FOURIER command

The effects of the circuit in the frequency domain were also characterized. The Fourier transform of the quasi-square waveform in Figure 8.41 was taken and the results shown in Fig. 8.44. Note that the third, fifth, seventh, and ninth harmonics are suppressed by about 40db, while the eleventh and thirteenth harmonics are about 20 dB less. The IsSpice simulation of this circuit was generated using the ICL feature of IsSpice. The format of the FOURIER command is shown below in Table 8.2. The resulting circuit characteristics in the frequency domain (Fig. 8.44) compare favorably to the resulting output from the IsSpice file (Table... 

To import the data resulting from the FOURIER command (as shown in Table 8.3) into a spreadsheet, such as Excel, first, open the output (.out) file. Highlight and copy the data you need in the. out file, and open Excel. After Excel opens, paste the contents into the spreadsheet. The next step should be to pull down the DATA menu and select the TEXT TO COLUMNS command. Follow the steps to convert the pasted data into... 

TABLE 8.2 FOURIER Command Syntax for IsSpice, Pspice, and Micro-Cap... 

TABLE 8.3 FOURIER Command Result from IsSpice Simulator... 

With 2D experiments the situation is a little more complicated as the size of the overall digitised matrix depends on the number of time increments in tl as well as parameters specific to the 2D acquisition mode. Nevertheless, a digitised matrix of TD(2) X TD(1) complex data points is acquired and stored. Similar to ID the effective number o measured data points used for calculation TD(used) and the total number of data points SI to be transformed in t2 and tl may be defined prior to Fourier transformation. These parameters may be inspected and defined in the General parameter setup dialog box accessible via the Process pull-down menu. With 2D WIN-NMR the definitions for TD(2) and TD(1) are the same as for TD with ID WIN-NMR. However, unlike ID WIN-NMR, with 2D WIN-NMR SI(2) and SI(1) define the number of pairs of complex data points, instead of the sum of the number of real and imaginary data points. Therefore the 2D FT command (see below) transforms the acquired data of the current data set into a spectrum consisting of SI data points in both the real and the imaginary part. 

Fourier transformation in ID WIN-NMR is accomplished by choosing either the FT command in the Process pull-down menu (Fig. 5.3) or by simply clicking the FT button in the button panel. 

Both Fourier transform commands perform a Fast Fourier Transform (FFT) on the FID. If a baseline correction has not yet been performed on the raw data, a message box will appear which provides the option for performing a baseline correction (see section 5.3.3) on the time domain data (FID) prior to Fourier transformation. 

With 2D WIN-NMR, 2D Fourier transformation may be accomplished with the commands xfb, xtrf, xf2 and xfl accessible via the Process pull-down menu (Fig. 5.5). 

Hint If problems arise the xfb command, perform a stepwise Fourier transformation using the commands xf2 and xfl. 

This operation performs a transformation in the Fl direction in a similar way to that described for xf2. The type of the Fourier transformation depends on the value of the MC2 parameter, which must be correctly set as described above for the xfb command. 

The command xtrf automatically performs a user defined Fourier transformation in both the F2 and Fl dimension. Unlike the xfb, the xf2 and xfl commands, xtrf takes the processing parameter FT mod into consideration. This option is used for special case.s and may be adjusted to your personal needs, e.g. for a real instead of complex FT. 

The corresponding menu for 2D data to set up the window functions and their parameters in F2 (rows) and Fl (columns) is shown in Figs. 5.18 and 5.19. Processing parameters for both F2 and Fl may both be set prior to the consecutive Fourier transformation in both dimensions started with the xfb command. Alternatively the processing and Fourier transformation in t2 - initialized with the xf2 command - may be performed first. Suitable columns may then be used to adjust and set the processing parameters in tl prior to the second Fourier transformation, started with the xfl command. 

With 2D WIN-NMR baseline corrections are automatically applied for FIDs in t2 and tl prior to any processing when the Fourier transformation is initialized with the xfl, xfl, xfb or xtrf commands. According to the parameter BC mod set for F2 and Fl separately, either a simple DC correction or more sophisticated algorithms are applied to correct the FID baselines in F2 and Fl (Table 5.2), thereby taking into account the detection mode (single/quadrature). 

With 2D WIN-NMR zero filling is defined simply by setting SI for the F2 and Fl dimension in the Parameters dialog box opened with the General parameters setup command in the Process pull-down menu prior to Fourier transformation. 

After 2D Fourier transformation J-Resolved spectra usually contain a distortion along the horizontal line leading through the centre of the matrix. In order to get rid of this distortion and to separate chemical shifts from homonuclear J-couplings, the whole matrix is tilted. With 2D WIN-NMR a Tilt command is available which automatically adjusts the corresponding parameters (Tilt factor) and performs a tilt operation. 

William Thomson (later Lord Kelvin) was bom in Ireland in the year of Carnot s Reflexions, and became known as one of the most commanding scientific personalities of his era. Both his father (James, later Professor of Mathematics at the University of Glasgow) and his elder brother (also James) were notable scientists as well. Like Carnot, Thomson and his brother were home-schooled by their father, who was widowed when William was only six years old. Both boys proved to be prodigies, and William was first enrolled in the University of Glasgow when only ten years old. Among other accomplishments, William taught himself French by reading Laplace and Fourier, and the latter s analysis of heat diffusion had a formative influence on Thomson s interest in thermodynamic questions. 

After Fourier transformation, the effects on the spectrum of data manipulations, such as phase adjustments, can be controlled on a display before giving final calculating commands. Communication with the computer is generally via keyboard and graphic display. Light pen control via oscilloscope is also possible. 

Bruker uses the command EM (exponential multiplication) to implement the exponential window function, so a typical processing sequence on the Bruker is EM followed by FT or simply EE (EF = EM + FT). Varian uses the general command wft (weighted Fourier transform) and allows you to set any of a number of weighting functions (lb for exponential multiplication, sb for sine bell, gf for Gaussian function, etc.). Executing wft applies the window function to the FID and then transforms it. 

Load the configuration fiie ch3235.cfg. Seiect the Go I Run Experiment command from the pull-down menubar to start the simulation. Process the FID prior to Fourier transformation using zero filling (Sl(r+i) 64K) and apodization (wdw function EM, LB 2.0 Hz). The Fourier transformed FID should resemble the spectrum in Fig. 3.10a. 

In 2D WIN-NMR the Fourier transformation of 2D raw data is accomplished in one step using the xfb command or stepwise using the xf2 and then the xfl command. In either case the processing parameters including the selection of the appropriate FT mode must be set in the General parameter setup dialog box prior to the Fourier transformation. 

The phase correction of a 2D spectrum follows essentially the same procedure as a ID spectrum except that the phase correction for the rows, the f2 dimension, and columns, the fl dimension, must be executed separately. The following discussion describes the phase correction in the f2 dimension the phase correction of the fl dimension is achieved in a similar way. After Fourier transformation the Manual phase correction command is selected from the Process pull-down menu. The phasing procedure is divided into three steps. 

A row of the data matrix prior to Fourier transformation can be extracted using the FID-Transmission command in the File pull-down menu. 

After Fourier transformation of the time domain data the 2D frequency data, the spectrum, can be described in terms of horizontal rows and vertical columns. To extract an individual row or column the Slice command of the button panel is used. 

The scheme corresponds to the standard HMQC experiment without gradient selection and as such does not indicate whether the experiment is either a ID or 2D data acquisition. To generate a 2D spectrum, the pulse sequence will have to be extended to include commands to increment the delay dO. It is the incrementation of delay dO that generates the second time domain which is Fourier transformed into the fl dimension. To increment the delay dO, the command idO is appended to the wr 0 statement. The individual experiments that make up the 2D data set are generated using an external loop that saves the FID measured for each value of dO in a separate data file. This is achieved using the statement lo to 3 times tdl, the loop counter tdl corresponding to the number of experiments required to make up the f 1 dimension. 

H)-resolved experiment. Fourier transform the data in 2D WIN-NMR using the Process 12D transform [xfb] command and the processing parameters defined in the configuration file. Scale the spectrum by clicking the Change all button and then the Options button in the Change all levels dialog box, set the Lowest level and Factor to optimum values. 

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