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NMRPipe Processing Functions
FT: Complex Fourier Transform.

FT applies a complex Fourier transform (FT) to produce a complex result. There is no requirement for a poweroftwo data size, but processing times will likely be slower for nonpoweroftwo cases. FT options include selection of forward or inverse transform, negation of imaginaries before transformation, and signalternation (negation of alternating points) of the data before transformation. An option to apply a complex FT to a real data sequence is also provided for TPPImode data. FT options can also be selected automatically from the header, provided that the acquisition mode information was recorded appropriately during conversion.
According to the usual convention, the forward FT arranges a frequencydomain result such that zero frequency is in the center of the spectrum, specifically, at point 1 + N/2 of 1 to N (e.g. point 513 of 1 to 1024). The forward/inverse Fourier transform pair are scaled in such a way that a forward FT followed by an inverse FT will recover the original intensities.
If a given dimension of a spectrum is reversed, then that dimension
should be processed using FT neg
... note that simply
reversing the order of data points via nmrPipe fn REV
alone
is not correct.
If a given dimension of a spectrum has its first and second halves
rotated, then that dimension should be processed using FT alt
.
In some cases, both neg
and alt
might
both be needed for a given dimension.
The automode option auto
is intended primarily for use in
specialpurpose applications which automate an entire conversion
and processing scheme, or for use in pulsesequence specific
examples. Its use for routine processing is not recommended.
BASIC 2D FOURIER TRANSFORM SCHEMES
The following are basic outlines of common 2D Fourier transform schemes (complete schemes would also include a window function and zero fill for each dimension):
FT  PS di  TP  FT  PS di
FT di  PS di  TP  FT real  PS di
FT  TP  FT  MC
COMMON OPTIONS
real
This flag selects a complex Fourier transform for a
realonly sequence. It is commonly used for data
recorded in the TPPI mode. This option will reduce the
data size by a factor of two.
alt
This flag causes sign alternation to be applied to the
data before the FT. In the case of complex data, sign
alternation has the effect of exchanging the left and
right halves of the corresponding spectrum:
 nmrPipe fn FT alt \is equivalent to:
 nmrPipe fn FT \  nmrPipe fn SHUF exlr \
neg
This flag causes the imaginary part of the data to be
negated before the FT. It is equivalent to reversal of
the corresponding spectrum followed by a onepoint
right circular shift:
 nmrPipe fn FT neg \is equivalent to:
 nmrPipe fn FT \  nmrPipe fn REV sw \  nmrPipe fn CS rs 1 sw \
bruk
This flag applies a signalternated real FT suitable
for Bruker Sequential Mode (QSEQ) data. This option
will reduce the data size by a factor of two. It is
equivalent to:
nmrPipe fn FT real alt
auto
This flag enables automatic selection of the FT modes.
Inverse mode will be selected if the data are in the
frequencydomain. Real transform mode will be selected
if the acquisition mode is recorded as Real, TPPI, or
Sequential (Bruker). Negation of imaginaries will be
selected if the acquisition mode is recorded as
ComplexN StatesN, or StatesTPPIN. Signalternation
will be selected if the acquisition mode is recorded as
StatesTPPI, StatesTPPIN, or Sequential (Bruker).
The general use of this flag is not recommended.
inv
This flag selects an inverse Fourier transform.
EXAMPLES
The following is a basic 2D Fourier transform scheme for States or StatesTPPI data. The same schemes are used for GradientEnhanced phasesensitive data, once such data have been appropriately shuffled.
nmrPipe in test.fid \  nmrPipe fn SP off 0.5 end 0.95 pow 1 c 0.5 \  nmrPipe fn ZF auto \  nmrPipe fn FT \  nmrPipe fn PS p0 0.0 p1 0.0 di verb \  nmrPipe fn TP \  nmrPipe fn SP off 0.5 end 0.95 pow 1 c 0.5 \  nmrPipe fn ZF auto \  nmrPipe fn FT \  nmrPipe fn PS p0 0.0 p1 0.0 di verb \ ov out test.ft2
The basic 2D Fourier transform scheme above needs only a
slight modification for TPPI data, which requires
the FT real
option for the indirect dimension:
nmrPipe in test.fid \  nmrPipe fn SP off 0.5 end 0.95 pow 1 c 0.5 \  nmrPipe fn ZF auto \  nmrPipe fn FT \  nmrPipe fn PS p0 0.0 p1 0.0 di verb \  nmrPipe fn TP \  nmrPipe fn SP off 0.5 end 0.95 pow 1 c 0.5 \  nmrPipe fn ZF auto \  nmrPipe fn FT real \  nmrPipe fn PS p0 0.0 p1 0.0 di verb \ ov out test.ft2The following is a basic magnitudemode (also called absolute value mode) 2D processing scheme; note that in this case, the imaginaries are not deleted after the first Fourier transform, and the magnitude calculation function MC is used after the second transform. Note also that the second FT is a complex one, which can be specified as
FT neg
if the YAxis of the result needs to
be reversed:
nmrPipe in test.fid \  nmrPipe fn SP verb \  nmrPipe fn ZF auto \  nmrPipe fn FT auto \  nmrPipe fn TP \  nmrPipe fn SP verb \  nmrPipe fn ZF auto \  nmrPipe fn FT \  nmrPipe fn MC \ out test.ft2 verb ov
The following is a general inverse Fourier transform
scheme, which will regenerate a 2D hypercomplex FID from a
realonly untransposed 2D spectrum. Note use of the generic nmrPipe
option ad
to make room for hypercomplex data,
and the use of the hypercomplex transpose option TP hyper
.
In this case, the generic window function APOD is used
in order to divide the data by whatever window was applied during processing.
This use of an inverse window requires that the original data was
processed using a window function with no values at or close to zero.
nmrPipe in test.ft2 \  nmrPipe fn TP \  nmrPipe fn HT auto verb \  nmrPipe fn PS inv hdr \  nmrPipe fn FT inv \  nmrPipe fn ZF inv \  nmrPipe fn APOD inv hdr ad \  nmrPipe fn TP hyper \  nmrPipe fn HT auto verb \  nmrPipe fn PS inv hdr \  nmrPipe fn FT inv \  nmrPipe fn ZF inv \  nmrPipe fn APOD inv hdr \ out test.fid ov
HEADER VALUES
The FT function toggles the NDFTFLAG to 0 or 1, depending on whether the result is timedomain or frequency domain, respectively.
The NDQUADFLAG of the result is set to 0, to indicate complex data.
In the case of a real
transform, NDSIZE, NDAPOD, and
NDTDSIZE are reduced by a factor of two.