Why we sometime use some values of fixed point and floating point both in dsp?
The transition from text-book math to product code can be a lot simpler with floating point than with fixed point. The latter requires some specialized knowledge that, while not rocket science, may be more common for electronic engineers or embedded engineers than computer science or math people. Simple stuff tends to be a lot simpler in floating point than in fixed point.
If you really need to know the numerical behaviour of your code (as in certain recursive algorithms), it tends to be the other way around - the «cruise control» of floating point also makes it more tedious to figure out what is actually going on, while the explicit requirements of fixed point makes the details more plain sight.