Please explain the steps on how to get this matrix based on the equation above
Posted: Tue Apr 26, 2022 8:52 pm
Please explain the steps on how to get this matrix based on the
equation above
Discrete Fourier Transform (DFT) n-1 . X k = n n-1 1 ΧΑ. = Σ; • e-2π) και Xiue ΣΧ; - e2πj4 i=0 i=0 The n-point DFT multiplies a vector with an n x n matrix 1 1 1 1 1 1 e-27j e-27j} e-27j"-1 1 e-27j e-2aja 1 e-27j e-2nja 72 e-27j1 e-27j 72 Fn = e-27;2(n-1) e-27j3(n-1) e-2njang 72 1 e-27j"1 e-27j2(n-1) n e-24j (n-1) e-2nj (n1)(n-1) CO Хо ΤΟ 11 Xo X1 X2 1 X1 X2 11 X2 Fn. 12 = . F* 72 n In-1) \Xn-1) Xn-1) en-1
equation above
Discrete Fourier Transform (DFT) n-1 . X k = n n-1 1 ΧΑ. = Σ; • e-2π) και Xiue ΣΧ; - e2πj4 i=0 i=0 The n-point DFT multiplies a vector with an n x n matrix 1 1 1 1 1 1 e-27j e-27j} e-27j"-1 1 e-27j e-2aja 1 e-27j e-2nja 72 e-27j1 e-27j 72 Fn = e-27;2(n-1) e-27j3(n-1) e-2njang 72 1 e-27j"1 e-27j2(n-1) n e-24j (n-1) e-2nj (n1)(n-1) CO Хо ΤΟ 11 Xo X1 X2 1 X1 X2 11 X2 Fn. 12 = . F* 72 n In-1) \Xn-1) Xn-1) en-1