Short-Time Fourier Transform (STFT) - Algorithm Implementation and Applications

The Short-Time Fourier Transform (STFT) is a fundamental signal processing technique used for analyzing the time-frequency characteristics of non-stationary signals. Unlike traditional Fourier Transform, STFT divides the signal into short, overlapping window segments and applies Fourier Transform to each segment, thereby obtaining a joint time-frequency distribution of the signal. The key advantage of this method lies in its ability to clearly visualize how frequency components evolve over time.

STFT implementation typically involves these critical steps: First, selecting an appropriate window function (such as Hanning window or rectangular window) to segment the signal; second, applying Fast Fourier Transform (FFT) to each signal segment; finally, arranging the results chronologically to form a spectrogram. The window length and overlap ratio are crucial parameters affecting STFT resolution, requiring a trade-off between temporal and frequency resolution. In code implementation, this can be achieved using functions like scipy.signal.stft in Python or spectrogram in MATLAB, where window size and overlap parameters directly control the resolution characteristics.

The Short-Time Fourier Transform finds extensive applications in speech recognition, music analysis, vibration signal processing, and other domains. The spectrogram obtained through STFT provides intuitive visualization of transient signal characteristics, serving as a vital foundation for subsequent feature extraction or pattern recognition tasks. Common implementation approaches include using overlapping window techniques with optimized FFT computations to balance computational efficiency and analytical precision.