Dual-Tone Multi-Frequency (DTMF)

DTMF projects using DFT and Goertzel algorithm based implementations developed in MATLAB
DTMF tone - A signal representing a digit, consisting the sum of two sinusoids or tones with frequencies from two exclusive groups (low and high group frequency)
DTFT tones for Digits 0-9 are sampled at F_s = 8192 Hz

A DTMF signal is expressed as $d_N[n] = sin(2 \times \pi \times \frac {f_{L}}{F_s} \times n) + sin(2 \times \pi \times \frac {f_{H}}{F_s} \times n)$ in Hz.

DFT Based Implementation

MATLAB codes: dtmf_a.m, dtmf_f.m, dtmf_g.m, dtmf_h.m, dtmf_h.m, & dtmf_i.m

A: DTMF tones corresponding to Digits 0-9 using the MATLAB function sound
- Matrix stores each DTMF tone as a pair of frequencies defined as $[f_L, f_H]$
F: Index $k$ for DTMF digits by computing 2048 samples of $X(e^{j\omega})$ using the MATLAB function fft
G: Energy spectrum of DTMF for Digit 8 by computing $|D_8(e^{j\omega_k})|^2$ using the MATLAB function fft
- Tabulated magnitude & energy and plotted energy spectrum for Digits 0-9
H & I: Decoding touch-tone signals to phone numbers
- ttdecode - Fixed length of 1000 samples for digits and 100 samples for silence
- ttdecode2 - Varying length digits and silence
  - MATLAB code loads touch.mat to decode two input signals stored as vectors named hardx1 and hardx2

MATLAB code: dtmf_goertzel_alg.m

DFT magnitude and energy spectrum of DTMF for Digit 8 by computing $|D_8[k]|$ and $|D_8[k]|^2$ using the MATLAB function goertzel
- Tabulated DFT magnitude & energy and plots for Digits 0-9