Parallel computation of the DFT suppose that we wish to compute an N = 2p2v points DFT

Question:

Parallel computation of the DFT suppose that we wish to compute an N = 2p2v points DFT using 2p digital signal processors (DSPs). For simplicity we assume that p = v = 2. In this case each DSP carries out all the computations that are necessary to compute 2v DFT points.(a) Using the radix-2 DIF flow graph, show that to avoid data shuffling, the entire sequence x(n) should be loaded to the memory of each DSP.(b) Identify and redraw the portion of the flow graph that is executed by the DSP that computes the DFT samples X(2), X(10), X(6), and X(14).(c) Show that, if we use M = 2r DSPs, the computation speed-up S is givenby