Signal Time-Shifting Effects on DFT Spectra

Abstract

Accurate frequency estimation is crucial for researchers and engineers engaged in audio processing, communication, and vibration analysis. In the case of short signals containing low-frequency components and a non-integer number of periods, conventional frequency estimation algorithms, such as DFT, prove inadequate in precisely identifying signal frequencies due to inherent limitations in frequency resolution and the presence of the leakage phenomenon. Interpolation methods offer the potential to enhance frequency estimation by discerning frequencies at intermediate positions within the spectrum. Precisely determining amplitude values across spectral bins is critical when employing such methods. Remarkably, while the initial phase of a signal can significantly alter the spectrum, its influence on amplitude distribution remains an aspect yet to be thoroughly researched. In this study, we use Python to implement the DFT algorithm and analyze how the initial phase affects the results. We are conducting tests using generated sinusoidal signals and signals processed with Hamming and Hanning windowing functions to determine the extent of changes in amplitude. The findings indicate that a signal's time shift can influence the spectrum significantly, resulting in inaccurate frequency estimations and erroneous conclusions in signal analysis.