Time-Frequency Analysis of Signals Using Short-Time Fourier Transform

Time-frequency analysis of signals based on the Short-Time Fourier Transform (STFT) facilitates the creation of three-dimensional waterfall plots. In implementation, the STFT algorithm typically involves segmenting the signal using a sliding window function (e.g., Hamming or Hann window), computing the Fourier Transform for each windowed segment, and assembling the results into a time-frequency matrix. The visualization process maps this matrix to a 3D plot where the x-axis represents time, y-axis frequency, and z-axis magnitude, creating a waterfall-like representation. This methodology provides intuitive insights into how signal energy distributes across time and frequency domains, supporting deeper understanding of time-frequency characteristics. Such analysis proves valuable for research and applications in fields like audio processing, vibration analysis, and biomedical signal processing where joint time-frequency behavior is critical. Code implementation often involves functions like spectrogram in MATLAB or stft in Python's librosa library, with customizable parameters for window size, overlap, and frequency resolution.