Speech Separation Method Using Non-Negative Matrix Factorization with MATLAB Implementation

The speech separation method based on Non-negative Matrix Factorization (NMF) represents a fundamental signal processing technique in audio analysis. This approach decomposes complex mixed speech signals into their original source components by representing the audio signal as a product of non-negative matrices. NMF operates on the principle that speech spectrograms can be factorized into basis matrices (representing spectral patterns) and activation matrices (encoding temporal information), effectively separating overlapping voices. In MATLAB implementation, key functions include spectrogram computation using `spectrogram()` or `stft()` functions, NMF decomposition via custom algorithms or optimization toolboxes, and signal reconstruction through inverse transformations. The implementation typically involves: 1. Preprocessing: Framing and windowing the input signal using `buffer()` and window functions 2. Feature extraction: Computing magnitude spectrograms with overlap-add processing 3. NMF optimization: Applying multiplicative update rules or alternating least squares to factorize the spectrogram matrix V ≈ WH 4. Source separation: Masking and reconstructing individual sources using Wiener filtering or binary masking 5. Signal synthesis: Inverse STFT transformation with `istft()` for time-domain reconstruction This method finds extensive applications in speech processing domains including speaker separation, noise reduction, and audio source identification, leveraging MATLAB's comprehensive signal processing toolbox for efficient implementation of the entire separation pipeline.