### 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''.

**Next Section:**

What is Noise?

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Generality of Maximum Likelihood Least Squares