Frequency-domain forward/backward LMS adaptive predictors with reduced complexity

The implementation of forward/backward least mean square linear predictors in the frequency-domain is known to require two DFT/FFT operations. Here, computationally efficient structures are derived using proper data augmentation methods. As a result, the following are achieved: (i) reduction of a DFT/FFT operation; and (ii) further reduction in complexity when the input signal is real-valued.