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 R (e j ) 2 4 cos(3), X(e j ) 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 ...

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

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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.

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