If you listen to the last bit of this video of a cheetah purring it is quite impressive. The recording is good which helps but the purr is very strong. Below the video is another showing the waveform of the sound.
The order of breathing in the video immediately above is: egressive (out) — ingressive (in) — out –- in -– out -– in
There is a bit of background noise in the video below of Rocky a domestic cat but the differences in the purr are apparent:
We all know that cats purr continuously which means they purr when breathing in and out and even when drinking (kitten suckling). The differences in sound between the egressive (out-breathing) and ingressive (in-breathing) phases of the cheetah’s purr are clear but less clear for the domestic cat.
The cheetah is Caine and the recording was made in South Africa. The roaring big cats cannot purr. All the other wild cat species can. The wild cats tend to have a wider repertoire of vocalisations than the domestic cat. That is the impression I get from my reading. The leopard makes a sound that is very much like someone sawing wood. It is continuous and similar to a purr. You can hear the sound in an audio file here. I hope it works for you.
Another species of animal can purr and the sound is very similar to the domestic cat. This is the genet. The genet is the only animal other than the cat that purrs as far as we know. You can listen to the genet purr on this page. It is an audio file. It might not work and it opens in a new tab or window.
The air in the throat and the muscles vibrate during purring as far as I am aware. This page discussed purring in simple language. The purring sound is not produced by the vocal cords.