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Find IDFT of the sequence X (K) = (5,0,1-j,0,1,0,1+j,0)
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Solution:

We have,

x(n)=1NN1k=0X(k)ej2πkn/Nn=0,1,.,N1

For N=8

x(n)=18N2k=0X(k)ejπn/4n=0,1,.7

For n=0;x(0)=7k=0X(k)=18[5+0+1j+0+1+j+0]=1

For $\mathrm{n}=1 ; \mathrm{x}(1)=\frac{1}{8} \sum_{k=0}^7 X(\mathrm{k}) \mathrm{e}^{j \pi k / 4}=\frac{1}{8}[5+-(1-\mathrm{j})(\mathrm{j})+1(-1)+(1+\mathrm{j})(-\mathrm{j})]=6 …

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