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

Time-frequency analysis using Short-Time Fourier Transform (STFT) is a widely adopted method for analyzing non-stationary signals. The STFT algorithm decomposes signals into spectral components over short, overlapping time segments, enabling observation of temporal variations in frequency content. In practical implementation, the scipy.signal.stft() function in Python or spectrogram() in MATLAB can be applied with configurable parameters including window type, window size, and overlap percentage.

Adjusting the window size significantly affects the trade-off between time and frequency resolution - smaller windows (e.g., 256 samples) provide better temporal localization but poorer frequency resolution, while larger windows (e.g., 1024 samples) enhance frequency resolution at the cost of temporal precision. The spectrogram visualization typically uses color-mapped 2D plots where the x-axis represents time, y-axis frequency, and color intensity indicates magnitude. Through comparative analysis of spectrograms generated with different window sizes, engineers can comprehensively characterize a signal's joint time-frequency properties, with implementations often involving FFT-based computation within each windowed segment and subsequent magnitude squared calculation for power spectral density representation.

Key implementation considerations include selecting appropriate window functions (Hanning, Hamming, etc.), determining optimal overlap ratios (typically 50-75%), and managing computational efficiency through frame-based processing. The resulting spectrograms reveal transient features, modulation patterns, and non-stationary behaviors critical for applications in audio processing, vibration analysis, and communication systems.