A Linear Phase Condition for Volterra Filters

In linear finite-impulse-response filter design, it is desirable that the filter frequency response has linear phase (LP). In this brief, we investigate the LP concept for nonlinear Volterra filters. The LP condition of Volterra filters is defined in terms of its output spectrum in which the phase term introduced by the Volterra kernels is linear. It is shown that under certain symmetry conditions, the LP condition is satisfied by Volterra filters. Moreover, the LP condition for Volterra filters can be considered as an extension to the linear filter case.