Logarithmic Fourier Transformation.
G.V. Haines and A.G. Jones
We present an exact and analytical expression for the Fourier transform of a function that has
been sampled logarithmically. The procedure is significantly more efficient computationally
than the fast Fourier transformation (FFT) for transforming functions or measured responses
which decay slowly with increasing abscissa value. We illustrate the proposed method with an
example from electromagnetic geophysics, where the scaling is often such that our logarithmic
Fourier transform (LFT) should be applied. For the example chosen, we are able to obtain
results that agree with those from an FFT to within 0.5 per cent in a time that is a factor of
10’ shorter. Potential applications of our LFT in geophysics include conversion of wide-band
electromagnetic frequency responses to transient responses, glacial loading and unloading,
aquifer recharge problems, normal mode and earth tide studies in seismology, and impulsive
shock wave modelling.
Geophysical Journal, 92, 171-178, 1988.
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