What are the minimum knowledge required to begin the study of Digital Signal Processing?
I personally believe that the approach of studying something just in order to "feel ready" to study something else later on is not efficient and tends to overwhelm the student. (This of course only applies because I assume that you know what a computer scientist should know anyway: basic math, and - most importantly - how to think clearly and logically.) I could give you a whole list of mathematical topics which are important for doing DSP, but this would just paralyze you and would make you feel that there is so much you need to know that you won't even know where to start. Note that DSP has become such a huge topic in itself that there is hardly anyone who can claim that he knows even the basics of all its different sub-fields.

So what do I recommend to you after all? Get a good book on DSP and simply start studying it. If you come across problems that you cannot solve yourself, dig deeper by searching the internet, asking questions on this site, etc. In this way you will learn all necessary basics that you might be lacking. But the point is that only in this way will you find out what it actually is that you are lacking, so filling the gaps in your knowledge will be most efficient.

One good (and free!) book I would like to recommend to you is Introduction to Signal Processing by Orfanidis. It contains a lot of necessary basics and it is very practical. I think you will learn a lot in quite a short time. Also take a look at this online-book.

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