What are window functions and why are they used?

Window functions taper signal at edges before DFT to reduce spectral leakage from finite-length analysis. Without windowing (rectangular window), sharp truncation causes sinc-like spectral spreading. Common windows: Hanning, Hamming (low sidelobes, moderate mainlobe), Blackman (very low sidelobes, wide mainlobe), and Kaiser (adjustable parameters). Trade-off: wider mainlobe (reduced frequency resolution) for lower sidelobes (reduced leakage). Also used in FIR filter design (window method) to truncate ideal infinite impulse response. Window selection depends on application requirements.