Consider a real, causal, finite-length signal x[n] with length N = 2 and with a 2-point DFT X[k] = XR[k] + jXI[k] for k = 0, 1. If XR 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 XR[k].
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