Is it possible to have a non-trivial signal (i.e. non-zero for all time) that is both time- limited and band-limited? Please explain and provide a brief proof. (b) One approach to designing FIR filters is to take a desired frequency response, Hd(w), compute the corresponding coefficients of the ideal filter ha[n], and then truncate this to make it finite by multiplying by a window function (h[n] = ha[n] • w[n]), and then setting these values as the coefficients or "taps" of the FIR filter. i) Which windowing function, w[n], provides the narrowest main lobe, and hence the sharpest transition width? ii) Why is this window function not necessarily the most desirable and how could the frequency response be improved?
