1. A Fortran Program for Fourier Transformation
Role of Information Technology Tools in Self-Learning Initiatives; and, in Classroom Teaching and Learning
A Fortran Program for Fourier Transformation
Examples of program output
Graphically plotted with MS EXEL
This presentation file is available for download at:
SANKARAMPADI ARAVAMUDHAN
NORTH EASTERN HILL UNIVERSITY
Click HERE to view the original .pdf version of the above .jpg image of the Certificate
A hotlink reference to the article published in the e-journal IJRDET:-
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2. Slides #3-7 contain introductory materials for the teachers, to be able to discern the scope of the curricular contents preferred for the basic aspects of DIGITAL PROCESSING in FT NMR systems.
In this presentation, Instead of beginning with the spin system physical descriptions, the mathematical forms and Fourier Transform aspects are illustrated as if it occurs in the display of NMR spectrometer.
A computer program to simulate the time-domain data usually acquired in the spectrometers, to Fourier Transform from time domain (64 points) into frequency domain in such a way that the outputs can be graphically obtained by importing the output text files to MS EXEL APPLICATION.
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3. “Modern Techniques in High Resolution FT NMR”
An excerpt from book:
“Modern Techniques in High Resolution FT NMR”
Experimentaly acquired
FID (time domain data) and the Fourier Transformed (frequency domain) Spectrum
In this presentation, Instead of beginning with the spin system physical descriptions, the mathematical forms and Fourier Transform aspects are illustrated as if it occurs in the display of NMR spectrometer.
The occurrence of these forms is because of the way spin system can be described; and how the spin system evolves under experimental conditions. Thus the NMR phenomenon is intrinsically capable of such responses in the experiments.
Such acquired shapes (FID) can be expressed in terms of mathematical functional forms and can be simulated using appropriate parameters of the functions
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4. HOTLINK:- http://aravamudhan-s. ucoz
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5. A steady Uniform Magnetic Field of 9.34 Tesla is applied
Elaboration on the even more basic Single spin Magnetic moment situation in a steady applied Magnetic field and the Consequent Magnetization can be viewed at YOUTUBE.COM
url OF ‘My Channel: at YOUTUBE
Obtaining FT NMR
A steady Uniform Magnetic Field of 9.34 Tesla is applied
Experimental sample is placed in the magnetic field
Uploaded files
1_NMR and 2_NMR
Magnetization Builds up due to Relaxation process in Time T1 z x y
A rectangular pulse of 400 MHz RF frequency is applied to bring the magnetization to XY Plane
Magnetization decay due to T2 process. Free Induction Decay F.I.D. acquired (as in slides # 5, & 10)
FID is digitized
FID Fourier Transformed to obtain Spectrum
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6. Frequency Domain Spectrum
Typical Program listing and with comments
PULSED NMR
Acquire F.I.D.
Free Induction Decay
NMR detection soon after a strong pulse: precessing nuclear magnetization induces a signal in coil when it is free of the perturbing EM radiation
Acquisition is automatically in the digitized form
Analogue signal
Computer memory
Address
Contents 15
1111 14
1110 8
1000 4
0100 7
0110 1
0001
0111
0000
Time domain 15 11
DIGITIZE
Analogue to Digital Converter A.D.C.
F.I.D.
Frequency Domain Spectrum
Computer output
This one-dimensional FT NMR spectrum is the same information as the C.W. NMR spectrum
Next Slide
FFT from FID
Computer input
Top of slide #10 find a file consisting of Fourier Transform program which can be copied into Fortran compiler and run.
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7. On Fourier Transformation: from the book on NMR cited earlier.
In the sample file linked a sinusoidal FID is considered. In fact, instead of such an FID function any of the functions listed above on LHS can be tried out.
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8. Sinusoidal periodic function :-
1 Osc ., Corresponds to 4 units; & if 1 unit=1μs then, the frequency of oscillation would be 250 KHz.
Sinusoidal periodic function :-
SIN (2.π. (n- 1)/4)
n is integer corresponding to the data point
64 data points, and each division = 1 unit. In time units, as may be appropriate for a context; 1 unit may be 1atto sec,1ps, ns, 1μs; 1ms; or 1 sec.
An exponential decay function below:-
When there are 64 time data points, there would be 63 time intervals. If the first point is addressed as ‘0’ the initial time, then the last point would be 63.
If the first point is counted as 1 then the last point would be 64
The number of data points are set to a number that would correspond to an integer value ‘n’ such that there would be 2n . 64 corresponds to 26
exp (-(n-1) / 11)
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9. Sinusoidal variation and exponential decaying are two independent processes occurring in the system affecting the same physical quantity measured:
When the sinusoidal evolution and the exponential decay of amplitude occur for the same quantity, the net process evolution may be obtained by multiplying the two functional !!!
…….> (next slide)
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10. Multiply point by point at each X-axis value…result would be:
Hotlink for -> A TYPICAL FORTRAN SOURCE PROGRAM FOR GENERATING TIME DOMAIN DATA, FOURIER TRANSFORMATION TO FREQUENCY DOMAIN
Multiply point by point at each
X-axis value…result would be:
Hotlink: output file of program-run
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11. Hotlink:- example
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12. Hotlink : ILLUSTRATION WITH MS EXEL
Till previous slide mostly SINE form
COS (2.π. (n-1) /4)
n is integer corresponding to the data point
Fourier transformation
REAL part ABSORPTION
IMAGINARY part DISPERSION
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13. Fourier transformation
SINE FORM
Fourier transformation
IMAGINARY part ABSORPTION
REAL part DISPERSION
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15. Illustration for two-line spectrum
Fourier transformation
FID-COSINE FT
FID-SINE FT
REAL & IMAGINARY PARTS
Differences in FID appearances with spectral characteristics---- Next slide
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16. But note the differences in the FID and the spectral intensity
But note the differences in the FID and the spectral intensity.(indicated by arrows) Correlate these features
16 18
16 18
16 18
Fourier spectrum in all cases has only two lines same line positions (and same separation).
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17. FT FT Line separations are same; positions are different 15 19 16 20
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18. F.T.
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20. POSSIBLE ARTEFACTS WITH FT PROGRAMS
SOMETIMES SUCH ARTEFACTS MAY BE NOTICEABLE IN THE
OUTPUT FROM SPECTROMETERS
COSINE FID WITH 64 DATA POINTS
COSINE FID WITH 64 DATA POINTS
FOURIER TRANSFORM OF THE ABOVE FID
8.5
FOURIER TRANSFORM OF THE ABOVE FID
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23. Digital Fourier Transformation :
The previous slides were illustrative of artifacts simulated using an FT program: Such similar artifacts occur in the experiments and the simulations could be helpful in disentangling these effects from the useful information
Similarly in the following slides an illustration of the time domain acquisition parameter settings are illustrated by simulation indicating how the Fourier transformed spectrum can be obtained for extracting maximum information.
Digital Fourier Transformation :
Time Domain Data Parameters and Consequences on the Frequency Domain Spectrum
Number of Time Domain Points; Decay Time Constant; FID; Frequency Domain Line-widths; Spectral Resolution; Signal Noise ratio
These terms are normally spectral quality determining factors
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24. An Illustration with simulation of this NMR pattern
256 time domain points
Note the depth to which the lines get separated
In the time domain pattern the oscillations are visible for longer duration till the end
Better resolved spectrum
F.T.
Overlap increases
Decay time constant increases
Resolution increases
128 time domain points
An Illustration with simulation of this NMR pattern
Faster decay; smaller time constant
Oscillations visible only till this point
Line separation is same
Faster decay; smaller time constant; same as in middle trace
Resolution is same as in middle spectrum above ; in this trace there are more number of points within each line than in middle trace; increased time data points
256 time domain points
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25. ACCOUNTS FOR ONE PROTON COUPLED TO THREE EQUIVALENT
ACCOUNTS FOR ONE PROTON COUPLED TO ONE EQUIVALENT
DOES NOT CORRESPOND TO ANY MOLECULE
NO MUTUAL COUPLING 3 1
ACCOUNTS FOR THREE EQUIVALENT PROTONS COUPLED TO ONE EQUIVALENT
MUTUAL COUPLING
ACCOUNTS FOR ONE PROTON COUPLED TO THREE EQUIVALENT
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26. of Typical Fortran Source program used in this context till now
Listing
of Typical Fortran Source program used in this context till now
Typical output results
A downloadable listing which can be copied and pasted to fortran compiler is linked at slide#10
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