MATLAB Code Implementation of STFT-Related Functions

The Short-Time Fourier Transform (STFT) is a fundamental time-frequency analysis tool particularly suitable for processing non-stationary signals. Implementing STFT-related functions in MATLAB requires addressing core components including frame segmentation, windowing, and Fourier transformation. Implementation Approach Frame Segmentation: Divide the signal into short-time overlapping frames where frame length and overlap ratio critically impact time-frequency resolution. In MATLAB, this can be implemented using buffer() function with specified overlap samples. Windowing Function: Apply window functions (e.g., Hamming window) to each frame using MATLAB's hamming() function to reduce spectral leakage caused by signal truncation. Fourier Transform: Perform FFT on each frame via fft() function, converting time-domain signals to frequency components with proper zero-padding for frequency interpolation. Result Integration: Arrange spectral results chronologically using matrix operations to form a time-frequency spectrogram, typically visualized through imagesc() or spectrogram() functions. Key Parameter Design Window Length: Determines frequency resolution - longer windows enhance frequency resolution but reduce time localization. Typical implementation involves fs/20 to fs/5 samples for audio signals. Overlap Points: Balances computational efficiency and temporal continuity, commonly set at 50%-75% of window length using floor() and ceil() functions for sample alignment. Window Selection: Hamming, Hanning windows (available through hann() function) mitigate edge effects from signal truncation with trade-offs between main lobe width and side lobe attenuation. Application Scenarios Speech signal analysis (e.g., pitch tracking through peak detection in spectrograms) Mechanical vibration fault detection (bearing defect frequency identification) Audio feature extraction (MFCC preprocessing using logarithmic frequency bins) Extension Directions Inverse STFT (ISTFT) for signal reconstruction via overlap-add method with phase synchronization Time-varying filtering combined with STFT magnitude modification for frequency enhancement Multi-resolution STFT implementing adaptive window lengths based on signal characteristics Through appropriate parameter tuning, STFT can flexibly adapt to diverse signal analysis requirements in time-frequency characterization. MATLAB's Signal Processing Toolbox provides optimized functions like spectrogram() for rapid implementation while custom code allows specific algorithm modifications.