Short-Time Fourier Transform (STFT) Example Implementation

In this example, I will demonstrate the application of Short-Time Fourier Transform (STFT) using a practical implementation scenario. Consider an audio file with a duration of 1000 units and a sampling rate of 250 Hz. The Short-Time Fourier Transform (STFT) is a fundamental signal processing technique that decomposes a signal into its frequency components while maintaining temporal localization. This implementation typically involves dividing the signal into overlapping windows using functions like hamming or hanning, then applying Fast Fourier Transform (FFT) to each window segment. In this specific case, we can utilize STFT to analyze frequency variations across different time segments of the audio signal. The algorithm workflow involves: 1) framing the signal into short overlapping segments, 2) applying a window function to reduce spectral leakage, 3) computing FFT for each windowed frame, and 4) generating a spectrogram for visualization. Key parameters like window size, overlap percentage, and FFT length significantly impact the time-frequency resolution trade-off. STFT serves as an essential tool for gaining deep insights into signal frequency characteristics, particularly useful for non-stationary signals where frequency content evolves over time. The repeated emphasis on Short-Time Fourier Transform (STFT) throughout this text underscores its central role in this demonstration, reinforcing readers' understanding of this critical spectral analysis methodology through consistent contextual repetition.