Is there a term for the noisy bringing up of phlegm in preparation to spit? There's a colloquial term in some regions in English I've seen spelled hoik and hoick to refer to the noisy act of clearing the throat/nasal cavity of mucus/phlegm, usually just before spitting it out. This is different from what would in English normally be meant by the term "to clear one's throat", which is a quieter action a bit like a closed-mouth cough.

Since this doesn't seem to be considered rude or vulgar in Chinese culture as it is in many western countries, it's a lot more common. So I'm wondering there are Chinese terms for it. (Mandarin preferred but all Chinese varieties are of interest.)
You can use 咳 (ke) for the sound of clearing one's throat. It's the same character in 咳嗽, which is "cough". It is also the character used when people clear their throat to draw others attention to themselves. In this case, it is 咳咳.