Compute the N-point DFT of the following finite-length sequences considered to be of length N (N is even):
![1, n odd 0, n even (a) x[n] = COS Tn](http://img.homeworklib.com/questions/12a9c4e0-849e-11eb-91f1-4950d0b82573.png?x-oss-process=image/resize,w_560)
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Compute the N-point DFT of the following finite-length sequences
considered to be of length N (N...
PROBLEM 1: Let xfn], O < n 3 N-1 be a length-N sequence with an N-point...
PROBLEM 1: Let xfn], O < n 3 N-1 be a length-N sequence with an N-point DFT X[k], 0 k N-1. Determine the N-point DFT's of the following length-N sequences in terms of X[k]: (a) w[n] = az[M-m1〉N] + β (n-m2)N], where m 1 and m 2 are positive integers less than N. (b) g[n] ={z[n] for n even for odd
The DFT is a sampled version of the DTFT of a finite-length sequence; i.e., N-1 (P9.25-1)...
The DFT is a sampled version of the DTFT of a finite-length sequence; i.e., N-1 (P9.25-1) Furthermore, an FFT algorithm is an efficient way to compute the values X Now consider a finite-length sequence xin] whose length is N samples.We want to evaluate X(z) the z-transform of the finite-length sequence, at the following points in the z-plane where ris a positive number. We have available an FFT algorithm (a) Plot the points z in the z-plane for the case N-8...
The DFT is a sampled version of the DTFT of a finite-length sequence; i.e., N-1 (P9.25-1) Furthermore, an FFT algorithm...
The DFT is a sampled version of the DTFT of a finite-length sequence; i.e., N-1 (P9.25-1) Furthermore, an FFT algorithm is an efficient way to compute the values X Now consider a finite-length sequence xin] whose length is N samples.We want to evaluate X(z) the z-transform of the finite-length sequence, at the following points in the z-plane where ris a positive number. We have available an FFT algorithm (a) Plot the points z in the z-plane for the case N-8...
I Need Help with 4,6,8,10,15,18 Problems 123 If f(n) is a periodic sequence with period N,...
I
Need Help with 4,6,8,10,15,18
Problems 123 If f(n) is a periodic sequence with period N, it is also periodic with period 2N. Tet 8(k) denote the DFS coefficients of X(n) considered as a periodic sequence with period N and X,(k) denote the DFS coefficients of x(n) considered as a periodic sequence with period 2N. X,(k) is, of course, periodic with period N and X2(k) is periodic with period 2N. Determine 8(k) in terms of X (k). 5. Consider two...
Consider a finite length DT sequence of length N -16 described below. 1, 0<n< 2 Use...
Consider a finite length DT sequence of length N -16 described below. 1, 0<n< 2 Use MATLAB built-in function dftmtx (N), and compute X[k] command and create stem plots for the following: DFT(X[k]. Use subplot (a) x n] vs n; (b) X[k] vs k; (c) angle (X [k) vs k. Label axes of these plots and include title for each of these plots
Assuming that a 20-point DFT is computed using the prime factor algorithm, (a) Determine the input...
Assuming that a 20-point DFT is computed using the prime factor
algorithm,
(a) Determine the input and output mapping tables.
(b) If the input sequence is
x[n] ={1/2, n even
{ 0, n odd
carry out the 20-point DFT of x[n] step-by-step using the prime
factor algorithm.
points) Assuming that a 20-point DFT is computed using the prime factor algorithm, a) Determine the input and output mapping tables. (b) If the input sequence is nn even 0, n odd carry...
5.34 Let xIn],0sns N-1, be a length-N sequence with an N-point DFT XIk],0sksN-1. (a) sa symmetric...
5.34 Let xIn],0sns N-1, be a length-N sequence with an N-point DFT XIk],0sksN-1. (a) sa symmetric sequence satisfying the condition x n] = 지(N 1 n)N] show that X [N/2] 0 for N even. (b) Ifx[n] is a antisymmetric sequence satisfying the condition x[n] = rKN-1-n)N], show that X[0] = 0 (c) If x[n] is a sequence satisfying the condition x[n] =-x[(n + M〉N] with N = 2M, show that X[21] = 0 for I=0, 1, ,M-1
5.34 Let xIn],0sns...
P-8.7 Consider two finite-length sequences, x[n] 0 n<0 1 0 <n<3 n> 3 0 and h[n]...
P-8.7 Consider two finite-length sequences, x[n] 0 n<0 1 0 <n<3 n> 3 0 and h[n] = 28[n] - 8[n - 1] - 8[n - 2]. (a) Determine and plot the discrete convolution y[n] = x[n] *h[n] for these two sequences.
please answer it in detail (a) Find the 10 point DFT of the sequence r(n) -1,1,1,1,1,0,0,0,0,0],...
please answer it in detail
(a) Find the 10 point DFT of the sequence r(n) -1,1,1,1,1,0,0,0,0,0], for n- 0,..,9. X(k)-4,1-j*2.414,0,1-j 0.414,0,1+j 0.414,0,1+j 2.414 help (formulas) Hint: You can use the formula used in example 7.1.2 in page 457 Compute the DFT of the following sequences in terms of X(k). Do not copy the entire formula of X(k) from part (a). (b) ri(n) - [0,0,0,1,1,1, 1, 1,0,0], for n-0,...,9. Xi(k)4,1+j 2.413,0,1+j0.414,0,1- 0.414,1-j2.413 You may use X(k) to denote the DFT of...
M-file dft.m function Xk = dft(x) [N,M] = size(x); if M ~=1, % makes sure that...
M-file
dft.m
function Xk = dft(x)
[N,M] = size(x);
if M ~=1, % makes sure that x is a column vector
x = x';
N = M;
end
Xk=zeros(N,1);
n = 0:N-1;
for k=0:N-1
Xk(k+1) = exp(-j*2*pi*k*n/N)*x;
end
Using the MATLAB M-file dft, compute the 32-point DFT of rn cos(₩), 0 〈 n < 10, x[n] 0 for all other n. COS
PROBLEM 1: Let xfn], O < n 3 N-1 be a length-N sequence with an N-point DFT X[k], 0 k N-1. Determine the N-point DFT's of the following length-N sequences in terms of X[k]: (a) w[n] = az[M-m1〉N] + β (n-m2)N], where m 1 and m 2 are positive integers less than N. (b) g[n] ={z[n] for n even for odd
The DFT is a sampled version of the DTFT of a finite-length sequence; i.e., N-1 (P9.25-1) Furthermore, an FFT algorithm is an efficient way to compute the values X Now consider a finite-length sequence xin] whose length is N samples.We want to evaluate X(z) the z-transform of the finite-length sequence, at the following points in the z-plane where ris a positive number. We have available an FFT algorithm (a) Plot the points z in the z-plane for the case N-8...
The DFT is a sampled version of the DTFT of a finite-length sequence; i.e., N-1 (P9.25-1) Furthermore, an FFT algorithm is an efficient way to compute the values X Now consider a finite-length sequence xin] whose length is N samples.We want to evaluate X(z) the z-transform of the finite-length sequence, at the following points in the z-plane where ris a positive number. We have available an FFT algorithm (a) Plot the points z in the z-plane for the case N-8...
I
Need Help with 4,6,8,10,15,18
Problems 123 If f(n) is a periodic sequence with period N, it is also periodic with period 2N. Tet 8(k) denote the DFS coefficients of X(n) considered as a periodic sequence with period N and X,(k) denote the DFS coefficients of x(n) considered as a periodic sequence with period 2N. X,(k) is, of course, periodic with period N and X2(k) is periodic with period 2N. Determine 8(k) in terms of X (k). 5. Consider two...
Consider a finite length DT sequence of length N -16 described below. 1, 0<n< 2 Use MATLAB built-in function dftmtx (N), and compute X[k] command and create stem plots for the following: DFT(X[k]. Use subplot (a) x n] vs n; (b) X[k] vs k; (c) angle (X [k) vs k. Label axes of these plots and include title for each of these plots
Assuming that a 20-point DFT is computed using the prime factor
algorithm,
(a) Determine the input and output mapping tables.
(b) If the input sequence is
x[n] ={1/2, n even
{ 0, n odd
carry out the 20-point DFT of x[n] step-by-step using the prime
factor algorithm.
points) Assuming that a 20-point DFT is computed using the prime factor algorithm, a) Determine the input and output mapping tables. (b) If the input sequence is nn even 0, n odd carry...
5.34 Let xIn],0sns N-1, be a length-N sequence with an N-point DFT XIk],0sksN-1. (a) sa symmetric sequence satisfying the condition x n] = 지(N 1 n)N] show that X [N/2] 0 for N even. (b) Ifx[n] is a antisymmetric sequence satisfying the condition x[n] = rKN-1-n)N], show that X[0] = 0 (c) If x[n] is a sequence satisfying the condition x[n] =-x[(n + M〉N] with N = 2M, show that X[21] = 0 for I=0, 1, ,M-1
5.34 Let xIn],0sns...
P-8.7 Consider two finite-length sequences, x[n] 0 n<0 1 0 <n<3 n> 3 0 and h[n] = 28[n] - 8[n - 1] - 8[n - 2]. (a) Determine and plot the discrete convolution y[n] = x[n] *h[n] for these two sequences.
please answer it in detail
(a) Find the 10 point DFT of the sequence r(n) -1,1,1,1,1,0,0,0,0,0], for n- 0,..,9. X(k)-4,1-j*2.414,0,1-j 0.414,0,1+j 0.414,0,1+j 2.414 help (formulas) Hint: You can use the formula used in example 7.1.2 in page 457 Compute the DFT of the following sequences in terms of X(k). Do not copy the entire formula of X(k) from part (a). (b) ri(n) - [0,0,0,1,1,1, 1, 1,0,0], for n-0,...,9. Xi(k)4,1+j 2.413,0,1+j0.414,0,1- 0.414,1-j2.413 You may use X(k) to denote the DFT of...
M-file
dft.m
function Xk = dft(x)
[N,M] = size(x);
if M ~=1, % makes sure that x is a column vector
x = x';
N = M;
end
Xk=zeros(N,1);
n = 0:N-1;
for k=0:N-1
Xk(k+1) = exp(-j*2*pi*k*n/N)*x;
end
Using the MATLAB M-file dft, compute the 32-point DFT of rn cos(₩), 0 〈 n < 10, x[n] 0 for all other n. COS
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