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Lab Exercise:

A DTMF Tone Generator

DTMF Tones

A DTMF tone is the sum of two tones:

• one tone of a low frequency f₁, and
• one tone of a high frequency f₂

DTMF Tone = tone of frequency f₁ + tone of frequency f₂.

The low frequency f₁ is one of 697 Hz, 770 Hz, 852 Hz, and 941 Hz.
The high frequency f₂ is one of 1209 Hz, 1336 Hz, 1477 Hz, and 1633 Hz.

Hence, there are 16 possible DTMF tones. One DTMF tone each is associated with the 10 digits, the symbols * and #, and the letters A, B, C, D as follows:

	f1 (Hz)	f2 (Hz)
1	697	1209
2	697	1336
3	697	1477
4	770	1209
5	770	1336
6	770	1477
7	852	1209
8	852	1336
9	852	1477
0	941	1336
*	941	1209
#	941	1477
A	697	1633
B	770	1633
C	852	1633
D	941	1633

DTMF tones are extensively used in the telephone system.

Tone Generation Exercise

For this lab exercise, you are to use the 'C542 kits in the lab to generate the DTMF tone assigned to you [tone assignments] by implementing a difference equation of the form

y(n) = - a₁ y(n-1) - a₂ y(n-2) - a₃ y(n-3) - a₄ y(n-4)

with appropriate initial conditions, and using a single circular buffer of length 4.

The coefficients a₁, a₂, a₃ and a₄ may be obtained by taking the z-transforms of two sinusoids and adding the z-transforms. The initial conditions may be obtained by relating the one-sided z-transform of the difference equation above with the sum of the one-sided z-transforms of two distinct digital sinusoidal oscillators.

NOTE: The code in dly_ac01.asm in the delay demo apparently sets the analog interface to operate at 5787 Hz.

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