![8.32. Considera finite-duration sequence x[n] of length P such that xlnj=Ofor n <0andn> P. We want to compute samples of the Fourier transform at the N equally spaced frequencies 2nk Determine and justify procedures for computing the N samples of the Fourier transform using only one N-point DFT for the following two cases: (a) N > /P (b) N < P](http://img.homeworklib.com/questions/5087a580-c35c-11ea-953d-b71cbbf15f74.png?x-oss-process=image/resize,w_560)
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8.32. Considera finite-duration sequence x[n] of length P such that xlnj=Ofor n <0andn> P. We want...
Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of...
Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given by 10 equally-spaced samples of X(e). Determine y[n]. Hint: N-point DFT of a sequence w[n] = 2-n (u[n]-u[n-N]) is W [k] = 1-22 1wk
Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given...
Let x[n] be infinite-duration sequence with DTFT of 2n X(e'"), Xi[n] is an N-point finite-duratio...
Let x[n] be infinite-duration sequence with DTFT of 2n X(e'"), Xi[n] is an N-point finite-duration sequence whose DFT X,(e N ) was obtained by sampling X(eW) at N equally spaced points on the unit circle. Determine xl[n] in terms of x[n]
Let x[n] be infinite-duration sequence with DTFT of 2n X(e'"), Xi[n] is an N-point finite-duration sequence whose DFT X,(e N ) was obtained by sampling X(eW) at N equally spaced points on the unit circle. Determine xl[n] in terms...
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...
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...
9. Consider a 20-point finite-duration sequence x[n] such that xfn]-0 outside 0 snSI (a) Ifit is...
9. Consider a 20-point finite-duration sequence x[n] such that xfn]-0 outside 0 snSI (a) Ifit is desired to evaluate X(e/o) at o 4x/S by computing one M-point DFT point DFT dete the smallest possible M, and develop a method to obtain X(eo) at 4x smallest M.
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
Problem 10: a) Given the following sequence: x[n]={1, 2, 3, 4} where x[?= 1. Use the...
Problem 10: a) Given the following sequence: x[n]={1, 2, 3, 4} where x[?= 1. Use the decimation in time FFT algorithm to compute the 4-point DFT of the sequence X[k]. Draw the signal flow & the butterfly structure and clearly label the branches with the intermediate values and the twiddle factors W = e- /2nk b) The inverse discrete Fourier transform can be calculated using the same structure and method but after appropriately changing the variable WN and multiplying the...
Exercise 4. Computing and displaying the Fourier Transform of a signal Later in the semester it will become useful to d...
Exercise 4. Computing and displaying the Fourier Transform of a signal Later in the semester it will become useful to determine the frequency response of a signal or system by taking the Fourier Transform empirically (rather than computing it analytically). To do so we make use of the fft and fftshift commands. The fft command is an efficient implementation of the Discrete Fourier Transform (DFT) known as the Fast Fourier Transform (FFT). When the FFT is computed the samples are...
[20 total pts) Consider the sequences x1n] = { 1, 2,-2, 1}, and x2 [n] =...
[20 total pts) Consider the sequences x1n] = { 1, 2,-2, 1}, and x2 [n] = { 1, 2,-2, 1, 0, 0, 0, 0). The sequence x2In] is known as a zero-padded version of x,[n]. When answering the questions below, please use Table 1, provided on Page 3. a. [3 pts] Compute X1(eo), the Discrete-Time Fourier Transform (DTFT) of x1 [n], and evaluate it for the following values of normalized frequency: a-63 笎哮,쯤뀨 write the values in the table b....
Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given by 10 equally-spaced samples of X(e). Determine y[n]. Hint: N-point DFT of a sequence w[n] = 2-n (u[n]-u[n-N]) is W [k] = 1-22 1wk
Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given...
Let x[n] be infinite-duration sequence with DTFT of 2n X(e'"), Xi[n] is an N-point finite-duration sequence whose DFT X,(e N ) was obtained by sampling X(eW) at N equally spaced points on the unit circle. Determine xl[n] in terms of x[n]
Let x[n] be infinite-duration sequence with DTFT of 2n X(e'"), Xi[n] is an N-point finite-duration sequence whose DFT X,(e N ) was obtained by sampling X(eW) at N equally spaced points on the unit circle. Determine xl[n] in terms...
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...
9. Consider a 20-point finite-duration sequence x[n] such that xfn]-0 outside 0 snSI (a) Ifit is desired to evaluate X(e/o) at o 4x/S by computing one M-point DFT point DFT dete the smallest possible M, and develop a method to obtain X(eo) at 4x smallest M.
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
Problem 10: a) Given the following sequence: x[n]={1, 2, 3, 4} where x[?= 1. Use the decimation in time FFT algorithm to compute the 4-point DFT of the sequence X[k]. Draw the signal flow & the butterfly structure and clearly label the branches with the intermediate values and the twiddle factors W = e- /2nk b) The inverse discrete Fourier transform can be calculated using the same structure and method but after appropriately changing the variable WN and multiplying the...
Exercise 4. Computing and displaying the Fourier Transform of a signal Later in the semester it will become useful to determine the frequency response of a signal or system by taking the Fourier Transform empirically (rather than computing it analytically). To do so we make use of the fft and fftshift commands. The fft command is an efficient implementation of the Discrete Fourier Transform (DFT) known as the Fast Fourier Transform (FFT). When the FFT is computed the samples are...
[20 total pts) Consider the sequences x1n] = { 1, 2,-2, 1}, and x2 [n] = { 1, 2,-2, 1, 0, 0, 0, 0). The sequence x2In] is known as a zero-padded version of x,[n]. When answering the questions below, please use Table 1, provided on Page 3. a. [3 pts] Compute X1(eo), the Discrete-Time Fourier Transform (DTFT) of x1 [n], and evaluate it for the following values of normalized frequency: a-63 笎哮,쯤뀨 write the values in the table b....
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