  We present numerical methods based on the fast Fourier transform (FFT) to
solve convolution integral equations on a semi-infinite interval (Wiener-Hopf
equation) or on a finite interval (Fredholm equation). We extend and improve a
FFT-based method for the Wiener-Hopf equation due to Henery, expressing it in
terms of the Hilbert transform, and computing the latter in a more
sophisticated way with sinc functions. We then generalise our method to the
Fredholm equation reformulating it as two coupled Wiener-Hopf equations and
solving them iteratively. We provide numerical tests and open-source code.
