DTMF (Dual-Tone Multi-Frequency) Signal Implementation and Analysis

DTMF (Dual-Tone Multi-Frequency) is an encoding technique that employs specific pairs of audio frequency tones to represent digit signals. In this method, two distinct frequencies are combined, with different frequency pairs corresponding to different numbers or functional commands. Specifically, the system uses 8 predefined frequencies to encode 16 telephone keypad buttons, including 10 numeric digits (0-9) and 6 function keys (*, #, A, B, C, D). The standard frequency combinations can be referenced from technical documentation. Implementation requires completing three main tasks: (1) Generating corresponding DTMF signals in MATLAB based on keyboard input symbols, involving tone pair synthesis using sine wave generation functions like sin() with proper sampling rates and duration parameters; (2) Performing spectral analysis using both FFT (Fast Fourier Transform) algorithm via MATLAB's fft() function and Goertzel algorithm implementation for efficient single-frequency detection, followed by spectral plotting using plot() or stem() functions to visualize frequency components; (3) Implementing symbol verification by analyzing spectral peaks to identify the two dominant frequencies and mapping them back to the original input symbol using a DTMF frequency lookup table, ensuring decoding accuracy through threshold-based peak detection algorithms.