# How to get the amplitude output of a single frequency from a Resonant Bandpass? (ie. Using a reso BP as an envelope…)

A resonant bandpass like this:

is resonating at a frequency of 125 Hz. You are controlling the decay time by modulating $$Q$$ accordingly. The BP is being excited by a MIDI triggered impulse.

At its resonant frequency it will decay at a natural rate of $$y= c^{-x}$$, i.e. it will give a nice exponential decay.

Is there any way to get the output level of the bandpass at its resonant frequency (125 Hz)?

If it is possible to get the output/amplitude level at this specified frequency, one could use the bandpass as a synth envelope.

This might be a bit computationally expensive, but resonant BPs have some unique properties that might be fun to exploit if this is possible. I'd at least like to see what I could get out of it.

For reference, the resonant BP filter I'm using in my projects is the one here:

From The Art of VA Filter Design by Vadim Zavalishin, TPT State Variable Filter: TPT -> Topology Preserving Transform

This filter is based off of the trapezoidal integrator, which produces a bilinear transformation. This filter does the proper cutoff prewarping needed for the TPT structure, as explained by Zavalishin. It also handles the problem of delayless feedback loops that the trapezoidal integrators introduce.

• It sounds a bit a like a second-order generalized integrator with a trapezoidal integrator... – Ben May 3 at 21:35