Temporal impulse responses from flicker sensitivities: causality, linearity, and amplitude data do not determine phase

Abstract

A recent paper [J. Opt. Soc. Am. A 4, 1130 (1987)] advances a method for the determination of an impulse response from amplitudes of a measured amplitude spectrum. The crucial step in this derivation is the assumption that if a transfer function is analytic and causal, then so is its logarithm. This assumption is tantamount to that of minimum phase and is not justified, both in principle and in practice. In the absence of additional information or assumptions, every amplitude spectrum is consistent with a multiplicity of phase spectra.