1. An enhancement speech system that improves the perceptual quality of a processed speech segment, comprising: a discrete input; a delay unit that digitally delays a signal received through the discrete input; a spectral modifier coupled to the delay unit programmed to substantially flatten the spectral character of a background noise; an adaptive filter coupled to the spectral modifier that adapts filter characteristics to match a response to the signal received through the discrete input before the signal is delayed; a programmable filter coupled to the delay unit having a transfer function functionally related to a transfer function of the adaptive filter; and an adder comprising circuitry, a non-transitory computer-readable storage medium with program instructions stored thereon, or both, where the adder sums an output signal of the programmable filter and the signal received through the discrete input to increase a first periodic signal component in the signal received through the discrete input that is at least partially in-phase with a second periodic signal component in the output signal of the programmable filter.