Original code copy from Professor Liang: https://osf.io/mg6zd/wiki/home/

HHSA_WK for Academic use only, source code owned by Wei-Kuang Liang. Do not use for commercial. All right reserved.

Limitation on IF computed from Analytic Functions Data need to be mono-component. Traditional applications using band-pass filter, which distorts the wave form. Bedrosian and Nuttall Theorems.

[1] Bedrosian Theorem Let f(x) and g(x) denotes generally complex functions in L 2 (-∞, ∞) of the real variable x. If (1) the Fourier transform F(ω) of f(x) vanished for │ω│> a and the Fourier transform G(ω) of g(x) vanishes for │ω│< a, where a is an arbitrary positive constant, or (2) f(x) and g(x) are analytic (i. e., their real and imaginary parts are Hilbert pairs), then the Hilbert transform of the product of f(x) and g(x) is given H { f(x) g(x) } = f(x) H { g(x) }. Bedrosian, E., 1963: A Product theorem for Hilbert Transform, Proceedings of the IEEE, 51, 868-869. [2] Nuttall Theorem For any function x(t), having a quadrature xq(t), and a Hilbert transform xh(t); then, where Fq(ω) is the spectrum of xq(t). Nuttall, A. H., 1966: On the quadrature approximation to the Hilbert Transform of modulated signal, Proc. IEEE, 54, 1458