DTMF Signal Decoding Program Using Goertzel Algorithm

In this documentation, we discuss the implementation of a program that utilizes the Goertzel algorithm to decode DTMF (Dual-Tone Multi-Frequency) signals. The Goertzel algorithm is a digital signal processing technique specifically designed for efficient frequency component detection, making it ideal for DTMF signal decoding applications. This algorithm works by analyzing input signals through selective frequency computation, identifying the specific frequency components present in DTMF signals that correspond to telephone keypad digits or characters. The program implementation involves three key stages: First, sampling the input audio signal at an appropriate rate (typically 8 kHz for telephone systems) to capture the DTMF tones. Second, applying the Goertzel algorithm to compute the energy at each of the eight fundamental DTMF frequencies (697 Hz, 770 Hz, 852 Hz, 941 Hz for low-group frequencies and 1209 Hz, 1336 Hz, 1477 Hz, 1633 Hz for high-group frequencies). The algorithm efficiently calculates the Discrete Fourier Transform (DFT) at specific frequency bins without computing the entire frequency spectrum, making it computationally optimal for this application. Key implementation details include: Pre-calculating the Goertzel coefficients for each target frequency, processing signal blocks through iterative filtering operations, and comparing the computed energy levels against predetermined thresholds to determine valid digit presence. The final stage involves mapping the detected frequency pairs to corresponding digital characters (0-9, *, #, A-D) and outputting the decoded results. This program provides a practical understanding of both the Goertzel algorithm's implementation and DTMF signal processing methodologies, demonstrating efficient real-time signal decoding capabilities with minimal computational resources.