This paper proposes the frequency domain multiplication-free adaptive filter (FDMAF) using the modified discrete Fourier transform (MDFT) pair. The proposed FDMAF employs the MDFT and differential pulse code modulation (DPCM) in an input part and the reference input vectors are used in the update equation for the adaptive filter coefficients. The FDMAF structure can remove the intersymbol interference (ISI) in fast data transmission channel, and analyses their convergence characteristics. Also, the proposed FDAF can be simply controlled by adjusting the amplitude of the MDFTP (MDFT pair) output signals and can obtain an output signal with stable convergence characteristics and without accumulated error. The FDMAF algorithm is analyzed under conditions of zero-mean, wide-sense stationary and white Gaussian noise.
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