Simple Demonstrations of Short-Time Fourier Transform

This document presents fundamental demonstrations of the Short-Time Fourier Transform (STFT). We examine two window functions: the rectangular window and the Gaussian window. The rectangular window represents a straightforward windowing approach where signal amplitudes within the window remain unchanged (amplitude = 1) while amplitudes outside the window are zeroed out. This can be implemented in code using simple array slicing operations. In contrast, the Gaussian window utilizes a more sophisticated approach by applying a Gaussian distribution shape to the signal segment, which better preserves frequency characteristics through reduced spectral leakage. The Gaussian window implementation typically involves generating a Gaussian curve using mathematical functions like exp() with appropriate standard deviation parameters. We conduct comparative analysis of both window functions, evaluating their respective advantages and limitations across different signal processing scenarios. The demonstrations include code snippets showing window function generation and STFT computation using overlapping window segments. Through these practical examples, we aim to provide readers with deeper understanding of STFT principles and their real-world applications in time-frequency analysis.