How well does the finite Fourier transform approximate the Fourier transform?
نویسندگان
چکیده
منابع مشابه
How Well Does the Finite Fourier Transform Approximate the Fourier Transform?
We show that the answer to the question in the title is “very well indeed.” In particular, we prove that, throughout the maximum possible range, the finite Fourier coefficients provide a good approximation to the Fourier coefficients of a piecewise continuous function. For a continuous periodic function, the size of the error is estimated in terms of the modulus of continuity of the function. T...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2005
ISSN: 0010-3640,1097-0312
DOI: 10.1002/cpa.20064