Numerical Hilbert Transform Algorithm for Causal Interpolation of Piecewise Polynomial Even and Odd Functions

Causal interpolation of frequency-domain experimental or simulation data known at discrete points is essential for an accurate time-domain analysis. Hilbert transform has a central role in causal interpolation, because it relates the real and imaginary parts of a causal quantity. This paper presents an algorithm for numerical Hilbert transform suitable for causal interpolation of data spanning several frequency decades. It does not suffer from aliasing and large number of points due to fixed frequency step, which are common problems in fast Fourier transform-based algorithms. The algorithm also exploits the symmetry property of frequency domain electrical quantities. Verification was performed by comparing the algorithm's output to published results for test cases of Cauchy pulse and causal interpolation of characteristic impedance.