The rectangular window is defined as

The Hamming window is defined as

(a) Show that the Fourier transform of the rectangular window is

(b) Sketch WR(ejω) as a function of ω. (Disregard the linear phase factor e−jω(L−1)/2 in making the sketch.)

(c) Express wH[n] in terms of wR[n] and thereby obtain an expression for WH(ejω) in terms of WR(ejω). 

(d) Sketch the individual terms in WH(ejω). (Disregard the linear phase factor e−jω(L−1)/2 that is common to each term.) Your sketch should illustrate how the Hamming window trades frequency resolution for increased suppression of higher frequencies.

Which of the following functions cannot be a valid autocorrelation function? For all invalid autocorrelations, explain the reason.