Consider the continuous-time rectangular window wR(t), defined by (13.16) and the Hamming...

Consider the continuous-time rectangular window wR(t), defined by (13.16) and the Hamming window, wH(t), defined by (13.26).

(a) Show that the continuous-time Fourier transform of the rectangular window wR(t) is as given in (13.23).

(b) Use the fact that

to show that

(c) Use the result of (b) to construct a sketch of ǀ WH (jω)ǀ, and from this sketch argue that the width of the main-lobe of ǀWH(jω)ǀ is Δωh = 8π/T.