Enhancing time-frequency signal analysis: integrating windowing with the fractional fourier transform for modern applications

Abstract

Applications based on sensor data collection, such as respiration and heartbeat monitoring, rely on accurate frequency-domain analysis. Fields such as digital communication and pattern recognition also rely on spectral analysis of sensor-derived data, often leveraging the Fourier Transform (FT) as a key tool. However, FT presents drawbacks, such as spectral leakage, which can be partially mitigated by applying window functions. For critical applications, though, window functions alone may not be enough for optimal performance. Recent studies have explored combining window functions with the Fractional Fourier Transform (FrFT) to enhance results, though success depends on the chosen window function. Among existing options, Nuttall windows offer high attenuation of side lobes, reducing spectral leakage but also presenting a wide main lobe, leading to signal distortion. In this article, we propose a new mathematical model combining Nuttall windows with FrFT. This model provides a closed-form expression, utilizing a parameter to control the main lobe width while maintaining reduced side lobe size, thereby enhancing adaptability for various sensor-based applications. Results show that adjusting the main lobe width using the FrFT expands Nuttall windows’ applications, such as in spectral analysis of respiratory signals, where it improves frequency recognition, as well as in Filtered-OFDM to address Out-of-Band Emission, offering an effective solution to one of the major challenges in ensuring spectral efficiency.