Numerical solution of the Hilbert transform for phase calculation from an amplitude spectrum

A method for the numerical solution of the Hilbert transform integral to obtain the phase corresponding to a given amplitude spectrum is presented. The method, which is based on the assumption that the amplitude spectrum at high and low frequencies can be approximated by constant slopes, can be used to calculate the phase over the entire frequency range for both lowpass, bandpass, and highpass characteristics. The numerical solution is carried out on a minicomputer by a Fortran IV program, and the calculation error can be brought down to the level of the truncation error. The usefulness of the method combined with FFT has been shown by calculating the step response of an amplifier from its measured amplitude spectrum.