How to check signal waveform.

I don't see why you need to do par/ser conversion. I can assume your input isn't that wide e.g. it could be ADC output with finite bitwidth.

If you are using altera fft then it will do the job of waiting for you.

So all you have to do is to input to your fft the correct set of inputs then read the output.

Normally fft will output one block late(receive time + processing time), this shouldn't matter. I don't know of any fft that can output straightaway because it needs to have all points ready first.

each ouput point is eventually computed from the scaled sum of products of all input points.

Since you are a beginner I don't see why you use floating point. You better use fixed point(2's complement) and 16 bit real/imag is adequate for the most demanding applications.