MATLAB Implementation of Short-Time Fourier Transform using Rectangular Window

The rectangular window function, also known as a boxcar window, is a fundamental window function commonly used in digital signal processing. Its distinctive characteristic is that signal values within the window remain constant (typically unity), while values outside the window are set to zero. The rectangular window finds extensive applications in spectral analysis, filter design, and time-frequency signal processing. By adjusting the width of the rectangular window, different degrees of weighting can be applied to signals in both time and frequency domains, enabling effective signal processing and analysis. In MATLAB implementation, the rectangular window can be generated using the built-in `rectwin` function or by manually creating a vector of ones with specified length. The basic syntax is `w = rectwin(N)` where N represents the window length. For signal processing applications, the rectangular window is particularly useful in Short-Time Fourier Transform (STFT) implementations where it provides uniform weighting across the analysis window without any tapering effects. Key implementation considerations include: - Window length selection impacts frequency resolution and spectral leakage - The rectangular window maintains original signal amplitude within the windowed region - When applied in STFT, it preserves temporal resolution but may introduce spectral leakage artifacts - MATLAB's signal processing toolbox provides optimized functions for window-based operations The rectangular window serves as the simplest window function and forms the basis for understanding more complex windowing techniques in digital signal processing.