Abstract: A known training sequence of binary, pseudo random signals, PN, is received over the channel and correlated with a modified pseudo random sequence PN−1 in which the zeros of the known sequence PN have been mapped to −1. A transform of the correlator output will be observed to contain strong tones that indicate the degree of frequency offset. To facilitate synchronization in the presence of an unknown amount of frequency offset, the received signals may be rectified and the correlation step performed with the absolute value of the incoming signal to obtain new output samples. When the frequency offset is small its measurement is facilitated by modulating the incoming signals with a known, comparatively large frequency offset, before the correlation step to make sure that the overall frequency offset occurs around a frequency that is an integral multiple of the symbol rate divided by the number of symbols in the pseudo random sequence.

Abstract: A modem monitor for monitoring full duplex communications comprises one receiver for each data stream and an echo canceler for canceling "far" echo. Prior to each receiver decoding the data stream it is designed to monitor, it replicates an echo expected to be found in its received data stream from a sample of each of the other predecoded data streams. The echo canceler then subtracts the expected echo from the received data stream to remove all far echoes caused by the other data streams. The echo canceled data stream is then decoded. The monitor can also include a data communications network interface and a sample rate converter operating with the PSTN for converting from the network transmission rate to the data transmission rate.