A Musical Time-Varying Filter Example
Note, however, that a gain may vary with time independently
of
to yield a linear time-varying filter. In this case,
linearity may be demonstrated by verifying
![$\displaystyle g(n) \left[ \alpha \cdot x_1(n) + \beta \cdot x_2(n)\right]
= \alpha \cdot [g(n)\cdot x_1(n)] + \beta\cdot[g(n)\cdot x_2(n)]
$](http://www.dsprelated.com/josimages_new/filters/img495.png)

![$ g(n) = 1
+ \cos[2\pi (4)nT]$](http://www.dsprelated.com/josimages_new/filters/img497.png)
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Nonlinear Filter Example: Dynamic Range Compression