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 http://www.ugc-inno-nehu.com/NMR-animation.html This presentation file is available for download at: http://www.ugc-inno-nehu.com/NMR_animation/evolving-funcns.ppt 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:-http://www.ijrdet.com/files/Volume4Issue8/IJRDET_0815_05.pdf 04-12-2018 03:30:59

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. 04-12-2018 03:30:59

“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 04-12-2018 03:30:59

HOTLINK:- http://aravamudhan-s. ucoz 04-12-2018 03:30:59

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 http://www.youtube.com/aram1121944/ 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 04-12-2018 03:30:59

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 1 0000 15 1111 2 0001 14 1110 3 0010 13 1101 4 0011 11 1011 5 0100 8 1000 6 0101 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. 04-12-2018 03:30:59

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. 04-12-2018 03:30:59

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) 04-12-2018 03:30:59

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) 04-12-2018 03:30:59

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 04-12-2018 03:30:59

Hotlink:- example 04-12-2018 03:30:59

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 04-12-2018 03:30:59

Fourier transformation SINE FORM Fourier transformation IMAGINARY part ABSORPTION REAL part DISPERSION 04-12-2018 03:30:59

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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 04-12-2018 03:30:59

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). 04-12-2018 03:30:59

FT FT Line separations are same; positions are different 15 19 16 20 15 19 16 20 04-12-2018 03:30:59

F.T. 04-12-2018 03:30:59

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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 04-12-2018 03:30:59

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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 04-12-2018 03:30:59

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 04-12-2018 03:30:59

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 0.06267 0.25003 0.18736 3 1 ACCOUNTS FOR THREE EQUIVALENT PROTONS COUPLED TO ONE EQUIVALENT MUTUAL COUPLING ACCOUNTS FOR ONE PROTON COUPLED TO THREE EQUIVALENT 04-12-2018 03:30:59

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 04-12-2018 03:30:59