Early in the pandemic I learned that I could ping a filter, record its impulse response, and convolve another signal with that impulse response to approximate that filter, admittedly in the most inflexible, CPU-hogging, and memory-wasting way. But hey--it was exciting to learn that it was possible!

Is it possible to go the other way, from an impulse response to the parameters for some arrangement of low pass/hi pass/band pass filters? Not for an arbitrary impulse response, but for decaying resonances, like the sound of a tap on the bottom of a plastic cup? The solution doesn't have to be exact, analytic, in real-time, or completely automated, nor does it have to use Pd exclusively. I just want to find a way to model these sounds other than using my ear + trial and error.

Edit: I just tried this--in Reaper, I recorded plastic cup tap, convolved it with white noise, listened and looked at its spectrum. On another track, I tried to match the sound and spectrum using the same white noise through 5 bands of parametric EQ and got closer than I thought I would. I then tried to port that parametric to Pd and pinged it. It only slightly resembles the original cup, but my port of that filter could be junk.

Edit 2: my port IS junk! I just made Pd ping the Reaper EQ and it sounds much closer!

Edit 3: but I still welcome any suggestions on how to do this better. I see that there is an FIR filter in Reaper that allows me to enter an arbitrary frequency response, but I can't alter that response dynamically so it defeats the purpose.

@jameslo I don't have an answer to the main question. I suspect it would be tricky, since the most common filters are second-order IIRs, while sampling an impulse response is a high-order FIR.

The Dodge/Jerse Computer Music book discusses sampled frequency responses. Effectively, if you plot out a desired gain per bin and do an inverse cosine transform on it, then you get an impulse response. For an FIR, the impulse response is the same as the coefficients. But it may be more efficient to resample the frequency response -- keep it in the frequency domain and do FFT multiplication. I guess it depends on how many bins you have. 30-50 bins, maybe brute force multiply-add might be faster? (At least in SC, Nick Collins' LTI Linear Time-Invariant unit might be faster for relatively short kernels.) A thousand bins, definitely FFT would be faster.

I should check the book, see if they have any ideas about estimating filter parameters from a sampled frequency response. But I don't recall that they take it in that direction.

A fun observation here is -- since you can do filtering by convolution, and you can also do reverb by convolution, then reverb is a special case of filtering. I'm overstating for dramatic effect, but... a typical filter's frequency response is smooth and predictable while a reverb's frequency response is irregular and noisy, even with the same mathematical process.

hjh

Just guessing here: Convolution backwards is deconvolution, isn't it?

For 'finding the FIR' I was lucky with the library called
adaptive
from Deken.

... but the whole topic of resynthesis is very broad and diverse, - plus a filter could be virtually anything.
The approach of matching resonant peaks calls for a vocoder!?

sure, if you know the exact formula which was used to construct the FIR, you can reverse the process.

not for "plastic cup".

Another technique is Linear Predictive Coding, which essentially builds a higher order filter for a frame of arbitrary input audio. It won't reproduce the audio exactly but you can get a lot of characteristics of the original audio, applied to a different signal.

hjh

@jameslo Not my subject..... and no idea if it is useful..... but I throw it into your thread anyway as it details a method (I think) for what you are aiming for..... and I know that you know how to logically construct a patch from a method.
David.

@ddw_music said:

estimating filter parameters from a sampled frequency response

That's probably how I should have asked my question because that's really the issue. It's easy enough to get the freq response of a filter characterized by an impulse response, so the convolution stuff I mentioned is just a distraction (i.e. an old guy telling war stories ).

@lacuna said:

Just guessing here: Convolution backwards is deconvolution, isn't it?
... but the whole topic of resynthesis is very broad and diverse, - plus a filter could be virtually anything.

It's not convolution that I want to invert (see comment above about distraction ). But you're right to point out how amorphous my question is. I thought maybe the kind of sound I'm interested in is so constrained that filter model would be simple (e.g. just a bunch of [vcf~]s in a row).

@ddw_music said:

Another technique is Linear Predictive Coding

Is there a tool you would recommend?

@whale-av Again, convolution is probably a red herring. I don't recall ever getting [partconv~] (bsaylor) to work but I've definitely rolled my own convolution using a delay line and a clone for every sample in one of the vectors (!). Optimization is the enemy of fun

the algorithm would be fairly complex. it would not only need to analyze the transfer function (oir its reversed) in various ways, it would also need to know all the filter externals you have installed and how they sound.

that is basically a deep learning application, which you first have to train and manually correct its output.