CN102570984B - Multi-frequency recursive demodulation method for electrical tomographic systems - Google Patents

Abstract

The invention relates to a multi-frequency recursive demodulation method for electrical tomographic systems. The method is characterized by comprising the following steps: (1) establishing an original equation and a recursive equation according to m component frequencies of an excitation signal and the sampling frequency of a system; (2) with a zero-phase time of the excitation signal as a starting time, according to data of 2m sampling points a measuring signal, which are closely following the starting time, calculating the initial values of a data matrix B and a state matrix P according to the original equation in the step (1); (3) substituting the initial values and the new sample point data into the recursive equation in the step (1) so as to update B and P; and (4) judging whether a demodulation result meets the accuracy requirements of the system, if so, completing the demodulation operation, and outputting the amplitude values and phase data of m frequency components of the measuring signal; otherwise, returning to the step (3). By using the recursive demodulation method disclosed by the invention, data of at least 2m sampling points is required, and due to the increase of the number of sampling points, the demodulation accuracy and the anti-noise capacity can be improved.

Description

A kind of multifrequency recursion demodulation method for electrical layer chromatographic imaging system

Technical field

The present invention relates to a kind of multifrequency recursion demodulation method for electrical layer chromatographic imaging system, belong to distribution parameter measurement field.

Background technology

Electricity tomography (Electrical Tomography) is by measurand is applied to electric excitation, and detects the variation of its boundary value, utilizes the electrical parameter of specific mathematical means inverting measurand inside to distribute, thereby obtains the species distribution of object inside.Compared with other chromatography imaging technique, that electricity tomography has is radiationless, fast response time, the advantage such as cheap.

Be applied to the fields such as industrial multiphase flow detection and medical science detection due to electricity tomography, measurand is usually expressed as relative complex electrology characteristic, and its variation with driving frequency changes more.Therefore, the spectral characteristic of more enriching for obtaining measurand inner electrical parameter, increasing electricity imaging system adopts the superimposed mixing frequency excitation mode mode of multi-frequency sinusoidal signal.But the mode of mixing frequency excitation mode has also been brought more difficulty to measurement, be especially embodied on demodulation mode.

For realizing the phase demodulation of multifrequency signal demodulation, conventionally by the respective components of each frequency component of measuring-signal and pumping signal respectively demodulation to obtain measuring-signal amplitude and phase information under different frequency component.The mode of traditional simulation multifrequency phase demodulation need to be identical with driving frequency number of components phase-sensitive demodulator, increased greatly hardware circuit scale and complexity, reduced the real-time of system.Along with the high speed development of digital technology, the digital phase-sensitive demodulation method based on digital processing unit is with its good measurement real-time and succinct hardware circuit and be subject to researcher and more and more pay close attention to.

First digital phase-sensitive demodulation method utilizes high-speed AD converter to sample to measured signal, then utilizes high-performance digital signal processor part, as FPGA, DSP etc., adopts the method for numerical computations to extract amplitude and the phase information of measured signal.The most conventional digital phase-sensitive demodulation method is orthogonal sequence demodulation method at present, while being applied in multifrequency electrical layer chromatographic imaging system, an integer cycle (signal period by lowest frequency components determines) that requires sample sequence length must cover mixing frequency excitation mode signal just can demodulate amplitude and the phase information of measuring-signal under all frequency components, this has reduced the flexibility of demodulation method to a great extent, has also limited the further raising of demodulation speed simultaneously.

Summary of the invention

The object of the present invention is to provide a kind of multifrequency recursion demodulation method for electrical layer chromatographic imaging system, can within the time that is less than a complete mixed frequency signal cycle, obtain the demodulation result that precision is higher, and along with the increase of the sampling number of substitution recursive process, can improve the noise robustness of demodulation result.

A kind of multifrequency recursion demodulation method for electrical layer chromatographic imaging system provided by the present invention, comprises the following steps:

Step 1, according to the m of system incentive signal component frequency f ₁, f ₂..., f _mand sample frequency f _sset up original equation and recurrence equation:

Original equation: $\left\{\begin{array}{c}P(2m-1)={[V{(2m-1)}^H\·V(2m-1)]}^{-1}\\ B_{2m-1}=P{(2m-1)}^{-1}\·V{(2m-1)}^H\·X(2m-1)\end{array}\right.---\left(1\right)$

Recurrence equation: $\left\{\begin{array}{c}P(k+1)=P\left(k\right)-\frac{P\left(k\right){V_{k+1}}^H{V}_{k+1}P\left(k\right)}{1+V_{k+1}P\left(k\right){V_{k+1}}^H}\\ B_{k+1}=B_k+P(k+1){V_{k+1}}^k(x_{k+1}-V_{k+1}{B}_k)\end{array}\right.,k\≥2m-1---\left(2\right)$

In equation (1) and equation (2), k is sampled point ordinal number and k>=0; x _kbe k sampling number certificate; P (k) is state matrix; B _kfor data matrix; V _kfor each component frequency by pumping signal and the well-determined constant vector of systematic sampling frequency, its concrete form is:

$V_k=\left[\begin{array}{cccccccc}{e}^{-k\·j2\mathrm{\π}{f}_1/f_s}& e^{-k\·j2\mathrm{\π}{f}_2/f_s}& ...& e^{-k\·j2\mathrm{\π}{f}_m/f_s}& e^{k\·j2\mathrm{\π}{f}_m/f_s}& ...& e^{k\·j2\mathrm{\π}{f}_2/f_s}& e^{k\·j2\mathrm{\π}{f}_1/f_s}\end{array}\right]---\left(3\right)$

2m V before V (2m-1) serves as reasons _kthe companion matrix forming,

V(2m-1)＝[V ₀V ₁… V _2m-1] ^T(4)

Before X (2m-1) serves as reasons, 2m sampling number be according to the measurement vector forming,

X(2m-1)＝[x ₀x ₁… x _2m-1] ^T(5)

Step 2, taking pumping signal zero phase moment of containing multiple frequency components as initial time, 2m sampling number certificate according to measuring-signal after next-door neighbour's initial time, calculates the amplitude and the data matrix B of phase information and the initial value B of state matrix P that comprise the each frequency component of measuring-signal according to the original equation in step 1 (1) _2m-1and P (2m-1);

Step 3, by the initial value of the data matrix B calculating in step 2 and state matrix P and the newly-increased individual sampling number of k (k>=2m) according to x _kbe updated in the recurrence equation (2) of setting up in step 1, progressively upgrade the value of data matrix B and state matrix P;

Step 4, judge whether demodulation result meets system accuracy requirement, if do not meet, return to step 3; If satisfied stop recursive process, and according to the final result of data matrix B calculate the amplitude of the each frequency component of measuring-signal and phase place

$\left\{\begin{array}{c}\widehat{A_1}=2\left|\widehat{b_1}\right|\\ \widehat{{\mathrm{\θ}}_1}=\arctan [\mathrm{Im}\left(\widehat{b_1}\right)/\mathrm{Re}\left(\widehat{b_1}\right)]\\ \widehat{A_2}=2\left|\widehat{b_2}\right|\\ \widehat{{\mathrm{\θ}}_2}=\arctan [\mathrm{Im}\left(\widehat{b_2}\right)/\mathrm{Re}\left(\widehat{b_2}\right)]\\ .\\ .\\ .\\ \widehat{A_m}=2\left|\widehat{b_m}\right|\\ \widehat{{\mathrm{\θ}}_m}=\arctan [\mathrm{Im}\left(\widehat{b_m}\right)/\mathrm{Re}\left(\widehat{b_m}\right)]\end{array}\right..---\left(6\right)$

The present invention's advantage is compared with prior art: can first utilize 2m (m is the frequency component number of mixing frequency excitation mode signal) measuring-signal sampling number certificate from next-door neighbour's initial time to obtain preliminary demodulation result, require suitably to increase sampling number according to certainty of measurement and the real-time etc. of system afterwards, improve demodulation accuracy and noise resisting ability by the method for recursion; In muting situation, the method does not need to adopt the sampled point in complete mixed frequency signal cycle can obtain demodulation result accurately, in the situation that there is noise, also can obtain comparatively desirable demodulation result, has good real-time and flexibility.

Brief description of the drawings

Fig. 1 is the flow chart of recursion demodulation method implementation process provided by the invention;

Fig. 2 (a) is 100kHz frequency component amplitude demodulation result when measuring-signal noiseless in emulation experiment;

Fig. 2 (b) is 100kHz frequency component phase demodulating result when measuring-signal noiseless in emulation experiment;

Fig. 2 (c) is 200kHz frequency component amplitude demodulation result when measuring-signal noiseless in emulation experiment;

Fig. 2 (d) is 200kHz frequency component phase demodulating result when measuring-signal noiseless in emulation experiment;

Fig. 2 (e) is 300kHz frequency component amplitude demodulation result when measuring-signal noiseless in emulation experiment;

Fig. 2 (f) is 300kHz frequency component phase demodulating result when measuring-signal noiseless in emulation experiment;

Fig. 2 (g) is 100kHz frequency component amplitude demodulation result when measuring-signal Noise in emulation experiment;

Fig. 2 (h) is 100kHz frequency component phase demodulating result when measuring-signal Noise in emulation experiment;

Fig. 2 (i) is 200kHz frequency component amplitude demodulation result when measuring-signal Noise in emulation experiment;

Fig. 2 (j) is 200kHz frequency component phase demodulating result when measuring-signal Noise in emulation experiment;

Fig. 2 (k) is 300kHz frequency component amplitude demodulation result when measuring-signal Noise in emulation experiment;

Fig. 2 (l) is 300kHz frequency component phase demodulating result when measuring-signal Noise in emulation experiment.

Embodiment

The present invention, a kind of multifrequency recursion demodulation method for electrical layer chromatographic imaging system, comprises the following steps:

Step 1, according to the m of system incentive signal component frequency f ₁, f ₂..., f _mand sample frequency f _sset up many original equations and recurrence equation.

The component frequency of supposing multi-frequency excitation electrical layer chromatographic imaging system pumping signal is respectively f ₁, f ₂..., f _m, in measuring-signal, the amplitude of respective frequencies component is respectively A ₁, A ₂..., A _mif, sample frequency f _s, measuring-signal can be expressed as:

$x_k=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{A}_i\cos (2\mathrm{\πk}{f}_i/f_s+{\mathrm{\θ}}_i)---\left(1\right)$

Wherein, k is sampled point ordinal number, θ _ifor the phase place of i frequency component of measuring-signal.According to Euler's formula, x _kcan be expressed as:

$x_k=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}(\frac{A_i}{2}{e}^{-j{\mathrm{\θ}}_i}\·e^{-2\mathrm{\πk}{f}_i/f_s}+\frac{A_i}{2}{e}^{j{\mathrm{\θ}}_i}\·e^{2\mathrm{\πk}{f}_i/f_s})---\left(2\right)$

The form of being write as matrix is:

$x_k=\left[\begin{array}{cccccccc}{e}^{-2\mathrm{\πk}{f}_1/f_s}& e^{-2\mathrm{\πk}{f}_2/f_s}& ...& e^{-2\mathrm{\πk}{f}_m/f_s}& e^{2\mathrm{\πk}{f}_m/f_s}& ...& e^{-2\mathrm{\πk}{f}_2/f_s}& e^{2\mathrm{\πk}{f}_1/f_s}\end{array}\right]\left[\begin{array}{c}\frac{A_1}{2}{e}^{-j{\mathrm{\θ}}_1}\\ \frac{A_2}{2}{e}^{-j{\mathrm{\θ}}_2}\\ .\\ .\\ .\\ \frac{A_k}{2}{e}^{-j{\mathrm{\θ}}_m}\\ \frac{A_k}{2}{e}^{j{\mathrm{\θ}}_m}\\ .\\ .\\ .\\ \frac{A_2}{2}{e}^{j{\mathrm{\θ}}_2}\\ \frac{A_1}{2}{e}^{j{\mathrm{\θ}}_1}\end{array}\right]---\left(3\right)$

Therefore, consider structure demodulation companion matrix V and the data matrix B that contains measuring-signal amplitude and phase information

$B={\left[\begin{array}{cccccccc}\frac{A_1}{2}{e}^{-j{\mathrm{\θ}}_1}& \frac{A_2}{2}{e}^{-j{\mathrm{\θ}}_2}& ...& \frac{A_m}{2}{e}^{-j{\mathrm{\θ}}_m}& \frac{A_m}{2}{e}^{j{\mathrm{\θ}}_m}& ...& \frac{A_2}{2}{e}^{j{\mathrm{\θ}}_2}& \frac{A_1}{2}{e}^{j{\mathrm{\θ}}_1}\end{array}\right]}^T---\left(5\right)$

The relation between the sample sequence of measuring-signal and demodulation companion matrix can be expressed as:

X＝[x ₀x ₁… x _k…] ^T＝VB (6)

Wherein

$\begin{array}{c}{V}_0=\left[\begin{array}{cccccccc}{e}^{-0\·j2\mathrm{\π}{f}_1/f_s}& e^{-0\·j2\mathrm{\π}{f}_2/f_s}& ...& e^{-0\·j2\mathrm{\π}{f}_m/f_s}& e^{0\·j2\mathrm{\π}{f}_m/f_s}& ...& e^{0\·j2\mathrm{\π}{f}_2/f_s}& e^{0\·j2\mathrm{\π}{f}_1/f_s}\end{array}\right]\\ V_1=\left[\begin{array}{cccccccc}{e}^{-1\·j2\mathrm{\π}{f}_1/f_s}& e^{-1\·j2\mathrm{\π}{f}_2/f_s}& ...& e^{-1\·j2\mathrm{\π}{f}_m/f_s}& e^{1\·j2\mathrm{\π}{f}_m/f_s}& ...& e^{1\·j2\mathrm{\π}{f}_2/f_s}& e^{1\·j2\mathrm{\π}{f}_1/f_s}\end{array}\right]\\ .\\ .\\ .\\ V_k=\left[\begin{array}{cccccccc}{e}^{-k\·j2\mathrm{\π}{f}_1/f_s}& e^{-k\·j2\mathrm{\π}{f}_2/f_s}& ...& e^{-k\·j2\mathrm{\π}{f}_m/f_s}& e^{k\·j2\mathrm{\π}{f}_m/f_s}& ...& e^{k\·j2\mathrm{\π}{f}_2/f_s}& e^{k\·j2\mathrm{\π}{f}_1/f_s}\end{array}\right]\\ .\\ .\\ .\end{array}---\left(7\right)$

$V\left(0\right)=V_0,V\left(1\right)=\left[\begin{array}{c}{V}_0\\ V_1\end{array}\right]=\left[\begin{array}{c}V\left(0\right)\\ V_1\end{array}\right],...,V\left(k\right)=\left[\begin{array}{c}V(k-1)\\ V_k\end{array}\right],...---\left(8\right)$

X(0)＝[x ₀],X ₁＝[x ₀x ₁] ^T＝[X(0) x ₁] ^T,…,X _k＝[X(k-1) x _k] ^T,… (9)

Equation (6) can be expressed as another kind of form so,

X(k)＝V(k)B (10)

If V (k) is square formation and its contrary existence, can pass through

B＝V(k) ^-1X(k) (11)

Directly calculate data matrix B, and then demodulate amplitude and the phase place of measuring-signal.But V (k) is the matrix of the capable 2m row of k+1, all can not solve B with equation (11) except in the situation of k+1=2m.

Consider the feature of matrix V (k), re-construct the formula that solves data matrix B, in the time of k >=2m-1, it can be expressed as:

B _k＝[V(k) ^HV(k)] ^-1V(k) ^HX(k) (12)

Order

P(k)＝[V(k) ^HV(k)] ^-1(13)

?

$\begin{array}{c}P(k+1)={\left[V{(k+1)}^{H}V(k+1)\right]}^{-1}\\ ={\left({\left[\begin{array}{c}V\left(k\right)\\ V_{k+1}\end{array}\right]}^H\left[\begin{array}{c}V\left(k\right)\\ V_{k+1}\end{array}\right]\right)}^{-1}\\ ={\left(\left[\begin{array}{cc}V{\left(k\right)}^H& {V_{k+1}}^H\end{array}\right]\left[\begin{array}{c}V\left(k\right)\\ V_{k+1}\end{array}\right]\right)}^{-1}\\ ={(V{\left(k\right)}^{H}V\left(k\right)+{V_{k+1}}^H{V}_{k+1})}^{-1}\\ ={(P{\left(k\right)}^{-1}+V_{k+1}^H{V}_{k+1})}^{-1}\end{array}---\left(14\right)$

According to the theorem of matrix inversion, have

(A+BCD) ^-1＝A ^-1-A ^-1B(C ^-1+DA ^-1B) ^-1DA ^-1(15)

Make A=P (k) ^-1, c=1, D=V _k+1, can obtain

P(k+1)＝(A+B·1·B ^H) ^-1

＝A ^-1-A ^-1B(1+B ^HA ^-1B) ^-1B ^HA ^-1(16)

＝P(k)-P(k)V _k+1 ^H(1+V _k+1P(k)V _k+1 ^H) ^-1V _k+1P(k)

Therefore in equation (12), if upgrade the relevant parameter calculating for the k+1 time by the result of the k time calculating,

$\begin{array}{c}{B}_{k+1}=P(k+1)V{(k+1)}^{H}X(k+1)\\ =P(k+1){\left[\begin{array}{c}V\left(k\right)\\ V_{k+1}\end{array}\right]}^H\left[\begin{array}{c}X\left(k\right)\\ x_{k+1}\end{array}\right]\\ =P(k+1)\left[\begin{array}{cc}{V\left(k\right)}^H& {V_{k+1}}^H\end{array}\right]\left[\begin{array}{c}X\left(k\right)\\ x_{k+1}\end{array}\right]\\ =P(k+1)[{V\left(k\right)}^{H}X\left(k\right)+{V_{k+1}}^H{x}_{k+1}]\\ =P(k+1)P{\left(k\right)}^{-1}{B}_k+P(k+1){V_{k+1}}^H{x}_{k+1}\end{array}---\left(17\right)$

Formula (14) is transformed to

P(k+1) ^-1＝P(k) ^-1+V _k+1 ^HV _k+1(18)

Thereby,

P(k) ^-1＝P(k+1) ^-1-V _k+1 ^HV _k+1(19)

By formula (19) substitution formula (17), can obtain

B _k+1＝P(k+1)[P(k+1) ^-1-V _k+1 ^HV _k+1]B _k+P _k+1V _k+1 ^Hx _k+1

＝B _k-P(k+1)V _k+1 ^HV _k+1B _k+P(k+1)V _k+1 ^Hx _k+1(20)

＝B _k+P(k+1)V _k+1 ^H(x _k+1-V _k+1B _k)

By formula (16) and (20), known recurrence equation is

$\left\{\begin{array}{c}P(k+1)=P\left(k\right)-\frac{P\left(k\right){V_{k+1}}^H{V}_{k+1}P\left(k\right)}{1+V_{k+1}P\left(k\right){V_{k+1}}^H}\\ B_{k+1}=B_k+P(k+1){V_{k+1}}^k(x_{k+1}-V_{k+1}{B}_k)\end{array}\right.,k\≥2m-1---\left(21\right)$

And its initial value can be by original equation

$\left\{\begin{array}{c}P(2m-1)={[V{(2m-1)}^H\·V(2m-1)]}^{-1}\\ B_{2m-1}=P{(2m-1)}^{-1}\·V{(2m-1)}^H\·X(2m-1)\end{array}\right.---\left(22\right)$

Calculate.

Step 2, taking pumping signal zero phase moment of containing multiple frequency components as initial time, 2m sampling number certificate according to measuring-signal after next-door neighbour's initial time, calculates the amplitude and the data matrix B of phase information and the initial value B of state matrix P that comprise the each frequency component of measuring-signal according to the original equation in step 1 (22) _2m-1and P (2m-1);

The value of the 2m measuring-signal sampled point after order next-door neighbour initial time is x ₀, x ₁..., x _2m-1, calculate according to equation (12) and (13):

$\left\{\begin{array}{c}P(2m-1)={\left[V{(2m-1)}^{H}V(2m-1)\right]}^{-1}\\ B_{2m-1}=P(2m-1)V{(2m-1)}^{H}X(2m-1)={\left[\begin{array}{cccc}{b}_{11}& b_{12}& ...& b_{1\left(2m\right)}\end{array}\right]}^T\end{array}\right.---\left(23\right)$

Now, can be according to primary data matrix B ₁calculate amplitude and the phase angle of measuring-signal:

$\left\{\begin{array}{c}\widehat{A_{11}}=2\left|\widehat{b_{11}}\right|\\ \widehat{{\mathrm{\θ}}_{11}}=\arctan [\mathrm{Im}\left(\widehat{b_{11}}\right)/\mathrm{Re}\left(\widehat{b_{11}}\right)]\\ \widehat{A_{12}}=2\left|\widehat{b_{12}}\right|\\ \widehat{{\mathrm{\θ}}_{12}}=\arctan [\mathrm{Im}\left(\widehat{b_{12}}\right)/\mathrm{Re}\left(\widehat{b_{12}}\right)]\\ .\\ .\\ .\\ \widehat{A_{1m}}=2\left|\widehat{b_{1m}}\right|\\ \widehat{{\mathrm{\θ}}_{1m}}=\arctan [\mathrm{Im}\left(\widehat{b_{1m}}\right)/\mathrm{Re}\left(\widehat{b_{1m}}\right)]\end{array}\right..---\left(24\right)$

Step 3, by the initial value of the data matrix B calculating in step 2 and state matrix P and the newly-increased individual sampling number of k (k>=2m) according to x _kbe updated in the recurrence equation (21) of setting up in step 1, progressively upgrade the value of data matrix B and state matrix P;

Step 4, judge whether demodulation result meets system accuracy requirement, if do not meet, return to step 3; If satisfied stop recursive process, and according to the final result of data matrix B calculate the amplitude of the each frequency component of measuring-signal and phase place

$\left\{\begin{array}{c}\widehat{A_1}=2\left|\widehat{b_1}\right|\\ \widehat{{\mathrm{\θ}}_1}=\arctan [\mathrm{Im}\left(\widehat{b_1}\right)/\mathrm{Re}\left(\widehat{b_1}\right)]\\ \widehat{A_2}=2\left|\widehat{b_2}\right|\\ \widehat{{\mathrm{\θ}}_2}=\arctan [\mathrm{Im}\left(\widehat{b_2}\right)/\mathrm{Re}\left(\widehat{b_2}\right)]\\ .\\ .\\ .\\ \widehat{A_m}=2\left|\widehat{b_m}\right|=2\left|\widehat{b_m}\right|\\ \widehat{{\mathrm{\θ}}_m}=\arctan [\mathrm{Im}\left(\widehat{b_m}\right)/\mathrm{Re}\left(\widehat{b_m}\right)]\end{array}\right..---\left(25\right)$

Below in conjunction with drawings and Examples, the present invention is described in further details.

In Matlab software for calculation, a kind of recursion demodulation method for electrical layer chromatographic imaging system provided by the present invention is carried out to emulation experiment.Experiment condition is as follows:

(1) measuring-signal is the stack of three ideal sinusoidal signal components, and the amplitude of sinusoidal component one is 1, phase place is that 60 °, frequency are 100kHz; The amplitude of sinusoidal component two is 5, phase place is that 45 °, frequency are 200kHz; The amplitude of sinusoidal component three is 2, phase place is that 30 °, frequency are 300kHz; The sample rate of system is 3MHz, has 30 sampled points in each mixed signal cycle;

(2) in the desirable mixing frequency measurement signal in experiment condition (1), add the random noise that average is 0, standard deviation is 0.01.

In the lower measuring-signal of experiment condition (1) the recursion demodulation result of three frequency component amplitudes and phase place respectively as (a) in Fig. 2-(f) as shown in, in experiment condition (2) time measuring-signal, the amplitude of three frequency components and the recursion demodulation result of phase place are respectively as shown in (g), (l) in Fig. 2.

Can be found out by the simulation experiment result, in the situation that measuring-signal is 3 ideal sinusoidal mixed frequency signals, 6 initial sampled points of recursion demodulation method provided by the present invention utilization can demodulate the exact value of each frequency component amplitude and phase place, and along with sampling number to increase demodulation result still accurate; And the mixed frequency signal that contains 3 frequency components at measuring-signal and containing random noise, 6 initial sampled points of recursion demodulation method provided by the present invention utilization can demodulate amplitude and the phase value of each frequency component that precision is higher, its relative error is all less than 1%, and along with the demodulation relative error that increases of sampling number presents the trend that concussion decays.

Emulation experiment has been verified the good result of multifrequency recursion demodulation method provided by the present invention.

Description to the present invention and execution mode thereof, is not limited to this above, is only one of embodiments of the present invention shown in accompanying drawing.In the situation that not departing from the invention aim, without creatively designing and the similar structure of this technical scheme or embodiment, all belong to protection range of the present invention.

Claims (1)

1. for a multifrequency recursion demodulation method for electrical layer chromatographic imaging system, it is characterized in that: it comprises the following steps:

Step 1, according to the m of system incentive signal component frequency f ₁, f ₂..., f _mand sample frequency f _sset up original equation and recurrence equation:

Original equation: $\left\{\begin{array}{c}P(2m-1)={[V{(2m-1)}^H\·V(2m-1)]}^{-1}\\ B_{2m-1}=P{(2m-1)}^{-1}\·V{(2m-1)}^H\·X(2m-1)\end{array}\right.---\left(1\right)$

Recurrence equation: $\left\{\begin{array}{c}P(k+1)=P\left(k\right)-\frac{P\left(k\right){V_{k+1}}^H{V}_{k+1}P\left(k\right)}{1+V_{k+1}P\left(k\right){V_{k+1}}^H}\\ B_{k+1}=B_k+P(k+1){V_{k+1}}^k(x_{k+1}-V_{k+1}{B}_k)\end{array}\right.,k\≥2m-1---\left(2\right)$

In equation (1) and equation (2), k is sampled point ordinal number and k>=0; x _kbe k sampling number certificate; P (k) is state matrix; B _kfor data matrix; V _kfor each component frequency by pumping signal and the well-determined constant vector of systematic sampling frequency, its concrete form is:

$V_k=\left[\begin{array}{cccccccc}{e}^{-k\·j2\mathrm{\π}{f}_1/f_s}& e^{-k\·j2\mathrm{\π}{f}_2/f_s}& ...& e^{-k\·j2\mathrm{\π}{f}_m/f_s}& e^{k\·j2\mathrm{\π}{f}_m/f_s}& ...& e^{k\·j2\mathrm{\π}{f}_2/f_s}& e^{k\·j2\mathrm{\π}{f}_1/f_s}\end{array}\right]---\left(3\right)$

2m V before V (2m-1) serves as reasons _kthe companion matrix forming,

V(2m-1)＝[V ₀V ₁… V _2m-1] ^T(4)

Before X (2m-1) serves as reasons, 2m sampling number be according to the measurement vector forming,

X(2m-1)＝[x ₀x ₁… x _2m-1] ^T(5)

Step 2, taking pumping signal zero phase moment of containing multiple frequency components as initial time, 2m sampling number certificate according to measuring-signal after next-door neighbour's initial time, calculates the amplitude and the data matrix B of phase information and the initial value B of state matrix P that comprise the each frequency component of measuring-signal according to the original equation in step 1 (1) _2m-1and P (2m-1);

Step 3, by the initial value of the data matrix B calculating in step 2 and state matrix P and the newly-increased individual sampling number of k (k>=2m) according to x _kbe updated in the recurrence equation (2) of setting up in step 1, progressively upgrade the value of data matrix B and state matrix P;

Step 4, judge whether demodulation result meets system accuracy requirement, if do not meet, return to step 3; If satisfied stop recursive process, and according to the final result of data matrix B calculate the amplitude of the each frequency component of measuring-signal and phase place

$\left\{\begin{array}{c}\widehat{A_1}=2\left|\widehat{b_1}\right|\\ \widehat{{\mathrm{\θ}}_1}=\arctan [\mathrm{Im}\left(\widehat{b_1}\right)/\mathrm{Re}\left(\widehat{b_1}\right)]\\ \widehat{A_2}=2\left|\widehat{b_2}\right|\\ \widehat{{\mathrm{\θ}}_2}=\arctan [\mathrm{Im}\left(\widehat{b_2}\right)/\mathrm{Re}\left(\widehat{b_2}\right)]\\ .\\ .\\ .\\ \widehat{A_m}=2\left|\widehat{b_m}\right|\\ \widehat{{\mathrm{\θ}}_m}=\arctan [\mathrm{Im}\left(\widehat{b_m}\right)/\mathrm{Re}\left(\widehat{b_m}\right)]\end{array}\right..---\left(6\right)$