Implementing classical transforms for audio signal processing on ESP32

Abstract

This study focuses on the practical implementation of classical digital signal processing techniques, specifically the Fast Fourier Transform (FFT) and the Z-transform, on the ESP32 microcontroller, an inexpensive and versatile hardware. Through the Arduino IDE environment, recurring examples of spectral analysis, frequency filtering, and manipulation of synthetic audio signals are demonstrated. The main objective is to illustrate how these tools enable the identification of spectral components, the removal of unwanted frequencies, and the reconstruction of signals in real time. The methodology combines a detailed theoretical review of these mathematical tools with their application in concrete examples employing synthetic signals. The research highlights how the FFT enables fast and accurate spectral analysis, facilitating tasks such as filtering and the removal of unwanted components in the frequency domain. Furthermore, the Z-transform offers a comprehensive approach for the analysis and design of digital systems, enabling the manipulation and stability of signals through the manipulation of poles and zeros. The results, presented through visual simulations, demonstrate the usefulness of these techniques in reconstructing and filtering audio signals in real time in low-cost embedded systems. The integration of these transformations into platforms such as the ESP32 constitutes an educational and practical resource for students and developers, promoting learning and innovation in digital audio processing in educational applications and prototypes.