![4. (12 points) (a) (4 points) Let x[n] = {1,2, 1, 2} and h[n] = {1,-1,1, -1} be two length-4 sequences defined for 0 <n<3. De](http://img.homeworklib.com/questions/fa3994d0-0ba7-11ec-b345-d111646530b3.png?x-oss-process=image/resize,w_560)
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![no ¥13 ) = Ê yen) e-*3n 2 -2 +22353 #2)-37572 000 = -2 +27 +2 -2; .: Y(K) = { 0,0,-8,0} (0) YDERT 2(k) z X (K? H[K] XFK1{ 6](http://img.homeworklib.com/questions/fd973420-0ba7-11ec-a610-01e0b5320e5a.png?x-oss-process=image/resize,w_560)
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4. (12 points) (a) (4 points) Let x[n] = {1,2, 1, 2} and h[n] =...
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to...
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to this system is the signal rn: ?[n-1) (a) Sketch h[n] and r[n] (b) Determine the output of the systern, ylnj, using convolution. Sketch y[n] (c) Determine the DTFTs H(e) and X(e. Make fully-labeled sketches of the magni- tudes of these DTFTs (d) Recall that the discrete Fourier transform (DFT) is simply defined as samples of the discrete-time Fourier transform (DTFT). Compute the 4-point (N-4)...
12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5...
12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5 sequence whose 5-point DFT, Gk], is made from uniform samples from X(eu): g[n] CH 0 for n<0and n > 4 = x(e,2 ) for k = 0, 1, 2,3,4 = Find g(0] and gl1].
12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5 sequence whose 5-point DFT, Gk], is made from uniform samples...
For x(n) = {1,2,3} and h(n) = (1,1), find the linear convolution y(n) =x(n)*h(n)
For x(n) = {1,2,3} and h(n) = (1,1), find the linear convolution y(n) =x(n)*h(n) using DFT and inverse DFT. Use the following formula.
2. (20 points) Let input x(n) (1 0 0) and impulse response h(n) (1 0). Each...
2. (20 points) Let input x(n) (1 0 0) and impulse response h(n) (1 0). Each has length of N-3 and N 2, respectively. Append zeros to x(n) and h(n) to make the length of both equal to N+N-1 Find the output y(n) by using the DFT and the inverse DFT method.
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...
5.34. Two signals æ[n] and h[n] are given by - 3, 4, 1, 6 arn]{2, t...
5.34. Two signals æ[n] and h[n] are given by - 3, 4, 1, 6 arn]{2, t n 0 h[n1, 1, , 0, 0} t n 0 Compute the circular convolution y[n] x[n]h[n] through direct application of the circular convolution sum a. b. Compute the 5-point transforms X k] and H[k] c. Compute Y[k] Xk] Hk, and the obtain y[n] as the inverse DFT of Y [k. Verify that the same result is obtained as in part (a)
1. Suppose length-4 discrete-time signalan) and h(n) have discrete Fourier transforms X and H. Xx =...
1. Suppose length-4 discrete-time signalan) and h(n) have discrete Fourier transforms X and H. Xx = 1,2,3,1 HR = 2,3,1,4, for k = 0,1,2,3. If y[n] = xinhin, find its discrete Fourier transform, Y.
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Pr...
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Provide a closed-form expression for the 8-point DFT of hin], de- (b) Consider the sequence xIn of length L 8 below, equal to a sum noted by H8 , as a function of k. Simplify as much as possible. of several finite-length sinewaves: n] is formed by computing X,lk as an 8-point DFT of n), Hslk) as an 8-point DFT of...
Using the 4-point DFT/IFFT in matrix form, determine: (a) The DFT of x[n] = [1, 2,...
Using the 4-point DFT/IFFT in matrix form, determine: (a) The DFT of x[n] = [1, 2, 1, 2]. (b) The IDFT of X[k] = [0, 4, 0, 4];
1. Let [n] = 6 cos(0.8nn). Note that [n] is periodic. (a) Find the period N...
1. Let [n] = 6 cos(0.8nn). Note that [n] is periodic. (a) Find the period N of 1 [n). (b) Let y[n] = [n(u[n] – z[n-N]). Find Y [k] = DFT(y[n]), k=0,1,..., N-1. Hint: x[n] = 3e08an + 3e-j0.8an (e) Find X(W) = DTFT (2[12]). How does it compare with part (b)? (a) Sketch 1 [n],y[n], X(w), Y [k]. 2. (a) Sketches in the 2D complex plane for n = 0,1,...,8. (b) Let i[n] = +2e ", n=0,1,...,8. Find X[k]...
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to this system is the signal rn: ?[n-1) (a) Sketch h[n] and r[n] (b) Determine the output of the systern, ylnj, using convolution. Sketch y[n] (c) Determine the DTFTs H(e) and X(e. Make fully-labeled sketches of the magni- tudes of these DTFTs (d) Recall that the discrete Fourier transform (DFT) is simply defined as samples of the discrete-time Fourier transform (DTFT). Compute the 4-point (N-4)...
12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5 sequence whose 5-point DFT, Gk], is made from uniform samples from X(eu): g[n] CH 0 for n<0and n > 4 = x(e,2 ) for k = 0, 1, 2,3,4 = Find g(0] and gl1].
12. Let X(e") be the DTFT of the discrete-time signal z[n] = (0.5)"u[n]. Let gin] be the length-5 sequence whose 5-point DFT, Gk], is made from uniform samples...
2. (20 points) Let input x(n) (1 0 0) and impulse response h(n) (1 0). Each has length of N-3 and N 2, respectively. Append zeros to x(n) and h(n) to make the length of both equal to N+N-1 Find the output y(n) by using the DFT and the inverse DFT method.
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...
5.34. Two signals æ[n] and h[n] are given by - 3, 4, 1, 6 arn]{2, t n 0 h[n1, 1, , 0, 0} t n 0 Compute the circular convolution y[n] x[n]h[n] through direct application of the circular convolution sum a. b. Compute the 5-point transforms X k] and H[k] c. Compute Y[k] Xk] Hk, and the obtain y[n] as the inverse DFT of Y [k. Verify that the same result is obtained as in part (a)
1. Suppose length-4 discrete-time signalan) and h(n) have discrete Fourier transforms X and H. Xx = 1,2,3,1 HR = 2,3,1,4, for k = 0,1,2,3. If y[n] = xinhin, find its discrete Fourier transform, Y.
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Provide a closed-form expression for the 8-point DFT of hin], de- (b) Consider the sequence xIn of length L 8 below, equal to a sum noted by H8 , as a function of k. Simplify as much as possible. of several finite-length sinewaves: n] is formed by computing X,lk as an 8-point DFT of n), Hslk) as an 8-point DFT of...
1. Let [n] = 6 cos(0.8nn). Note that [n] is periodic. (a) Find the period N of 1 [n). (b) Let y[n] = [n(u[n] – z[n-N]). Find Y [k] = DFT(y[n]), k=0,1,..., N-1. Hint: x[n] = 3e08an + 3e-j0.8an (e) Find X(W) = DTFT (2[12]). How does it compare with part (b)? (a) Sketch 1 [n],y[n], X(w), Y [k]. 2. (a) Sketches in the 2D complex plane for n = 0,1,...,8. (b) Let i[n] = +2e ", n=0,1,...,8. Find X[k]...
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