Reconstruction of non-minimum phase function from only amplitude data

A procedure for a non-minimum-phase reconstruction from magnitude data alone is presented. A non-minimum-phase component is recovered, based on the fact that the auto-correlation of the time domain sequence is equal to a discrete cosine transformation of the square of the magnitude response. An all-pass filter is also utilized in order to reduce the optimization variables. Since a non-minimum-phase reconstruction does not have a unique solution, a causal time-domain response is selected along with the smallest poles in magnitude. This theory is applied to antenna pattern synthesis and scattering parameters of microwave filters to illustrate the applicability of the proposed approach.