The rms (root-mean-square) value of a periodic signal is defined to be where is defined to be the signal's period: the smallest positive number such that .
The word "modem" is short for "modulator-demodulator." Modems are used not only for connecting computers to telephone lines, but also for connecting digital (discrete-valued) sources to generic channels. In this problem, we explore a simple kind of modem, in which binary information is represented by the presence or absence of a sinusoid (presence representing a "1" and absence a "0"). Consequently, the modem's transmitted signal that represents a single bit has the form Within each bit interval , the amplitude is either or zero.
To transmit symbols, such as letters of the alphabet, RU computer modems use two frequencies (1600 and 1800 Hz) and several amplitude levels. A transmission is sent for a period of time (known as the transmission or baud interval) and equals the sum of two amplitude-weighted carriers. We send successive symbols by choosing an appropriate frequency and amplitude combination, and sending them one after another.