"Wavelets act to decompose both a high-frequency and a low-frequency component at each decomposition level providing (a) better resolution and (a) finer splitting of the time-frequency domain"
I'm not really sure whether or not we need any articles in the sentence above. It seems to me in the second case "a" is needed, while in the first case - it's not.
Like Mike, I'd probably not use an article. If think that if you are going to use articles, you need to use two, in my opinion. I would use a comma after 'level'.