### Why Analyze Noise?

An example application of noise spectral analysis is denoising, in which noise is to be removed from some recording. On magnetic tape, for example, ``tape hiss'' is well modeled mathematically as a noise process. If we know the noise level in each frequency band (its power level), we can construct time-varying band gains to suppress the noise when it is audible. That is, the gain in each band is close to 1 when the music is louder than the noise, and close to 0 when the noise is louder than the music. Since tape hiss is well modeled as stationary (constant in nature over time), we can estimate the noise level during periods of ``silence'' on the tape.

Another application of noise spectral analysis is spectral modeling synthesis (the subject of §10.4). In this sound modeling technique, sinusoidal peaks are measured and removed from each frame of a short-time Fourier transform (sequence of FFTs over time). The remaining signal energy, whatever it may be, is defined as ``noise'' and resynthesized using white noise through a filter determined by the upper spectral envelope of the ``noise floor''.

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What is Noise?
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Generality of Maximum Likelihood Least Squares