A modem for more efficiently processing a received analog signal into a digital output. The modem preferably features an adaptive equalizer with coefficients which are saved and reused for processing of subsequent analog signals, in order to reduce the time required to reach convergence. In addition, preferably the modem features an automatic carrier frequency control which adjusts the sampled digital signal according to both the carrier phase offset and the carrier frequency offset. Again, in order to process the signal more quickly and efficiently, preferably the carrier frequency offset is stored and reused for processing subsequent signals.