The first five points of eight point DFT of real valued signal are $\{0.25, 0.125 -j0.3018, 0, 0.125-j0.0150, 0\}$. Determine the remaining three points.

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The first five points of eight point DFT of real valued signal are

$\{0.25, 0.125 -j0.3018, 0, 0.125-j0.0150, 0\}$ . Determine the remaining three points.

written 8.6 years ago by

teamques10 ★ 69k

modified 3.2 years ago by

sagarkolekar ★ 11k

discrete time signal processing

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written 8.6 years ago by

teamques10 ★ 69k

The given DFT is $\{0.25, 0.125 -j0.3018, 0, 0.125-j0.0150, 0\}$

Now, here

$X[0]= 0.25, \\ X[1]= 0.125 -j0.3018, \\ X[2]= 0, \\ X[3]= 0.125-j0.0150 , \\ X[4]= 0$

By Symmetry Property of DFT,

$X* [k ] = X[ N-k ]$

$X* [ N-k ] = X[ k ]$

Here, $N = 8, \\ X* [k ] = X[8-k ] \\ X[ 5 ] = X*[ 8 - 5 ] = X* [3] \\ = 0.125+ j0.0150 \\ X[ 6 ] = X*[ 8 - 6 ] = X* [2 ] \\ = 0\\ X[ 7 ] = X*[ 8 - 7 ] = X* [ 1 ] \\ = 0.125 + j0.3018$

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