An Accurate Discrete Fourier Transform for Image Processing
نویسندگان
چکیده
The classical method of numerically computing the Fourier transform of digitizedfunctions in one or in ddimensions is the so-called discrete Fourier transform ( D F T ) , efficiently implemented as Fast Fourier Transform ( F F T ) algorithms. In m n y cases the D F T is not an adequate appmximation of the continuous Fourier transform. The method presented in this contribution provides accurate approximations of the continuous Fourier transform with similar time complexity. The assumption of signal periodicity is no longer posed and allows to compute numerical Fourier transforms in a broader domain of frequency than the usual halfperiod of the D F T . In imagepmcessing this behavior is highly welcomed since it allows to obtain the Fourier transform of an image without the usual interferences of the periodicity of the classical D F T . The mathematical method is developed and numerical examples are presented.
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