In Figure, two sequences x 1 [n] and x 2 [n] are shown. Both sequences are zero

Question:

In Figure, two sequences x₁[n] and x₂[n] are shown. Both sequences are zero for all n outside the regions shown. The Fourier transforms of these sequences are X₁(e^j?) and X₂(e^j?), which, in general, can be expected to be complex and can be written in the form?

X₁(e^j?) = A₁(?) e^j?1(?),

X₂(e^j?) = A₂(?) e^j?2(?),

Where A₁(?), ?₁(?), A₂(?), and ?₂(?) are all real functions chosen so that both A₁(?) and A₂(?) are nonnegative at ? = 0, but otherwise can take on both positive and negative values, Determine appropriate choices for ?1(?) and ?2(?), and sketch these two phase functions in the range 0