>> The real part may be used as a resonant
>> bandpass filter and the imaginary as a
>> resonant low-pass filter, but they can be
>> combined to make other possibilities."
> what sort of possibilities???
I wouldn't expect much about this. I guess it's like any other filters that can be combined in many ways.
Another thing I wanted to inquire is about bp~ having a frequency response that is not symmetric. The lower part of the spectrum has more energy. Could one consider it more of a "resonant low-pass filter", similar to [vcf~]'s second outlet?
By the way, while we're at it, I'd like to share something that may not be too important, but it's related. I was able to implement [cpole~] in [fexpr~]. Here it goes:
expr 1:
[fexpr~ $x1 + ($x3 * $y1) - ($x4 * $y2);
$x2 + ($x4 * $y1) + ($x3 * $y2)]
if we consider $x3 and $x4 as variables named, respectively, coefr (coeficient for the real part) and coefi (coeficient for the imaginary part), we then have:
expr 2:
[fexpr~ $x1 + (coefr * $y1) - (coefi * $y2);
$x2 + (coefi * $y1) + (coefr * $y2)]
Now, by checking the code of [vcf~] I was able to narrow down to its core formula, which is something like this
expr 3:
ampcorrect * oneminusr * f1 + (coefr * re2) - (coefi * im);
(coefi * re2) + (coefr * im)
the bolded letters in "expr 3" seem to match perfectly to "expr 2". The differences are underlined ($x2 in expr 2 and ampcorrect/oneminusr in expr 3).
That gets me closer to being able to implement [vcf~] with a [cpole~] I guess, but I find it weird that the imaginary output does not have the $x2 signal input to be added to the rest of the expression. I worry that actually prevents it from being successfully implemented with [cpole~]. Am I missing something?
Anyway, the thing is that I'm still really curious to learn wether vcf~ is a "two pole" filter or a "one complex pole" filter, and the reason behind it is because I believe we could make a biquad~ version of [vcf~] (at least for its real output). That's the bottom line.
cheers