[partconvEQ10~] is a 10 band equalizer abstraction based on minimum-phase FIR filtering and partitioned convolution. Even though it uses a 2048 point FIR filter, it adds no more than a few samples latency to your patch. This is because the energy of the filter kernel is concentrated right at the start (minimum-phase instead of zero-phase). FIR filtering does not suffer from phase distortion.

The low latency makes this EQ suitable for live performance. I use it for microphone correction with -12 to +12 dB range, but it can be used with more extreme amplitude effect as well, to kill frequency bands like it is done in DJ mixers. The help patch has examples of both applications.

Average CPU load of this EQ is modest, ~1% on a regular laptop. However, computing a minimum-phase kernel (done for every filter parameter update) is CPU intensive and causes a short spike in CPU load. Therefore the technique may not be suitable for small platforms like Raspberry Pi. On my 1 GHz core2duo laptop tablet it performs well.

The abstraction uses Pd-extended objects [bsaylor/partconv~], [cyclone/speedlim] and [iemlib/for++].

If you want to read yourself a headache on minimum-phase filtering, here's the background documentation:

http://www.katjaas.nl/minimumphase/minimumphase.html

Katja

http://www.pdpatchrepo.info/hurleur/partconvEQ10~.zip

Nice! Excellent background material too.

I have always enjoyed the time-domain explanation of minimum phase IRs: Any N-tap FIR can be factored into N-1 duplets convolved with each other. If any duplet has its largest amplitude second, then time-reverse it, which changes its phase response but not its magnitude response. Then convolve them all back together, and the resulting FIR will have its energy maximally concentrated at the beginning but the same magnitude response as the original. The cepstral method is easier, though!

I am not sure, however, what you mean by "FIR filtering does not suffer from phase distortion." Linear phase FIR filters give the same delay at all frequencies, but minimum phase FIRs do not.

@emacpher said:

I am not sure, however, what you mean by "FIR filtering does not suffer from phase distortion." Linear phase FIR filters give the same delay at all frequencies, but minimum phase FIRs do not.

Thanks for your feedback. You're right this is not expressed correctly. Time delay depends on phase so the signal does not come out with the same phase relations as the original. What I meant to say is, that unlike a bank of FIR/IIR filters (biquad cascades), pure FIR doesn't do phase cancellations.

Katja

I wish I could pretend to understand all of the theory... excellent work compiling it all into a patch! I'm enjoying it, slowly trying to understand how it works.