Consider a real, causal sequence x[n] with discrete-time Fourier transform X(e j ), where the following two facts are given about X(e j ): X

Consider a real, causal sequence x[n] with discrete-time Fourier transform X(e^jω), where the following two facts are given about X(e^jω):

X_R(e^jω) = 2 – 4 cos(3ω),

X(e^jω)|_ω=π = 7.

Are these facts consistent? That is, can a sequence x[n] satisfy both? If so, give one choice for x[n]. If not, explain why not.