Abstract: One embodiment of the present invention relates to an adaptive filtering apparatus comprising first and second real valued adaptive filters, respectively configured to receive an adaptive filter input signal based upon a transmission signal in a transmission path. The first real valued adaptive filter is configured to operate a real valued adaptive filter algorithm on the input signal to estimate a first intermodulation noise component (e.g., an in-phase component) in a desired signal and to cancel the estimated noise. The second real valued adaptive filter is configured to operate a real valued adaptive filter algorithm on the input signal to estimate a second intermodulation noise component (e.g., a quadrature phase component) in the desired signal and to cancel the estimated noise. Accordingly, each filter operates a real valued adaptive algorithm to cancel a noise component, thereby removing complex cross terms between the components from the adaptive filtering process.