Frequency Domain Processing of Speech Signals

Frequency domain processing of speech signals acknowledges that speech is a time-varying, non-stationary stochastic process. However, over short durations, it can be approximated as stationary. Thus, speech enhancement can be achieved by estimating the short-time spectrum of "clean" speech from the noisy speech spectrum. Since noise is also a random process, this estimation must be based on statistical models. These enhancement algorithms primarily target short-time spectral magnitude estimation, exploiting human auditory perception's insensitivity to phase in speech spectral components. In implementation, this typically involves windowing the signal (e.g., using Hamming windows) and applying Fourier transforms to analyze frequency content.

The objective of speech enhancement is to improve speech signal quality and intelligibility. By analyzing frequency domain characteristics, we can process speech signals effectively. Although speech is time-varying and non-stationary, its short-term stationarity allows us to estimate clean speech spectra from noisy counterparts. Code implementations often involve overlapping windowed segments, FFT analysis, and spectral subtraction or Wiener filtering techniques for noise reduction.

As noise is stochastic, estimation must rely on statistical models. These algorithms focus on spectral magnitude estimation, utilizing phase insensitivity in human auditory perception. Key algorithmic approaches include spectral subtraction where noise statistics are subtracted from the magnitude spectrum, and MMSE-based estimators that minimize mean-square error in spectral domain.

Applying these speech enhancement algorithms significantly improves speech quality and provides clearer auditory experiences. Practical implementations typically include steps like voice activity detection (VAD) for noise estimation, real-time processing capabilities using frame-based analysis, and perceptual weighting to match human hearing sensitivity.