Numerical evaluation of the Hilbert transform by the Fast Fourier Transform (FFT) technique

Summary. Three Fast Fourier Transform numerical methods for computing the Hilbert transform have been evaluated for their accuracy by numerical examples. All three methods employ the property that the Hdbert transform is a convolution. The first method uses the result that the Fourier transform of 1/πx is — isgn(ω). The second method is based on a discrete Hilbert transform introduced by Saito. The third method, introduced in this research note, uses linear interpolation to transform the Hilbert transform integral into a discrete convolution. The last method is shown by numerical examples from fault dislocation models to be more accurate than the other two methods when the Hilbert transform integral has high‐frequency components.