1887

Abstract

In this study a new method is proposed for the determination of the Fourier transform by using the tools of inverse problem theory. In this approach the Fourier spectrum is calculated after solving a (highly) over-determined inverse problem. This makes the proposed procedure more robust than the DFT or FFT. It is proved in two synthetic examples that – compared to DFT- the noise sensitivity of the IFT method (applying LSQ in the inversion) is appreciably reduced. Using an Iteratively Re-weighted Least Squares algorithm (with Cauchy weights) a robust and resistant method (W-IFT) is developed and tested. It can be expected, that the newly developed methods can serve as robust and noise-resistant alternatives of the common Fourier transforms in various fields of practical application.

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/content/papers/10.3997/2214-4609.201402756
2006-09-04
2020-08-08
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http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201402756
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