In Figure P2.72, two sequences x1[n] and x2[n] are shown. Both sequences are zero for al...

In Figure P2.72, 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^jω) and X₂(e^jω), which, in general, can be expected to be complex and can be written in the form

where A₁(ω), θ₁(ω),A₂(ω), and θ₂(ω) are all real functions chosen so that both A₁(ω) and A₂(ω) are nonnegative at ω = 0, but otherwise can take on both positive and negative values. Determine appropriate choices for θ₁(ω) and θ₂(ω), and sketch these two phase functions in the range 0 < ω < 2π.