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This paper presents novel modulation and pre-equalization methods to minimize a signal processing time delay in the equalization digital on-channel repeater (EDOCR) for the ATSC terrestrial digital TV system. The proposed modulation method uses equi-ripple (ER) filter for vestigial side bands (VSB) pulse shaping instead of conventional square root raised cosine (SRRC) filter. And the proposed pre-equalization method calculates pre-equalizer filter coefficients by comparing a baseband signal as a reference signal and a demodulated repeater output signal, and then creates new VSB pulse shaping filter coefficients by the convolution of the ER filter and the pre-equalizer filter coefficients. The new VSB pulse shaping filter minimizes the time delay of EDOCR by adjusting the number of its pre-taps and also compensates the linear distortions due to the use of the ER filter and mask filter.