Understanding the DFT

Define a vector W containing all N frequency values PU[n], n = 1, 2, . . .N — 1, and a vector w containing all N time values w[k], k = 1,2, . .. N — 1. Then the IDFT

2To be precise, this should be circular convolution. However, for the purposes of designing a workable receiver, this distinction is not essential. The interested reader can explore the relationship of discrete-time convolution in the time and frequency domains in a concrete way using waystof ilt .m on page 148.

equation (7.4) can be rewritten as a matrix multiplication w[0] W[l] w[ 2] w[3]

1 gj'27r/N

1 gj'47r/N

I ej6n/N

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