The equations for IDFT (Inverse Discrete Fourier Transform-x[n]) and DFT (Discrete Fourier Transform-X[*]) are defined as...

Transcribed Image Text:

The equations for IDFT (Inverse Discrete Fourier Transform-x[n]) and DFT (Discrete Fourier Transform-X[*]) are defined as It is given that x[n] =√x[k]e * k=0~(N-1) X[k]=x[n]e -0 n=0~(N-1) -1/2k [x[n] =X [K]e***][x = A³X] [X-Ax] <-/2 mak N [x[k] = x[n]e x[n] = [123] where "7" in [] indicates transpose of the vector and [N] is the length of the vector, [x]. The equations (1) and (2) can be written in shorter form as a) Find matrix [A] in the equation (4), [X-Ax] b) Find the matrix [A¹] in the equation (3), [X-A*X] (1) (2) e) Prove that AA-AA f) Find the rank of the matrix, [A] g) Find eigenvalues and corresponding eigenvectors. (3) c) Express your answers, [X-A¹x] and [x= AX] with proper values x, X, and A d) What kind of matrix is [A]? The equations for IDFT (Inverse Discrete Fourier Transform-x[n]) and DFT (Discrete Fourier Transform-X[*]) are defined as It is given that x[n] =√x[k]e * k=0~(N-1) X[k]=x[n]e -0 n=0~(N-1) -1/2k [x[n] =X [K]e***][x = A³X] [X-Ax] <-/2 mak N [x[k] = x[n]e x[n] = [123] where "7" in [] indicates transpose of the vector and [N] is the length of the vector, [x]. The equations (1) and (2) can be written in shorter form as a) Find matrix [A] in the equation (4), [X-Ax] b) Find the matrix [A¹] in the equation (3), [X-A*X] (1) (2) e) Prove that AA-AA f) Find the rank of the matrix, [A] g) Find eigenvalues and corresponding eigenvectors. (3) c) Express your answers, [X-A¹x] and [x= AX] with proper values x, X, and A d) What kind of matrix is [A]?

Answer rating: 100% (QA)

Analysis of DFT and IDFT a Finding Matrix A in XAx In equation 4 XAx represents a subtraction between two vector quantities both of which consist of N ... View the full answer