When you dial a phone number on a touch tone telephone, the telephone generates a dual tone multifrequency (DTMF). In other words, the sound that you hear is the sum of 2 sinusoidal signals at different frequencies; therefore the name DTMF. Every time a key is pressed, a combination of a high frequency tone and a low frequency tone represents a specific digit or character, * and #.
The tone frequencies depend on the digit dialed and are shown in the
table below. The table is intentionally left incomplete and you will be
asked to complete the table in the exercises.




















The frequencies were chosen to avoid harmonics. No frequency in the table is a multiple of another. Furthermore, no frequency is equal to the difference or the sum of two other frequencies in the table.
At the receiver, a discrete time fourier transform (DTFT) or a power
spectral density (PSD) analysis is performed in order to detect which two
frequencies are present in a signal. For instance, the PSD analysis
for the received signals corresponding to the digits 2 and 9 would give
the following results.
Once the pair of frequencies is detected, the lookup table is
sufficient to know which key was dialed.
The experiment allows you to select a digit, listen to its tones, see
its time waveform, as well as its power spectral density function (i.e.,
the squared magnitude of the DFT of the time waveform).
Note: Touch Tone is a registered trademark of AT&T.