Perfect reconstruction linear phase FIR filterbank for audio without reconstruction filterbank?

I want to make a perfect reconstruction linear phase FIR filterbank for audio that does not need a reconstruction filter bank.

Does anybody know the theory behind this? When I search I keep coming across filter bank designs which use analysis and reconstruction filters.

I know it must be possible to create a filter bank where you simply run the audio through the filterbank and then sum the inidividual bands again to get perfect reconstruction. Similar to a 2 channel Linkwitz-Riley crossover filter, only then for many subbands.

I know the octaveFilterBank can come close, but it doesn't give true perfect reconstruction and it's not linear phase.

Any help / pointers on how to create such a filter bank in Matlab are greatly appreciated!

[Rik]

Edits restored from Google cache.

Answer 1

[jibrahim]

Hi Pythagorean,

Audio Toolbox has a crossoverFilter that supports up to 5 bands. The summed magnitude response is flat.

https://www.mathworks.com/help/audio/ref/crossoverfilter-system-object.html