A theoretical analysis of the small-signal frequency response (SSFR) of a wavelength converter based on cross-gain modulation in a semiconductor optical amplifier with a finite waveguide loss is presented. We use a transfer function formalism to explain the resonant behavior of the frequency response. The limitations to the magnitude of the spectral overshoot are also accounted for. Operating with the data and CW signals in a co-propagating configuration, we End that the resonance only exists for a finite waveguide loss. In a counter-propagating scheme, a resonance can exist regardless of the presence of loss.