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The Fourier transform of the complex muon polarization
gives a good approximation of the actual internal
field distribution. The Fourier transform is

| |
(29) |

Due to the finite counting rates, the Fourier transform contains
statistical noise.
The noisy or distorted portions of the asymmetry spectrum can be eliminated
from the Fourier transform through ``apodization''. Apodization is achieved
by multiplying the asymmetry spectrum by a weighting function
which varies between one and zero [48].
For example, the Fourier transform can be apodized with a Gaussian function
so that
| |
(30) |

Unfortunately, this apodization procedure also broadens the Fourier
transform. The apodization parameter is chosen
to provide a compromise between the statistical noise in the spectrum
and the additional broadening of the spectrum which such a procedure introduces.
The Fourier transform will also appear broader than the actual
field distribution in the sample because the muon
spin precession signal is measured over a finite time interval.
Because of the finite number of recorded events, the integral in
Eq. (3.34) is replaced with a sum.
Examples of the Fourier transform of the muon precession signal in the
vortex state will be presented in the next chapter. Since
, the
Fourier transform can be presented as a function of either magnetic
field *B* or the muon precession frequency .

** Next:** 3.3 The Rotating Reference
** Up:** 3.2 Measuring the Internal
** Previous:** 3.2.4 Four-Counter Geometry and