In this chapter we discuss the application of DFT basis representation—a special case of DFT filter banks—to the problem of multitone modulation for data transmission. The concept of multitone modulation (MTM) has been known since the middle 1960’s [77, 349], but has attracted much interest since the late 1980’s [189, 219, 54, 144, 346, 83]. MTM is also referred to as Orthogonal Frequency Division Multiplexing (OFDM), Multi-Carrier Modulation (MCM), and Discrete Multitone (DMT). It has been proposed as a standard for the High-Speed Digital Subscriber Line (HDSL)  and Asymmetric Digital Subscriber Line (ADSL)  transmission over twisted-pair cable at data rates of 1.544 Mbps and above (as much as six or seven megabits/sec). It has also been used as a modulation technique for high-speed data transmission  over the telephone switched network. In recent years MTM has also attracted much interest in wireless transmission for Direct Audio Broadcasting (DAB) , and for Personal Communication Services (PCS) . We will concentrate on the use of MTM for data transmission over physical wire lines, e.g., the twisted-pair cables, which introduce amplitude and phase distortion in the signal. HDSL and ADSL are transmitted over these lines and, at the time of this writing, appear to be the major utilization of MTM.
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