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Dual-tone multi-frequency (DTMF) generation and detection based on Goertzel algorithm

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rymshasaeed/dtmf-decoder

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Dual-tone multi-frequency (DTMF) signals are used in touch-tone telephones and other industries including interactive power, telephone banking, and pager systems. Due to its strong anti-noise and anti-attenuation performance as well as ease of implementation, it is a frequently utilized approach in the transmission of medium and low-speed data. A DTMF codec consists of an encoder that converts keystrokes or digits data into dual tone signals, as well as a decoder that detects the presence and content of incoming DTMF tones.

A DTMF signal is made up of two sinusoidal tones. Their frequencies are set such that harmonics are avoided. To put it another way, there are no multiples of a particular frequency, no sum of two frequencies, and no difference of two frequencies that equals another. This enables for reliable long-distance communication. The transmitted signal is thus analogous to equation below.

x(t) = sin⁡(2πfLt) + sin(2πfHt)

The first sinusoidal tone is chosen from a set of low-frequency tones that comprise 697 Hz, 770 Hz, 852 Hz, and 941 Hz. While the second one is selected from a set of high frequency group: 1209 Hz, 1336 Hz, 1477 Hz, and 1633 Hz. By combining two sinusoidal tones with four frequencies from each group, a total of 16 permutations representing ten decimal digits (0-9) are obtained, four alphabets (A,B,C,D) and two special characters (*,#).

Decoder Design

The repository presents a DTMF-tones generator and DTMF-keys decoder. Two design approaches have been followed: i) via a straightforwardMATLAB program, ii) via aMATLAB GUI. The workflow of the GUI design approach is shown in Figure 1.

workflow
Figure 1: Design Workflow

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gui
Figure 2: Touch tones generation and detection

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