(k) is the 8-point discrete Fourier transform (DFT) of a real-valued, discrete-time sequence x[n]. The known DFT values of the discrete sequence x[n] are: x[o]=1, x[i]=2 + j5, x=-5, X=-1-j, X=0-j Determine the remaining DFT values X, x and X. State clearly the property of the DFT that enables you to do this. (b) Sketch the twiddle factors used to compute a 5-point DFT as vectors in the complex-plane. (C) State and prove the periodicity property of the DFT.
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