Write The Expression Of One-dimensional Discrete Fourier Transforms?

1.	Write The Expression Of One-dimensional Discrete Fourier Transforms?
Answer» FORWARD TRANSFORM The sequence of x(n) is GIVEN by x(n) = { X0,x1,x2,… xN-1}. X(k) = (n=0 to N-1) _ x(n) exp(-j 2* pi* nk/N) ; k= 0,1,2,…N-1 Reverse TRANSFORMS X(n) = (1/N) (k=0 to N-1) _ x(k) exp(-j 2* pi* nk/N) ; n= 0,1,2,…N-1 Forward transform The sequence of x(n) is given by x(n) = { x0,x1,x2,… xN-1}. X(k) = (n=0 to N-1) _ x(n) exp(-j 2* pi* nk/N) ; k= 0,1,2,…N-1 Reverse transforms X(n) = (1/N) (k=0 to N-1) _ x(k) exp(-j 2* pi* nk/N) ; n= 0,1,2,…N-1

Answer»

The sequence of x(n) is GIVEN by x(n) = { X0,x1,x2,… xN-1}.

X(k) = (n=0 to N-1) _ x(n) exp(-j 2* pi* nk/N) ; k= 0,1,2,…N-1

X(n) = (1/N) (k=0 to N-1) _ x(k) exp(-j 2* pi* nk/N) ; n= 0,1,2,…N-1

Forward transform

The sequence of x(n) is given by x(n) = { x0,x1,x2,… xN-1}.

X(k) = (n=0 to N-1) _ x(n) exp(-j 2* pi* nk/N) ; k= 0,1,2,…N-1

Reverse transforms

X(n) = (1/N) (k=0 to N-1) _ x(k) exp(-j 2* pi* nk/N) ; n= 0,1,2,…N-1

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