This paper derives an adaptive coherence filter for canceling interference from a signal of interest whose power spectral density is symmetric. A basic property of the Fourier transform of real signals is that their spectra are Hermitian symmetric. This property is exploited to determine which part of a spectrum is interference and which part is the signal of interest. An unconstrained Wiener filter is derived that exploits the frequency domain symmetry of the signal of interest. While the adaptive coherence filter is based on the Fourier transform property of real signals, an extension of the algorithm is provided so the filter can be used on any signal that displays spectral symmetry. A practical method for implementing the filter is provided. The filter has application in the area of telecommunications, but is applicable in wireless communication applications where a signal, that displays spectral symmetry, is corrupted by interfering signals within the signal of interest's bandwidth.