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Dennis,
> The time domain response actually looks similar to a Cauer elliptical
> filter, the way it rolls off steeply and then goes fairly flat with some
> ripple in the stopband. I've never tried coding a Cauer in TS but I've
> seen them used in speaker crossovers. Conceptually, it would be a 4-pole
> IIR filter with a notch filter about an octave above Fc. In a passive
> crossover, it's just one extra cap in parallel with the second coil to
> create the notch.
Interesting... It's an elliptical filter, which means it would have ripple
in both the passband and stopband. My _SMA3 doesn't ripple in the
passband, but it's likely not as "brick-wall"-ish as this Cauer filter.
Also, I know that Cauer filters don't have good phase linearity, which
implies (I'm guessing) that they might overshoot some signals.
At first glance, this might be tough to implement. I know enough that an
RC lowpass filter is identical to an exponential moving average (actually
any RC filter can be implemented as a pile of EMAs). I know the time
constant of an RC filter is RC, the time constant of an RL filter is L/R,
but what's the time constant for an LC filter having no R? sqrt(LC)?
This Cauer filter also has 5 degrees of freedom (3 caps and 2 coils) to
adjust. It would take a lot of fiddling to get it working right.
All I did with _SMA3, I just tuned the natural notches in three simple
moving averages so that the sidelobes canceled out. I thought of this
while falling asleep last night, and when I tried it today, I was
surprised how well it worked. The most recent code I posted executes very
fast, too.
Trouble is, my _SMA3 is an FIR filter. Doing something similar with an
IIR filter would be nice, because I have another application that requires
using the previous value as an input. I'm pretty close to coming up with
something that behaves like Jurik's JMA -- I can already reproduce his
older version, Jurik's AMA, exactly. Jurik's AMA has a lot of overshoot
compared to JMA, though.
I'll think about it a bit.
-Alex
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