FFT calculation of an N-tap FIR filter
hint only, since this is homework and you could get a lot out of this!
The mathematical operation a filter performs between filter impulse response and signal is called __________(1). When we process both filter and signal with an FFT (which is just a fast implementation of __________(2)), then that operation on the originals is equivalent to __________(3) after the (2).
To do (3) on both (2)'ed vectors, these vectors need to be of the same  __________(4), here 256. Often, the signal itself is longer than 256 - (length of filter). This is a problem, because (1) under the (2) is not  __________(5) as the filtering operation normally is, but  __________(6) due to the periodic nature of the (2).
To alleviate this, a segmented approach is chosen.