Design one of 4 type of FIR filter by window function? There're 4 type of FIR to chose from


symetry ,even 
symetry ,odd
antisymetry, even
antysymetry, odd


Also, there are many type of window like rectangular, Hanning, Kaiser,etc So how to use a window function to design the N-length filter and what's the point of doing it? That's what my teacher ask me to do but I don't understand the reason

What I confuse here is that for example I want the ideal filter $H(\omega)$ that have passband in $\omega_a &lt;\omega&lt;\omega_b$ then what I need to do is just use the inverse Fourier transform to the frequency response of the ideal filter to find $h[n]$ that is infinite then use the window function to make it finite. Then what's the point of make it look like the form of one of those 4 type? Moreover, what I need to do after doing inverse Fourier Transform and window function to make it in the form of FIR digital filter with N-length?
The topic your referring to goes by various names such as "FIR Filter Design Using Windows", "Windowing Method of FIR Filter Design", "Window Designed FIR Filters", etc. I'll bet your class textbook covers this topic (most DSP books do). Meaningful answers to your questions require more space than is available here. I suggest you have a look at the following web page (and its following three pages) for a decent introductory discussion of that topic:

http://www.bores.com/courses/intro/filters/4_fir.htm

Then have a look at Section 2.2 of the following web page:

http://www.mikroe.com/chapters/view/72/chapter-2-fir-filters/