Three real-valued seven-point sequences (x1[n], x2[n], and x3[n]) are shown in Figure P8...

Three real-valued seven-point sequences (x₁[n], x₂[n], and x₃[n]) are shown in Figure P8.40. For each of these sequences, specify whether the seven-point DFT can be written in the form

where A_i[k] is real-valued and 2α_i is an integer. Include a brief explanation. For each sequence which can be written in this form, specify all corresponding values of α_i for 0 ≤ α_i < 7.