Short-Time Fourier Transform (STFT)

This document discusses the implementation of time-frequency analysis using the Short-Time Fourier Transform (STFT) method. STFT operates by applying Fourier transform to windowed segments of a signal, effectively capturing both temporal and frequency characteristics - commonly implemented in Python using libraries like Librosa with functions such as stft() that require parameters like window size and hop length. While STFT provides effective time-frequency analysis, several related techniques expand signal processing capabilities: Continuous Wavelet Transform (CWT) offers multi-resolution analysis through scalable wavelets, Discrete Wavelet Transform (DWT) enables efficient signal decomposition using filter banks, and standard Fourier Transform delivers pure frequency-domain representation. These methods can be optimized for specific applications through parameter adjustments (e.g., window types for STFT, wavelet selection for CWT) and algorithmic improvements like overlap-add processing. For practical implementation, Python's SciPy offers signal.stft for basic STFT calculations, while MATLAB's spectrogram function provides integrated visualization. Interested practitioners should explore these complementary techniques to enhance signal analysis applications, considering factors like temporal resolution trade-offs and computational efficiency when selecting appropriate methods.