Numerical Hilbert Transform Algorithm for Causal Interpolation of Functions Represented by Cubic and Exponential Splines

This paper presents an algorithm for numerical Hilbert transform of functions represented by cubic and exponential splines, which is suitable for causal interpolation of data spanning several frequency decades. It does not suffer from excessive number of data points due to large frequency span, and does not exhibit aliasing, both of which are characteristic for Hilbert transform algorithms based on FFT. The proposed algorithm was used for causal interpolation of characteristic impedance of microstrip line over conductive substrate, and the results were compared to the output of CausalCat.