The Fourier Transform

  • David F. Walnut
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


We have seen that if f(x) is a function supported on an interval [−L, L] for some L > 0, then f(x) can be represented by a Fourier series as
$$f\left( x \right) = \sum\limits_n {c\left( n \right){e^{2\pi in\left( {x/2L} \right)}}\quad where\quad c\left( n \right) = \frac{1}{{2L}}\int_{ - L}^L {f\left( t \right){e^{ - 2\pi it\left( {n/2L} \right)}}dt.} } $$


Fourier Transform Fourier Series Prove Theorem Approximate Identity Fourier Inversion 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • David F. Walnut
    • 1
  1. 1.Department of Mathematical SciencesGeorge Mason UniversityFairfaxUSA

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