This paper describes theories and implementation techniques of a digital high-definition television(HDTV) modem based on 32-QAM for terrestrial broadcasting. We proposed a digital demodulation scheme and a symbol timing recovery structure based on the band edge component maximization(BECM) method. The adaptive equalizer has 256 complex taps to remove the multipath of delays ranging from -2.mu.s~+24.mu.s with a new T/2-spaced blind equalization algorithm. computer simulation results reveal that the proposed algorithm outperforms other conventional blind equalization algorithm a digital HDTV modem with 4.91MHz symobol rate is implemented by utilizing the proposed algorithms. All processings for modem operations such as demodulation, estimation of symbol timing phase error, adaptive equalization, and carrier recovery except IF signal processing and sampling phase control part of the AD converter are done in digital domain. Especially, the carrier recovery loop can track a carrier offset of upto .+-.350KHz.