CN109101461A - A method of it is independent to calculate the Lorentz curve parameter with 90 degree of phase differences - Google Patents
A method of it is independent to calculate the Lorentz curve parameter with 90 degree of phase differences Download PDFInfo
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Abstract
The invention discloses a kind of independent methods for calculating the Lorentz curve parameter with 90 degree of phase differences.The present invention is from the nuclear magnetic resoance spectrum signal curve of single metabolin, define first parameter and the second parameter with the Lorentz curve of 90 degree of phase differences, after Fourier transformation and inverse Fourier transform, by the time-domain expression appropriate for changing member and being translated into exponential integral.The value of exponential integral is found out in special circumstances at some, and is generalized to ordinary circumstance.The equation of final simultaneous the first parameter and the second parameter, obtains its method independently calculated mutually.This method can remove signal noise for nuclear magnetic resoance spectrum and provide theoretical foundation, solve the technical issues of directly abandoning loss of learning caused by spectrum signal imaginary part information.The deep technical effect for excavating spectrum signal information is also played simultaneously.
Description
Technical field
The present invention relates to the Lorentz curves that nuclear magnetic resonance field more particularly to a kind of independent calculating have 90 degree of phase differences
The method of parameter.
Background technique
Nuclear magnetic resonance technique not only can carry out structure elucidation to reactant or product and configuration determines in organic synthesis,
Also extensive application in terms of studying distribution of charges in synthetic reaction and its orientation effect, inquiring into.Nuclear-magnetism
Resonance wave spectrum can subtly symbolize the distribution of charges situation of each proton, pass through metal ion and ligand in research complex
Interaction, the property of complex and the relationship of structure are illustrated from microcosmic level.
Nuclear magnetic resonance is an important means of organic compound structure identification, generally identifies group according to chemical shift；
Group connection relation is determined by coupling division peak number, coupling constant；Each group proton ratio is made according to each peak H integral area.Core
The research that magnetic resonance spectrum can be used in terms of chemical kinetics, such as Internal Rotations of Molecules, Chemical Exchange etc., because they are all influenced outside core
The situation of chemical environment, to should all be reflected on spectrogram.Nuclear magnetic resonance is also used to study polymerization reaction mechanism, high polymer sequence
Array structure, metabolism group, Medical Imaging etc..
However, due to inevitably generating signal noise in nuclear magnetic resoance spectrum collection process, and it is current in existing skill
In art, there is no quantitative theoretical research was done to signal denoising.Therefore it can only be extracted with the experience of researcher wherein real
Signal message, or even directly abandon nuclear magnetic resoance spectrum imaginary part information and only with real part information, this believes comprehensive data
It is very big waste that breath, which excavates, while also reducing the accuracy of the information of acquisition.
Linear due to nuclear magnetic resonance time-domain signal determine by free induction decay process, this decaying substantially exponentially shape
Formula, obtaining nuclear magnetic resonance spectral function (frequency domain) by the Fourier transform of free induction decay curves (time domain) function to this is long-range navigation
Hereby curve, and the real number of nuclear magnetic resoance spectrum and imaginary part curve are the Lorentz curves with 90 degree of phase differences.If can be right
The property of Lorentz curve with 90 degree of phase differences is preferably studied, then can be provided the information for excavating nuclear magnetic resoance spectrum
Strong theoretical foundation.
Therefore, those skilled in the art is dedicated to developing a kind of independent Lorentz curve of the calculating with 90 degree of phase differences
The method of parameter.This method can remove signal noise for nuclear magnetic resoance spectrum and provide theoretical foundation, solve and directly abandon spectrum letter
The technical issues of loss of learning caused by number imaginary part information.The deep technical effect for excavating spectrum signal information is also played simultaneously.
Summary of the invention
In view of the above drawbacks of the prior art, the technical problem to be solved by the present invention is to how independently calculate to have
The figure parameters of real part and imaginary part in the Lorentz curve of 90 degree of phase differences.
To achieve the above object, the present invention provides the Lorentz curve parameters that a kind of independent calculating has 90 degree of phase differences
Method, which comprises the following steps:
Step 1: the theoretical free induction decay curves time-domain function of single metabolin chromatography is obtained by Fourier transformation
Then metabolin nuclear magnetic resoance spectrum frequency-domain function carries out inverse Fourier transform to this spectrum signal again and is expressed as time t and frequencies omega
Function；
Step 2: the inverse Fourier transform of real part coefficient in nuclear magnetic resoance spectrum signal function obtained in step 1 is determined
Justice is the first parameter, and the inverse Fourier transform of imaginary part coefficient in nuclear magnetic resoance spectrum signal function obtained in step 1 is determined
Justice is the second parameter；
Step 3: the expression work of first parameter, second parameter suitably being changed into member, enables them
Be converted to the expression formula of exponential integral；
Step 4: obtaining the reality of first parameter under the special case of φ=0 using the characteristic of the exponential integral
The relational expression of portion's coefficient and imaginary part coefficient obtains the real part coefficient of second parameter and the relational expression of imaginary part coefficient, and finds out
The value of the exponential integral；
Step 5: the exponent product score value acquired in step 4 being substituted into the general scenario of φ ≠ 0, verifies first ginseng
The relational expression of the relational expression of several real part coefficient and imaginary part coefficient, the real part coefficient of second parameter and imaginary part coefficient φ ≠
It is still set up in the case where 0；
Step 6: the real part coefficient of the first parameter described in simultaneous and the relational expression of imaginary part coefficient, the real part of second parameter
The relational expression of coefficient and imaginary part coefficient acquires the independent calculation formula of first parameter, second parameter, i.e., and known first
Parameter, so that it may the second parameter be calculated；Or known second parameter, so that it may the first parameter be calculated.
Further, the mathematic(al) representation of the theoretical free induction decay curves of metabolin chromatography described in step 1 are as follows:
Wherein, s (t) is the nuclear magnetic resonance time domain chromatography of single metabolin, and M is maximum signal amplitudes, and e is natural logrithm bottom, j
For imaginary unit, φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency.
Further, the expression of the first parameter described in step 2 are as follows:
Wherein, A is the first parameter, and M is maximum signal amplitudes, and e is natural logrithm bottom, and j is imaginary unit, and φ is phase, α
For attenuation constant, t is time, ω0For eigenfrequency, ω is frequency.
Further, the replacement variable of member is changed described in step 3 are as follows:
X'=- (ω0-ω)t
Wherein, x ' is the replacement variable for changing member, and t is time, ω0For eigenfrequency, ω is frequency.
Further, the first parameter described in step 3 is converted into the expression formula of exponential integral are as follows:
Wherein, E is used1For the exponential integral and E of p- α t-jx'2For the exponential integral to α t-jx', M is peak signal width
Degree, e are natural logrithm bottom, and j is imaginary unit, and φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency, ARIt is
The real part coefficient of one parameter, AIFor the imaginary part coefficient of the first parameter.
Further, the second parameter described in step 3 is converted into the expression formula of exponential integral are as follows:
Wherein, E is used1For the exponential integral and E of p- α t-jx'2For the exponential integral to α t-jx', M is peak signal width
Degree, e are natural logrithm bottom, and j is imaginary unit, and φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency, BRIt is
The real part coefficient of two parameters, BIFor the imaginary part coefficient of the second parameter.
Further, the relational expression of the real part coefficient Yu imaginary part coefficient of the first parameter described in step 4 are as follows:
Wherein, E is used1For the exponential integral and E of p- α t-jx'2For the exponential integral to α t-jx', M is peak signal width
Degree, e are natural logrithm bottom, and j is imaginary unit, and φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency, ARFor institute
State the real part coefficient of the first parameter, AIFor the imaginary part coefficient of first parameter.
Further, the relational expression of the real part coefficient Yu imaginary part coefficient of the second parameter described in step 4 are as follows:
Wherein, E is used1For the exponential integral and E of p- α t-jx'2For the exponential integral to α t-jx', M is peak signal width
Degree, e are natural logrithm bottom, and j is imaginary unit, and φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency, BRFor institute
State the real part coefficient of the second parameter, BIFor the imaginary part coefficient of second parameter.
Further, the value of the exponential integral are as follows: E1=2 π j, E2=0, in the case of φ=0 and φ ≠ 0 at
It is vertical.
Further, the independent calculation formula between first parameter and second parameter are as follows:
A=-B1+jBR
B=A1-jAR
Wherein, ARFor the real part coefficient of first parameter, AIFor the imaginary part coefficient of first parameter, BRIt is described
The real part coefficient of two parameters, BIFor the imaginary part coefficient of second parameter.
This method defines the Lorentz with 90 degree of phase differences from the nuclear magnetic resonance chromatographic signal curve of single metabolin
The first parameter and the second parameter of curve, after Fourier transformation and inverse Fourier transform, by member appropriate of changing by its turn
Turn to the time-domain expression of exponential integral.The value of exponential integral is found out in special circumstances at some, and is generalized to ordinary circumstance.Most
The equation of whole simultaneous the first parameter and the second parameter, obtains its method independently calculated mutually.
This method can remove signal noise for nuclear magnetic resoance spectrum and provide theoretical foundation, solve and directly abandon spectrum signal void
The technical issues of loss of learning caused by portion's information.The deep technical effect for excavating spectrum signal information is also played simultaneously.
The technical effect of design and generation of the invention will be described further below, it is of the invention to be fully understood from
Purpose, feature and effect.
Specific embodiment
Multiple preferred embodiments of the invention introduced below keep its technology contents more clear and are easy to understand.The present invention
It can be emerged from by many various forms of embodiments, protection scope of the present invention is not limited only to the reality mentioned in text
Apply example.
The present invention is an attempt to find a kind of method that can theoretically analyze NMR signal noise.And Lorentz is bent
Line is the base curve of nuclear magnetic resonance (NMR) spectrum.The coefficient curve of the real and imaginary parts of nuclear magnetic resoance spectrum is that have 90 degree of phases
The Lorentz curve of difference.So if the Lorentz curve real and imaginary parts with 90 degree of phase differences can be independently calculated
Coefficient can provide strong theoretical foundation to NMR signal noise reduction.
The present invention provides a kind of independent coefficients for calculating the Lorentz curve real and imaginary parts with 90 degree of phase differences
Method specifically includes the following steps:
Step 1: by theoretical free induction decay (FID) the curve negotiating Fourier transformation of single metabolin chromatography and Fourier
Inverse transformation is expressed as the spectrum signal function of time t and frequencies omega；
Theoretical free induction decay (FID) curve of single metabolin chromatography can indicate are as follows:
Wherein, s (t) is the nuclear magnetic resonance free induction decay curves function of single metabolin, and M is maximum signal amplitudes, and e is
Natural logrithm bottom, j are imaginary unit, and φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency.
This curve is made into Fourier transformation, is obtained:
Wherein, s (ω) is the frequency domain nuclear magnetic resoance spectrum after Fourier transformation, and α is attenuation constant, and M is maximum signal amplitudes,
E is natural logrithm bottom, and j is imaginary unit, and ω is frequency, ω0For eigenfrequency.
Inverse Fourier transform is carried out to the spectrum signal again:
So far, the nuclear magnetic resoance spectrum signal curve of single metabolin is expressed as to the function of time t and frequencies omega.
Step 2: by the Fourier of the real part coefficient (Re) in nuclear magnetic resoance spectrum signal function obtained in step 1
Inverse transformation value is defined as the first parameter, by the Fourier of the imaginary part coefficient (Im) in spectrum signal function obtained in step 1
Inverse transformation value is defined as the second parameter；
In above-mentioned expression formula A+jB, A is the inverse fourier transform value of the real part coefficient (Re) of function, and A is defined as first
Parameter；B is the inverse fourier transform value of the imaginary part coefficient (Im) of function, and B is defined as the second parameter.
Step 3: the expression work of first parameter, second parameter suitably being changed into member, enables them
Be converted to exponential integral；
The expression of first parameter A are as follows:
In order to be converted into exponential integral, therefore it is carried out to change member:
If x'=- (ω0- ω) t, then have
Wherein x ' is to change member replacement variable, has no actual mathematical meaning.
The theory then proposed according to Abramowitz and Stegun in 1964, the first parameter A can be expressed as index
The expression formula of integral:
Wherein, E1It (z) is the exponential integral to z.
Use E1And E2Respectively instead of E1(- α t-jx') and E1(α t-jx'), obtains:
Wherein, ARAnd AIThe respectively coefficient of the real and imaginary parts of the first parameter A.
Similar operation is done to the second parameter B, available:
Step 4: obtaining the reality of first parameter under the special case of φ=0 using the characteristic of the exponential integral
The relational expression of portion's coefficient and imaginary part coefficient obtains the real part coefficient of second parameter and the relational expression of imaginary part coefficient, and finds out
The value of the exponential integral；
Due to E1And E2The value of φ is all relied on, therefore as φ=0, is had:
Step 4 is applied on the second parameter B, the available expression formula similar with the first parameter A:
It is available by the relational expression simultaneous of the first parameter A and the second parameter B:
And [e-αtE1-eαtE2]2=[e-αtE1+eαtE2]2, E can be obtained1=0 or E2=0.
Further according to:
E can be obtained1=2 π j；Therefore E2=0；
Then the relationship of the first parameter A and the second parameter B can abbreviations are as follows:
Step 5: the exponent product score value acquired in step 4 being substituted into the general scenario of φ ≠ 0, verifies first ginseng
The relational expression of the relational expression of several real part coefficient and imaginary part coefficient, the real part coefficient of second parameter and imaginary part coefficient φ ≠
It is still set up under 0 general scenario；
The E that will be acquired1And E2Value substitute into the first parameter A and the second parameter B exponential integral expression formula, can verify,
It is same to meet under the general scenario of φ ≠ 0:
Step 6: the real part coefficient of the first parameter described in simultaneous and the relational expression of imaginary part coefficient, the real part of second parameter
The relational expression of coefficient and imaginary part coefficient acquires the independent calculation formula of first parameter, second parameter.
The relation equation of first parameter A, the second parameter B obtained in simultaneous step 3:
Finally obtain the independent calculation method of the first parameter A and the second parameter B:
A=-B1+jBR
B=A1-jAR
I.e., it is only necessary to learn one of the first parameter A, second parameter B, so that it may calculate another parameter.And
First parameter A, the second parameter B be actually the real part of the nuclear magnetic resonance spectrum signal of single metabolin, imaginary part coefficient Fourier
Inverse transformation value, therefore one of the two known parameters, can be calculated another parameter.It can be surveyed to studying in practical operation
The signal denoising etc. with noise measured plays the role of theoretical direction.
The preferred embodiment of the present invention has been described in detail above.It should be appreciated that the ordinary skill of this field is without wound
The property made labour, which according to the present invention can conceive, makes many modifications and variations.Therefore, all technician in the art
Pass through the available technology of logical analysis, reasoning, or a limited experiment on the basis of existing technology under this invention's idea
Scheme, all should be within the scope of protection determined by the claims.
Claims (10)
1. a kind of independent method for calculating the Lorentz curve parameter with 90 degree of phase differences, which is characterized in that including following step
It is rapid:
Step 1: the theoretical free induction decay curves time-domain function of single metabolite profile is obtained into single metabolism by Fourier transformation
Then object nuclear magnetic resoance spectrum frequency-domain function carries out the letter that inverse Fourier transform is expressed as time t and frequencies omega to this spectral function again
Number；
Step 2: the inverse Fourier transform value of real part coefficient in nuclear magnetic resoance spectrum signal function obtained in step 1 is defined
For the first parameter, the inverse Fourier transform value of imaginary part coefficient in nuclear magnetic resoance spectrum signal function obtained in step 1 is determined
Justice is the second parameter；
Step 3: the expression work of first parameter, second parameter suitably being changed into member, them is enable to convert
For the expression formula of exponential integral；
Step 4: obtaining the real part system of first parameter under the special case of φ=0 using the characteristic of the exponential integral
Several and imaginary part coefficient relational expression obtains the real part coefficient of second parameter and the relational expression of imaginary part coefficient, and finds out described
The value of exponential integral；
Step 5: the exponent product score value acquired in step 4 being substituted into the general scenario of φ ≠ 0, verifies first parameter
The relational expression of the relational expression of real part coefficient and imaginary part coefficient, the real part coefficient of second parameter and imaginary part coefficient is in φ ≠ 0
In the case of still set up；
Step 6: the real part coefficient of the first parameter described in simultaneous and the relational expression of imaginary part coefficient, the real part coefficient of second parameter
With the relational expression of imaginary part coefficient, the independent calculation formula of first parameter, second parameter is acquired, i.e., known first ginseng
Number, so that it may the second parameter be calculated；Or known second parameter, so that it may the first parameter be calculated.
2. the independent method for calculating the Lorentz curve parameter with 90 degree of phase differences as described in claim 1, feature exist
In the mathematic(al) representation of the theoretical free induction decay curves of metabolin chromatography described in step 1 are as follows:
Wherein, s (t) is the nuclear magnetic resonance time domain chromatography of single metabolin, and M is maximum signal amplitudes, and e is natural logrithm bottom, and j is void
Number unit, φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency.
3. the independent method for calculating the Lorentz curve parameter with 90 degree of phase differences as described in claim 1, feature exist
In the expression of the first parameter described in step 2 are as follows:
Wherein, A is the first parameter, and M is maximum signal amplitudes, and e is natural logrithm bottom, and j is imaginary unit, and φ is phase, and α is to decline
Subtract constant, t is time, ω0For eigenfrequency, ω is frequency.
4. the independent method for calculating the Lorentz curve parameter with 90 degree of phase differences as described in claim 1, feature exist
In, changed described in step 3 member replacement variable are as follows:
X'=- (ω0-ω)t
Wherein, x ' is the replacement variable for changing member, and t is time, ω0For eigenfrequency, ω is frequency.
5. the independent method for calculating the Lorentz curve parameter with 90 degree of phase differences as described in claim 1, feature exist
In the first parameter described in step 3 is converted into the expression formula of exponential integral are as follows:
Wherein, E is used1For the exponential integral and E of p- α t-jx'2For the exponential integral to α t-jx', M is maximum signal amplitudes, e
For natural logrithm bottom, j is imaginary unit, and φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency, ARFor the first ginseng
Several real part coefficients, AIFor the imaginary part coefficient of the first parameter.
6. the independent method for calculating the Lorentz curve parameter with 90 degree of phase differences as described in claim 1, feature exist
In the second parameter described in step 3 is converted into the expression formula of exponential integral are as follows:
Wherein, E is used1For the exponential integral and E of p- α t-jx'2For the exponential integral to α t-jx', M is maximum signal amplitudes, e
For natural logrithm bottom, j is imaginary unit, and φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency, BRFor the second ginseng
Several real part coefficients, BIFor the imaginary part coefficient of the second parameter.
7. the independent method for calculating the Lorentz curve parameter with 90 degree of phase differences as described in claim 1, feature exist
In the real part coefficient of the first parameter described in step 4 and the relational expression of imaginary part coefficient are as follows:
Wherein, E is used1For the exponential integral and E of p- α t-jx'2For the exponential integral to α t-jx', M is maximum signal amplitudes, e
For natural logrithm bottom, j is imaginary unit, and φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency, ARIt is described
The real part coefficient of one parameter, AIFor the imaginary part coefficient of first parameter.
8. the independent method for calculating the Lorentz curve parameter with 90 degree of phase differences as described in claim 1, feature exist
In the real part coefficient of the second parameter described in step 4 and the relational expression of imaginary part coefficient are as follows:
Wherein, E is used1For the exponential integral and E of p- α t-jx'2For the exponential integral to α t-jx', M is maximum signal amplitudes, e
For natural logrithm bottom, j is imaginary unit, and φ is phase, and α is attenuation constant, and t is time, ω0For eigenfrequency, BRIt is described
The real part coefficient of two parameters, BIFor the imaginary part coefficient of second parameter.
9. the independent calculating as described in Arbitrary Term in claim 5,6,7,8 has the Lorentz curve parameter of 90 degree of phase differences
Method, which is characterized in that the value of the exponential integral are as follows: E1=2 π j, E2=0, it is set up in the case of φ=0 and φ ≠ 0.
10. the independent method for calculating the Lorentz curve parameter with 90 degree of phase differences as described in claim 1, feature exist
In independent calculation formula between first parameter and second parameter are as follows:
A=-B1+jBR
B=A1-jAR
Wherein, ARFor the real part coefficient of first parameter, AIFor the imaginary part coefficient of first parameter, BRFor second ginseng
Several real part coefficients, BIFor the imaginary part coefficient of second parameter.
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