Consider a real, causal, finite length signal x n with length N 2 and with a 2 point discrete Fourier transform X k X R k j X I k for k 0, 1 If X R k 2 k 4 k1 , is it possible to determine x n uniquely If so, give x n If not, give several choices for x n satisfying the stated condition on X R k ...

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Consider a real, causal, finite-length signal x[n] with length N = 2 and with a 2-point discrete-Fourier

Question:

Consider a real, causal, finite-length signal x[n] with length N = 2 and with a 2-point discrete-Fourier transform X[k] = X_R[k] + j X_I[k] for k = 0, 1. If X_R[k] = 2δ[k] – 4δ[k–1], is it possible to determine x[n] uniquely? If so, give x[n]. If not, give several choices for x[n] satisfying the stated condition on X_R[k].