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Are the rolloffs in filters always (log) linear? Are there cases where it nees a steeper growth/decay?

Very commonly, filters will show power-law frequency response ( $\propto \omega^n$) over particular frequency regimes. This looks like a straight line on a log-log plot.

These are approximations--they are not usually exact power laws. In particular, the transitions between the regimes tends to be smooth rather than abrupt ``knees''. We'll see a bunch of examples.

In general frequency response can be anything, though, and not necessarily a power law.

Kate Scholberg 2017-02-13