Short-Time Fourier Transform and Its Inverse Transform
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The Short-Time Fourier Transform (STFT) is a time-frequency analysis method that enables frequency analysis of non-periodic signals. It decomposes signals into multiple sine and cosine functions to reveal their spectral composition. The inverse transform then reconstructs the original signal by combining these sinusoidal components. This method is computationally feasible and widely applied in signal processing applications.
Implementation typically involves dividing the signal into overlapping segments using a window function (e.g., Hamming or Hann window), applying Fourier transform to each segment, and creating a spectrogram representation. Key MATLAB functions include stft() for forward transformation and istft() for reconstruction. The algorithm maintains perfect reconstruction capability when proper window overlap and phase alignment are maintained.
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