Minimum phase response reconstruction of sampling oscilloscopes based on the NTN calibration

This paper describes an algorithm for determining the minimum phase response of sampling oscilloscopes of a linear time-invariant response function from its magnitude. The procedure is based on Kramers-Kronig relations in combination with the harmonic phase response measurement of the NTN calibration. Although the truncation of the Hilbert transform gives rise to large errors in estimated phase, these errors may be approximated by using three basis functions. As an example, we got the minimum-phase response reconstruction of sampling oscilloscopes in the frequency domain; its frequency resolution achieves 1 MHz.