I have checked this and this Question in this site very much similar to my question. But I want to know are they Qt compatible? I want to start learn developing DSP application in Qt framework so I want some library compatible with Qt so that it can later be translated into Qtpython also? Can we use same libraries with Qt as it is? Will it make effect on changing data types to and from this library to QtObject? I am new to DSP and Qt. so may be the question seems silly.
Not quite the answer you requested, but I think the sanest thing(OOP wise) to do in most of the situations is to have the backend of the application separated from the frontend.
You could create a standalone library(either static or dynamic) for your dsp code and separate it from the QT code.
This way your DSP code would be independent of the frontend you are using. You could switch from QT to anything else(wxWidgets/GTK+ etc) and your DSP functions inside the lib would remain the same.