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 power-of-two data size, but processing times will likely be slower for non-power-of-two cases. FT options include selection of forward or inverse transform, negation of imaginaries before transformation, and sign-alternation (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 TPPI-mode 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 frequency-domain 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 auto-mode option -auto is intended primarily for use in special-purpose applications which automate an entire conversion and processing scheme, or for use in pulse-sequence 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):

• Hypercomplex, States, States-TPPI, Gradient-Enhanced Rance-Kay, Echo-AntiEcho:

     FT | PS -di | TP | FT | PS -di
  

• TPPI (-yMODE Real -aq2D TPPI):

     FT -di | PS -di | TP | FT -real | PS -di
  

• Magnitude (Absolute Value) Mode (-yMODE Real -aq2D Magnitude):

     FT | TP | FT | MC
  

COMMON OPTIONS

-real
This flag selects a complex Fourier transform for a real-only 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 one-point 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 sign-alternated 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 frequency-domain. 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 Complex-N States-N, or States-TPPI-N. Sign-alternation will be selected if the acquisition mode is recorded as States-TPPI, States-TPPI-N, 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 States-TPPI data. The same schemes are used for Gradient-Enhanced phase-sensitive 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.ft2

The following is a basic magnitude-mode (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 Y-Axis 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 real-only 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 time-domain 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.