1. Assume that two sampled time domain signal are given as x[n]=[12345] [x [n] = [1...

 

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1. Assume that two sampled time domain signal are given as x[n]=[12345] [x [n] = [1 2 3 4 5 6] You are going to find the DFT (discrete Fourier Transform) of the two functions using DFT matrix, W as shown in the class. DFT equation pair X[k]=x[n]e n=0 N-1 |x[n] = - - * *X [k]e ^*** N N k=0 X[k]=W-x[n] |x[n] = _ w-'. .W-. X[k] And you saw some patterns how the W matrix looks like. j2rnk N a) Do [W-W- vs. W. W and verify that they produce same outputs. where W- is inverse of W matrix and Wis transpose & conjugate of W b) Do the DFT of the given {x, [n] & x [n]} Note: it is called 5 point & 6 point DFT. c) Find {x, [n] & x [n]} from the part (b) using s {x[n] = _ W X[k]} / N . X[4]} and verify that you got the original values as you expected. d) Write a Matlab program to verify the solutions of part (b) & (c)(Simply talking, make DFT and IDFT function and plug part (b) & (c) values using two for loops each.) 1. Assume that two sampled time domain signal are given as x[n]=[12345] [x [n] = [1 2 3 4 5 6] You are going to find the DFT (discrete Fourier Transform) of the two functions using DFT matrix, W as shown in the class. DFT equation pair X[k]=x[n]e n=0 N-1 |x[n] = - - * *X [k]e ^*** N N k=0 X[k]=W-x[n] |x[n] = _ w-'. .W-. X[k] And you saw some patterns how the W matrix looks like. j2rnk N a) Do [W-W- vs. W. W and verify that they produce same outputs. where W- is inverse of W matrix and Wis transpose & conjugate of W b) Do the DFT of the given {x, [n] & x [n]} Note: it is called 5 point & 6 point DFT. c) Find {x, [n] & x [n]} from the part (b) using s {x[n] = _ W X[k]} / N . X[4]} and verify that you got the original values as you expected. d) Write a Matlab program to verify the solutions of part (b) & (c)(Simply talking, make DFT and IDFT function and plug part (b) & (c) values using two for loops each.)