratio.During recursion, high fdrequency component is more
The demodulation of fast completion a cycle, but its computational accuracy is limited to the demodulation accuracy of low frequency component.Therefore, high fdrequency component early period
Demodulation noise it is higher, but after one complete cycle of recursion, each component signal-to-noise ratio is close.Emulation experiment demonstrates the present invention
The good result of the recursive demodulation method provided.
Above to the description of the present invention and embodiments thereof, it is not limited to which this, is only the reality of the present invention shown in attached drawing
Apply one of mode.Without departing from the spirit of the invention, it is similar with the technical solution without creatively designing
Structure or embodiment, belong to the scope of the present invention.
Claims (1)
1. a kind of multifrequency information filter recursive demodulation method, it is characterised in that include the following steps：
Step 1: according to known to frequency multi-frequency excitation system m frequency component f1, f2..., fmWith sample frequency fsFoundation is passed
Push away demodulation equation：
Wherein, k be sampled point ordinal number, xkFor k-th of sample point data, VkIt is by m exciting signal frequency and system sampling frequency
The constant vector uniquely determined：
And it defines：
U (k) is information matrix：
U (k)=V (k)HV(k) (5)
K (k)=U (k) BkFor recursion intermediary matrix, BkFor data matrix：
AiFor the amplitude of i-th of frequency component of measuring signal, θiThe phase of i-th of frequency component for measuring signal；
Step 2: risen in measuring signal initial time, according to 2m sample point data later calculate information matrix U (k) with
The initial value of recursion intermediary matrix K (k), initial value by：
It calculates；
Step 3: the initial value being calculated in step 2 and newly-increased sample point data are substituted into the recurrence equation in step 1
In, update U (k) and K (k)；
Step 4: judge whether demodulation result meets system accuracy requirement, return to step three if being unsatisfactory for；Stop if meeting
Recursive process, and according to the following formula：
Bk=[U (k)]-1K(k) (8)
The final result of data matrix B is calculated, if b1, b2..., bmEach first prime component of respectively B, then can calculate
The amplitude and phase of each frequency component of measuring signal：
。
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| CN107505507B (en) * | 2017-08-16 | 2019-10-01 | 北京航空航天大学 | A kind of recursive demodulation device for demodulating containing gaussian colored noise signal |
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| CN103412189A (en) * | 2013-07-30 | 2013-11-27 | 北京航空航天大学 | Information filtering demodulation method for electrical tomography system |
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| DE3532857A1 (en) * | 1985-09-14 | 1987-03-26 | Bosch Gmbh Robert | Non-recursive digital filter |
| JPH088863A (en) * | 1994-06-22 | 1996-01-12 | Clarion Co Ltd | Fm receiver |
| CN1663212A (en) * | 2002-06-24 | 2005-08-31 | 罗德施瓦兹两合股份有限公司 | Method for equalising and demodulating a data signal which is transmitted via a time-variant channel |
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