DTMF Signal Detection and Parameter Optimization Based on Goertzel Algorithm

Abstract

In recent years, Dual-Tone Multi-Frequency (DTMF) signaling has become a cornerstone technology in a wide array of communication systems and interactive services, including telephone banking, vehicle navigation terminals, voicemail systems, and automated teller machines (ATMs). The integrity of these services is critically dependent on the reliable transmission and accurate demodulation of DTMF signals to retrieve the encoded digital commands. Consequently, the development of robust and efficient DTMF detection methodologies is of paramount importance. While the Fast Fourier Transform (FFT) is a common choice for spectral analysis, the Goertzel algorithm presents a superior alternative for DTMF detection due to its exceptional computational efficiency and high frequency resolution, particularly when only a small number of specific frequency components need to be identified. This algorithm is exceptionally well-suited for extracting the precise low and high-frequency group tones that constitute a DTMF symbol, thereby achieving the goal of accurate digit identification. This paper conducts a comprehensive study and implementation of the Goertzel algorithm for this specific application. A central focus of our investigation is the critical selection of key parameters that govern detection performance, most notably the number of sampling points (N), which directly impacts frequency resolution, computational load, and detection speed. We provide a rigorous, step-by-step elucidation of the complete DTMF detection process, from signal acquisition to decision logic. Furthermore, the paper presents a detailed analysis and discussion on strategies to optimize the algorithm's efficiency without compromising accuracy. The theoretical framework and performance claims are validated through extensive MATLAB simulations. These simulations demonstrate the algorithm's efficacy in correctly decoding DTMF digits under various conditions, confirming its practical utility as a highly efficient solution for embedded and real-time telecommunication systems.