Explain the Short-Time Fourier Transform and spectrogram.

STFT analyzes how frequency content changes over time by computing DFT of successive windowed segments: X(m,k) = sum(x[n]*w[n-m]*e^(-j2*pi*k*n/N)). Parameters: window length (frequency resolution), hop size (time resolution), and window type. Spectrogram displays |STFT|^2 as time-frequency image. Trade-off: longer window = better frequency resolution, worse time resolution (uncertainty principle). Applications: Speech analysis, music processing, biomedical signals, and vibration analysis. Variants: reassigned spectrogram (sharper localization), multi-resolution STFT.