Short-Time Fourier Transform

In time-domain signal analysis, we can employ the Short-Time Fourier Transform (STFT) for spectral examination. STFT is a method that divides a signal into short, overlapping segments and applies Fourier transform to each segment to track frequency content evolution over time. To implement STFT, we first sample 1000 data points from the original signal. A key preprocessing step involves applying window functions (e.g., Hamming or Hanning windows) to minimize spectral leakage by reducing edge discontinuities in each segment. The STFT algorithm typically uses overlapping frames with 50-75% overlap and window sizes balancing time-frequency resolution. After computing the STFT, the results can be visualized through two primary methods: 3D spectrograms (plotting magnitude versus time and frequency axes) and contour plots (displaying iso-magnitude lines on time-frequency planes). These visualizations help intuitively analyze time-varying spectral characteristics, with implementations possible using MATLAB's spectrogram function or Python's librosa.stft with matplotlib visualization tools. The 3D plot displays signal energy distribution across time-frequency coordinates, while contour maps highlight specific frequency components' intensity transitions, both crucial for non-stationary signal analysis in audio processing or vibration monitoring applications.