PEST 4.0- FTEPR - Fourier Transform program



The Fourier transform program is intended to compute the FFT of experimental 
data and perform some basic manipulations of data as well as serve as a 
platform for more extensive computations not yet ported to the PC.  The 
Import/Export utility provides for file loading and saving.

4.0.1	The data screen

message area
The top line of the screen is reserved for status messages and user prompts.

display box
The two large boxed areas are reserved for spectral display.  The upper box is 
for Real data display and the lower box is for Imaginary data display.  The 
display can be zoomed to either the Real of Imaginary display occupying the 
entire display area.  A scale is printed along the X-axis in data point units.  
The top line of the display box is used for :

Filename:	name of the imported file
Clipboard #	Clipboard number used to load the data
YS:		the y-scale multiplier applied to the data, constant for Real 
		and Imaginary data.

menu area
The menu options are displayed on the left of the screen with the current choice 
printed in a different color.  The up and down arrows move the current choice, 
the enter key will initiate that action.  You must choose EXIT to leave the 
program.

4.0.2	Function keys

No function keys are active in this program.

4.1.0	The FTEPR menu

The main FTEPR menu has the following choices:

Import		Load a data file.
Export		Write a data file.
Parameters	Display the current spectral parameters.
FFT +1		Calculate a forward FFT.
FFT  -1		Calculate a reverse FFT.
Filter		Filter the FT spectrum by zero-fill(s).
Zero		Zero either the Real or Imaginary data arrays.
Zoom		Zoom the display to either all Real or all Imaginary.
X-Y-scale	Change the X and Y scale display parameters
Combine		Combines the Real and Imaginary data sets to one 
		array for simulation.
Enhance		FT based spectral enhancements.
Power		Calculate a power spectrum from the Real and Imaginary 
		components of FT data.
Autocor		Calculate an FT-generated autocorrelation of a spectrum 
		using original CW data
Exit		Exits this program


Each function is described in more detail.

Import
Loads an exported data file.  You will be prompted for R or I for 
Real and Imaginary data.  Next, enter the clipboard page number 
( 1-99 ) to transfer experimental data into the Simepr.exe program.

Export
Saves data to a file.  You will be prompted for R or I if the display is 
Real and Imaginary.  After that, you will be prompted for the clipboard 
page number ( 1-99 ).  

Parameters
Displays the current spectral parameters on screen.

FFT +1
Compute a forward Fourier transform of the current data.  

FFT -1
Compute a inverse Fourier transform of the current data.

After each FFT operation, the display shows both Real and Imaginary data.  If 
the number of forward and inverse transforms is equal, the Y-scale is set to be 
the original value when the data was imported into the program.; otherwise, the 
Y-scale is set to produce a display with the data set (R or I) having the most 
intensity to be nearly full screen in its display window.  The FT calculations are 
performed in double precision for speed and accuracy.  

Filter
Filter the data by zeroing a portion of the Fourier transformed data.  You are 
prompted to zero either a Low or High frequency region.  You are next 
prompted for n, the highest or lowest filtered frequency accordingly.  The low 
frequency filter is particularly useful for removing non-linear baseline effects 
and the typical value of n is 2 or 3.  The high frequency filter is useful for 
'noisy' spectra, the value of n should then be something just above the region of 
visible spectral information.

Zero
Zero's either the Real or Imaginary data.  This option is especially useful when 
the Real and Imaginary data do not belong together.  When you import CW 
data into the Real display and the Imaginary data is non-zero, you should Null 
the Imaginary display

Zoom
Zooms the display.  You will be prompted to zoom either the Real or Imaginary 
displays.  A subsequent zoom will revert to a split screen display.

X-Y-scale
Use the arrow keys to change the X and Y display scale parameters.   Press 
ESC or Backspace to return to the menu.

Combine
Combines the Real and Imaginary data sets to one array for exporting to the 
Simepr.exe program.  You must use this feature to Optimize or Tune an FT 
spectrum.  This feature has no meaning for a CW spectrum.  Only a symmetric 
spectrum which is centered in the data array will produce a Fourier transform 
which is purely either Real or Imaginary depending on the harmonic with the 
exception of noise.  A first derivative CW spectrum will produce a purely 
Imaginary display after an FFT+1.  To simulate the FT of non-symmetric 
and/or non-centered spectra, this feature has been added.  Because the spectral 
information is compressed into the low frequency region of an FT by the 
exponential linewidth function, the high frequency region may be discarded.  
This now empty space of the Imaginary array is used to hold the low frequency 
information of the Real array.  You will be prompted for n, the frequency value 
(data point) for combination.  This number should be above the region of 
significant low frequency spectral information.  The left n values will now 
contain Imaginary array values and the n+1 to 2n+1 values will now contain 
the Real array values.  The display is now scaled to show 2n frequency values 
which will be in the Imaginary display and the Real display will be null.  This 
new Imaginary array may then be exported to the Simepr.exe program for 
efficient simulation of FT data.  This is an unrecoverable process.

Enhance
This feature is reserved for future FT based apodization style applications.

Power
Computes the Power spectrum from Real and Imaginary FT data; do not use 
CW data.  The power spectrum is defined as the square of the complex 
coefficients.  P= (a+bi)(a+bi)= aa + 2abi + bb = aa + bb + 2abi .  This is often a 
useful product in FT calculations.

Autocor
Computes the Autocorrelation spectrum of the experimental spectrum stored in 
the Real display.  The starting data should be a CW spectrum.  First, a forward 
FFT is computed, then a Power spectrum, then an inverse FFT.  Data with 
value below zero is eliminated.  The result is comparable to the output of the 
Autocor.exe program, however this result is a new spectral map of the splitting 
constants.  The Gauss units remain constant and splittings are measured by the 
distance from the low field limit to a peak.