Common Window Functions and Their Characteristics

This text introduces several common window functions along with their corresponding time-domain waveforms and frequency-domain responses. For readers unfamiliar with signal processing fundamentals, these terms may require clarification. We therefore provide a brief overview of core signal processing concepts. Signal processing encompasses techniques for manipulating digital signals to extract meaningful information from input data. The time domain represents signals as functions of time, while the frequency domain characterizes signals through their frequency components. Window functions serve as essential signal processing tools that mitigate spectral leakage and enhance frequency resolution by applying weighting coefficients to signal segments. Understanding window functions' fundamental properties and their dual-domain representations constitutes a critical step in mastering signal processing techniques.

From an implementation perspective, window functions are typically applied using mathematical expressions that define their shape. Common examples include rectangular, Hanning, Hamming, and Blackman windows, each with distinct spectral characteristics. In MATLAB, window functions can be implemented using built-in functions like hann(), hamming(), and blackman(), or by defining custom window expressions. The choice of window involves trade-offs between main lobe width and side lobe attenuation, which directly impacts frequency resolution and spectral leakage suppression in Fourier analysis.