Abstract: A preceding apparatus for calculating a difference between an inputted signal point and an output signal obtained one timing before and outputting the difference has a position information judging unit for judging which position on a vector plane the output signal obtained one timing before is located in, and a signal point selecting storage for outputting any signal point among a plurality of signal points generated correspondingly to a signal point inputted from the outside with a result of the judgement fed form the position information judging unit nd the signal point inputted from the outside as an address, thereby decreasing the number of cycles required by a DSP process and realizing a precoder process in a degree achieved hitherto.

Abstract: The invention provides a training method for a non-Nyquist transmission system and a training data transmission apparatus for a non-Nyquist transmission system by which initialization processing of a reception section can be performed with certainty even where a non-Nyquist transmission system is employed.

Abstract: A method of controlling a line equalizer such as a modem includes an extracting step of extracting plural tone signals each superimposed on a transmission signal and having a specific frequency component; a judging step of judging levels of the extracted tone signals; and a controlling step of controlling characteristic of a line equalizer which equalizes a receive signal, based on the levels of the judged tone signals. A line equalizer is controlled without performing an exchange of a training signal prior to starting a data transmission and without increasing the amount of hardware of a modem or the like.

Abstract: A modulation and demodulation system suitable for use with a modem (modulator and demodulator apparatus) of a first polling type. The system allows reproduction of a signal necessary for initialization of a reception section of a modulator and demodulator apparatus with certainty in a short training time. The modulation and demodulation system is constructed such that, upon transmission of data, training data of a particular pattern are modulated and transmitted prior to transmission of the data, and such training data are demodulated by demodulation means and initialization of a reception section of the modulation and demodulation system is performed using the demodulation training data. The pattern of the training data to be transmitted includes an arrangement of signals wherein signals having phases different by 180.degree. from each other are arranged alternately, and a signal having the same phase as the last signal is arranged intermediately.

Abstract: A modulation and demodulation system which modulates and demodulates a signal in a main channel for main data and a secondary channel for secondary data obtained by frequency division and uses, upon demodulation, a frequency timing extracted from the secondary channel as a sampling timing for an analog to digital conversion device for the main channel. The modulation and demodulation system is improved in that it can rapidly restore, when a timing error occurs, a processing condition in which a normal timing is used, and comprises a demodulation device which includes a phase timing error detection device for detecting an error of phase timing information extracted from the main channel and a storage device for storing the phase timing information. When the phase timing error detection device detects the error of the phase timing information, the demodulation device performs demodulation processing of main data using the phase timing information stored in the storage device.