Consider direct computation of the DFT using fixed-point arithmetic with rounding. Assume that the register length is B bits plus the sign (i.e., a total of B + 1 bits) and that the round-off noise introduced by any real multiplication is independent of that produced by any other real multiplication. Assuming that x[n] is real, determine the variance of the round-off noise in both the real part and the imaginary part of each DFT value X[k].
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