Echo cancellation eliminated this problem. Measuring the echo delays and magnitudes allowed the modem to tell if the received signal was from itself or the remote modem, and create an equal and opposite signal to cancel its own. Modems were then able to send over the whole frequency spectrum in both directions at the same time, leading to the development of 4,800 and 9,600 bit/s modems.
Increases in speed have used increasingly complicated communications theory. Twelve hundred and 2,400 bit/s modems used the phase shift key (PSK) concept. This could transmit two or three bits per symbol. The next major advance encoded four bits into a combination of amplitude and phase, known as Quadrature Amplitude Modulation (QAM).
The new V.27ter and V.32 standards were able to transmit 4 bits per symbol, at a rate of 1,200 or 2,400 baud, giving an effective bit rate of 4,800 or 9,600 bit/s. The carrier frequency was 1,650 Hz. For many years, most engineers considered this rate to be the limit of data communications over telephone networks.