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State and prove shifting properly of DFT
1 Answer
written 6.5 years ago by |
If x(n)(↔)DFT X(k),then
x(n−l)(↔)DFTX(k).e−j2πklN
Proof:We have IDFT equation
x(n)=1N∑N−1k=0X(k).e−j2πknN
IDFT[X(K).e−j2πklN]=1/N∑N−1k=0X(k).e−j2πklN.ej2πknN
1/N∑N−1k=0X(K).e−j(2πk(n−l))N
Comparing with DFT equation we have
x(n−l)<−DFT>X(K).e−j2πklN