Short-Time Fourier Transform for Speech Signals

The following code implements Short-Time Fourier Transform (STFT) for speech signal analysis. This algorithm converts time-domain signals into frequency-domain representations through spectral analysis. The core implementation involves treating each time segment as independent by applying a sliding window function (commonly Hamming or Hanning windows) to divide the signal into overlapping frames. Each frame is then transformed to the frequency domain using Fast Fourier Transform (FFT), calculating signal energy distribution across frequencies. Key implementation aspects include proper window size selection, overlap ratio configuration, and power spectrum computation. The final output generates time-frequency spectrograms showing spectral representations at each time instant. This transformation is fundamental in speech processing applications such as speech recognition and synthesis, enabling extraction of frequency-specific features like formants and pitch information through matrix operations and magnitude spectrum calculations.