I wrote some DSP stack and would like to share it. I am thinking of licensing the stack under GPLv3 because I like the license (except the patents clause). I do not own any patents yet. However, since this license forces the developer to give away his/her patents related to the stack will the license actually prevent me from applying for and getting a possible patent for an implementation of my stack?
If the software you license under the GPLv3 (or any artistic/creative commons license) can be discovered as prior art for an undisclosed invention, then it will absolutely prevent you from obtaining a patent.
Your first action should be to get your priority date: file a provisional patent and supply important parts of the source code in that, along with the novel ways it can be applied to solving problems. The provisional will never be opened to third parties, but it will put your stake in the ground on a specific date. You then have one year to publish your application.
Treat your source code the same way you treat other patentable unpublished work; keep it private until the disclosure is made.
Additionally, you need to keep in mind that providing an open source implementation of patented work might be considered to be inducing infringement, which could weaken your case for enforcing licenses of your patent, since you are giving it away.
That said, whenever you publish anything that is associated with a patent, you need to make absolutely certain that your provisional patent number, patent application(s) and/or patent grant(s) are attached to every bit of the code.
You can always create an open source API around a closed-source library after the fact, but you can never un-publish source code. If you publish such an API (around your closed-source library/service), you may be better off with the Apache or BSD license, because it will be more amenable to commercial use. The GPLv3 is supposed to accommodate commercial use, but it is not well tested.
However, since this licence forces the developer to give away his/her patents related to the stack will the licence actually prevent me from applying for and getting a possible patent for an implementation of my stack?
No, releasing under GPLv3 will not directly prevent you from applying for and obtaining a patent.
If the GPLv3 patent clauses turn out to work as intended in court, they will limit your ability to target, as infringers, developers and users of code derived from your GPLv3 code.
However, releasing under GPLv3 may also diminish your patent rights in other respects, chiefly because preserving patent rights is (A) more complicated than the FOSS crowd believes and (B) not something the FOSS crowd loses sleep over anyhow.