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State and prove shifting properly of DFT
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If x(n)()DFT X(k),then

x(nl)()DFTX(k).ej2πklN

Proof:We have IDFT equation

x(n)=1NN1k=0X(k).ej2πknN

IDFT[X(K).ej2πklN]=1/NN1k=0X(k).ej2πklN.ej2πknN

1/NN1k=0X(K).ej(2πk(nl))N

Comparing with DFT equation we have

x(nl)<DFT>X(K).ej2πklN

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