A Fast Method for the Numerical Evaluation of Continuous Fourier and Laplace Transforms
David A. Bailey, Paul N. Swarztrauber · SIAM Journal on Scientific Computing · 1994
The fast Fourier transform (FFT) is often used to compute numerical approximations to continuous Fourier and Laplace transforms. However, a straightforward application of the FFT to these problems often requires a large FFT to be performed, even though most of the input data to this FFT may be zero and only a small fraction of the output data may be of interest. In this note, the “fractional Fourier transform,” previously developed by the authors, is applied to this problem with a substantial savings in computation.