Auxiliary Factor Method for Nyquist Filters with Reduced Complexity and Delay

The Nyquist first condition promises data transmission without intersymbol interference (ISI). However, the implementation using any finite impulse response (FIR) filter cannot get rid of the ISI completely because the window's length truncates the Fourier transform, thus, preventing calculations from reaching the intended approximation in the frequency domain. Our previous work introduced an auxiliary factor (AF) method that uses the AFs to compensate the truncated Fourier transform and eliminates the ISI in practice. In this paper, we propose a decomposition solution to further reduce the computational complexity and system delay caused by the AF method. In consequence, an efficient algorithm is exploited to calculate the AFs and numerical results confirm the effectiveness of the proposed solution.