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What is the difference between Magnitude spectral subtraction and Power spectral subtraction in terms of performance?

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If by "performance" you mean the quality of the processed (speech) signal, then this question cannot be answered. The reason is that the quality of the output of a spectral subtraction algorithm depends on so many factors, and the precise subtraction rule is just one detail. What is much more important is the noise estimation algorithm, certain smoothing operations, etc.

What you can say is that the dynamic range of algorithms working with magnitudes is much smaller than when powers are used. This can be a great advantage when such systems need to be implemented in fixed-point arithmetic.

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