MATLAB Implementation of DTMF Signal Generation and Detection

DTMF (Dual-Tone Multi-Frequency) is a signal encoding technique commonly used in telephone dialing, which represents digits or symbols by superimposing two sinusoidal waves of different frequencies. Implementing DTMF signal generation and detection in MATLAB helps beginners understand fundamental concepts of signal processing through practical code examples.

### Theoretical Analysis DTMF encoding employs a 4x4 frequency matrix combining low-frequency group (697Hz, 770Hz, 852Hz, 941Hz) and high-frequency group (1209Hz, 1336Hz, 1477Hz, 1633Hz) to generate specific signals. For example, digit "1" is synthesized from 697Hz and 1209Hz frequencies. Signal detection typically uses the Goertzel algorithm, which calculates energy at specific frequencies to identify key presses more efficiently than full FFT for targeted frequency analysis.

### Implementation Approach Signal Generation: Use MATLAB's `sin()` function to synthesize two sinusoidal waves with specified frequencies, adjusting sampling rate (fs) and duration parameters. Example code: `tone1 = sin(2*pi*f1*t); tone2 = sin(2*pi*f2*t);` Signal Superposition: Add the two frequency signals using vector addition: `dtmf_signal = tone1 + tone2;` to form the complete DTMF waveform. Detection Analysis: Implement Goertzel algorithm through DFT computation at specific bins or use FFT (`fft() function`) for spectral analysis to identify frequency components. Key Mapping: Create a frequency-pair lookup table to map detected frequencies to corresponding digits or symbols using logical comparisons.

### Beginner-Friendly Enhancements Visualization: Plot time-domain waveforms using `plot()` and frequency spectra using `spectrogram()` or `pwelch()` for intuitive signal composition understanding. Adjustable Parameters: Implement GUI sliders or input parameters for modifying frequencies, sampling rates, and durations to observe signal variations dynamically. Noise Simulation: Add Gaussian white noise using `awgn()` function to analyze system robustness and anti-interference capabilities under realistic conditions.

This implementation serves as an introductory experiment for communication systems or digital signal processing courses, facilitating understanding of frequency domain analysis and practical applications through hands-on MATLAB coding.