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Fourier Transforms

Fourier Transforms


Fourier Transforms

Conversion from time domain data (FID) to frequency domain data (spectrum) is accomplished via a forward Fourier Transform. There are 3 types of forward transforms, but NUTS should be able to determine which is appropriate for the current data set, and will apply the correct function when Fourier Transform (FT) is selected.  

FT — Fourier Transform

Does a forward Fourier Transform of the current data set. If the data set is real, a Real FT is performed. If the data set is complex, a Complex FT is performed. If the data is a complex interleaved data set (acquired as alternating real and imaginary points, rather than as simultaneous pairs), a Bruker FT is performed.

Using the non-2-letter command mode, the type of transform can be specified by entering FT followed by one of the following arguments:


BT — Bruker Transform

Bruker data from older spectrometers (using the Aspect computer) are usually acquired using a single A-to-D converter, so real and imaginary points are acquired sequentially, rather than simultaneously. The data is sampled at twice the sampling rate and the data points are placed alternately into the 2 channels to achieve quadrature detection. Therefore, the nth real data point and the nth imaginary data point are not acquired at the same time. This necessitates performing the FT differently. If the data set was converted properly, NUTS will correctly identify the data as "TPPI" (Time-Proportional Phase Incrementation) and typing FT automatically performs the appropriate transform. Typing BT forces NUTS to do a "Bruker Transform" regardless of how the data were acquired.

See also: Special considerations for Bruker data

DF — Digital Filter and FT

This command is an alternative to RD plus FT for digitally filtered data.  

First, some background:  Digitally filtered FIDs have zeroes at the beginning of the data, and FT creates a very wiggly baseline that requires very large linear phase correction (hundreds or more degrees).  To avoid this, the zeroes are removed by a cyclic rotation, performed with the RD command.  NUTS determines how many points to rotate from parameters found in the original data file.

However, sometimes the information found in the data header is incorrect or insufficient for NUTS to determine the correct number of points.  The DF command examines the beginning of the FID to determine where the "real" start of the data should be, and calculates the linear phase correction needed, then executes an FT and applies that phase correction.  This will not work properly for all data, so users are advised to experiment.

See also: Rotate Data (RD)

TJ — Transform JEOL

JEOL spectrometers also have the option of acquiring data using a digital filter (see explanation for DF command, above).  Newer versions of the Delta software manipulate the data to compensate for the distorted ends of the spectrum.  The Delta software "knows" that 10% of the spectral window at each end will be distorted.  To avoid possible loss of peaks at the edge of the window, the spectral width actually acquired is increased automatically.  After the FT, 10% of the data points at each end are automatically discarded, so the resulting spectral width is the value originally input by the user.  However, this results in a reduction of the number of data points in the final spectrum from the user’s settings.  For example, if the user sets a spectral width of 6000 Hz and 16384 data points, the spectral width acquired will be (6000 / 0.8) = 7500 Hz.  After FT, 10% of the data at each end is discarded, giving a final spectral width of 6000 Hz, but the final number of data points is reduced to 13107.  This is a consequence of needing to perform the FT on data which is 2n number of points.  The digital resolution the user intended was 0.37 Hz/pt but the final spectrum is 0.46 Hz/pt.  Note that this may create problems in homonuclear 2D experiments if it is desired to perform symmetrization, as the number of data points is changed in the process.

The TJ command in NUTS performs the same operation as the Delta software does during processing.  As described above, the early data points are zero, but we have not identified a parameter in the data header that would let NUTS know how many points need to be cyclically rotated, using the RD command.  NUTS examines the early data points in the FID to determine where the "real" start of the data is.  An FT is performed, and then a linear phase correction is applied based on how many zeroed points were found at the beginning of the FID.  Lastly, 10% of the data points at each end of the spectrum are discarded.

CT — Complex Fourier Transform

Forces NUTS to execute a complex FT, regardless of the nature of the current data set. Normally, it is better to use FT and let NUTS apply the type of Fourier Transform which is appropriate.

RT — Real Transform

Performs a forward real Fourier transform of the current data set. Any data in the imaginary part of the current data set will be zeroed and ignored. Normally, NUTS correctly identifies when data are real and applies a real FT when the FT command is given. Typing RT will override this and apply a real FT regardless of the nature of the data.

IT — Inverse Transform

Performs an inverse complex transform of the current frequency domain data set to generate an FID.

HT — Hilbert Transform

Hilbert inverse Transform allows the creation of a complex FID from a reals only spectrum.

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Last updated: 3/9/04.