Question

Given the following signal:  x(n) = {4, −1, 2, 5, − 2, 3}  Compute the 6-point DFT of x(n) directly from the DFT equation  − = − = 1 0 2 / ( ) ( ) N n k nk N K k a n e  Show all steps!

Answer 1

Answer:

Computing the 6-Point DFT of x(n), where X = 0,1,2,3,4,5

x(0) = 11

x(1) = 21/8 -j13/8

x(2) = 27/8 + j33/32

x(3) = 1139/256 + j91/256

x(4) = 4389/1024

x(5) = 4.14685 - j1379/8192

Step-by-step explanation:

See the picture for workings.

Given X(n) = { 4, -1, 2, 5, -2, 3}

Six point DFT implies that N = 6

Step 1 = write out equation X(k)

Step 2 = substitute "Wn" in the equation X(k) to give a new equation

Step 3 = when N=6, substitute for "N" in the new equation and simplify the new X(k) equation.

Step 4 = use 0, 1, 2, 3, 4, 5 in finding the DFT