MATLAB Code Implementation of Original Spectral Subtraction Algorithm

In the field of signal processing, spectral subtraction is a widely used noise suppression technique extensively applied in speech enhancement, audio denoising, and related domains. The core concept involves analyzing the characteristics of the noise spectrum, subtracting the noise components from the spectrum of the noisy signal, thereby recovering a relatively clean signal.

Fundamental Principles: The implementation of spectral subtraction typically includes preprocessing operations such as signal framing, windowing, and Fourier Transform (FFT). Subsequently, statistical characteristics of the noise spectrum (such as mean or maximum values) are calculated, followed by subtraction operations in the magnitude or power domain of the signal spectrum. Finally, the time-domain signal is reconstructed through inverse transform (IFFT) and overlap-add (OLA) methods.

MATLAB Implementation Approach: Noise Estimation: Extract background noise spectral characteristics during the initial silent segment of the signal, typically calculating the average magnitude spectrum. In MATLAB, this can be implemented using `mean(abs(fft(noise_frame)))` across multiple noise frames. Spectral Processing: Perform FFT on noisy signal frames sequentially, adjusting the signal magnitude spectrum based on noise spectrum estimates. This can be optimized using parameters like over-subtraction factor and spectral floor to enhance subtraction robustness. Key functions include `fft()` for transformation and element-wise operations for spectral subtraction. Phase Preservation: Since human auditory perception is relatively insensitive to phase, the original signal's phase information is preserved directly while only modifying the magnitude spectrum. This is implemented by storing the phase angle using `angle(fft(signal_frame))` and reapplying it during reconstruction. Signal Reconstruction: Perform IFFT on the processed spectrum and synthesize the final denoised signal using the overlap-add method. MATLAB's `ifft()` function combined with proper windowing and frame overlapping (typically 50% overlap) completes this process.

Application Extensions: Improved algorithms can incorporate psychoacoustic models (such as Wiener filtering) to further enhance perceptual quality. Real-time processing requires balancing computational complexity and latency, which can be addressed using sliding windows or subband decomposition methods.

While spectral subtraction is simple and efficient, it may introduce "musical noise" artifacts in strongly non-stationary noise environments. Subsequent optimizations can be achieved through time-frequency masking or deep learning approaches. The MATLAB implementation should include parameters for adjusting subtraction aggressiveness and spectral floor values to minimize these artifacts.