23 Dec
2012
23 Dec
'12
11:01 p.m.
Filters that sharp ring unavoidably. You can sine
wave
sweep them and they look great, feed then a 2 kilohertz square wave with
microsecond rise & fall times and go surfing on the edge ripples.
Gibbs effect ripples aren't a filter artifact. They're a feature of
any bandlimited signal.
Using a less-sharp filter does not eliminate or mitigate the effect,
it simply changes the appearance. It's no different from a little kid
spreading his peas all over his plate so that it looks like there's
less there and he's eaten some.
Spreading the transition band over more space to make it less
noticeable is a) irrelevant once the transition band is above the
hearing range and b) has nothing directly to do with the ripples.
Ringing from an IIR filter with significant internal energy storage
also happens, but that's a different phenomenon.
Monty