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Signals and Systems
Problem 1: Given: x[n] = [0 0 2 -2] y[n] = [1 0...
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)
Problem 3 20 points Let f[n]- 1,2,1,0 Use MATLAB to compute the DFT F[k] and turn in the some com...
Problem 3 20 points Let f[n]- 1,2,1,0 Use MATLAB to compute the DFT F[k] and turn in the some comments and inclilcle the answer % Compute DFT from FFT x-[1 2 1 0] N-length(x) F-fft(x,N)
Problem 3 20 points Let f[n]- 1,2,1,0 Use MATLAB to compute the DFT F[k] and turn in the some comments and inclilcle the answer % Compute DFT from FFT x-[1 2 1 0] N-length(x) F-fft(x,N)
Digital processing signals For SYSTEM 4", characterized by: y(n) x(n) - x(n-2) + 0.2 y(n-1)-0.04 y(n-2)...
Digital processing signals
For SYSTEM 4", characterized by: y(n) x(n) - x(n-2) + 0.2 y(n-1)-0.04 y(n-2) a) Draw its block diagram b) b.1 - Obtain its transfer function H(z) b.2-Calculate and PLOT | H(e*)l, for θ 0, π/4. π/2. 3π/4, and π. Obtain and plot its poles and zeros, in the z-plane c)
Suppose the sequence x(n) = 5 * n-15, n-0,-. . , 16 is the input to...
Suppose the sequence x(n) = 5 * n-15, n-0,-. . , 16 is the input to the filter with the impulse response h(n) = (2,5,1). (a) Compute the output y/i(n) using MATLAB. ] help (numbers). b) Use the overlap-save method to compute the filter output using MATLAB. Suppose L 5 new data points are employed in each block. Use MATLAB function ovrlpsav ] help (numbers). What is the filter size? help (numbers). What is the block size (the size of...
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...
signal & system cours Signals and Systeme Q2 b) Given two signals x1(n)=[-1 2 0 -2...
signal & system cours
Signals and Systeme Q2 b) Given two signals x1(n)=[-1 2 0 -2 l) and x3[n] = [5 -4 0 4 -51 (5 Marks) Prove that sum of two signals is an odd signal. Prove that the product of two signals is an even signal. 1) 1 Signals and Systems Q5 b) How can you derive the Discrete-Time Fourier transform from the z-transform? (5 marks)
Problem 4. The goal of this problem is to compute y(n)-x(n)'h(n) when xin)- (2, 0, 1)...
Problem 4. The goal of this problem is to compute y(n)-x(n)'h(n) when xin)- (2, 0, 1) and h(n)- 1, 34) Find the length of yin) Use the "brute-force" table method presented in class to determine y(n) Show all work to earn credit. Your answer should be: yn) (2 2 5 9 3 4) a. b. Problem 5. Repeat the previous problem but now using the signals given by: x(n) - 1.1,1 1, 1) and h(n)- u 2, 1). Be y...
Prob.1.(6pts) Compute the 4-point i) (3pts) DFT for x(n)-l-5 4-7 -2] ii) (3pts) IDFT for X(k)-1-10...
Prob.1.(6pts) Compute the 4-point i) (3pts) DFT for x(n)-l-5 4-7 -2] ii) (3pts) IDFT for X(k)-1-10 2-j6 -14 2+j6] Prob. 2. (5pts) i) (3pts)Derive the 4-point DIT (Decimation-InTime) FFT and draw its signal-flow graph representation. ii) (2pts) Using the signal-flow graph representations of the 4-point DIF FFT, calculate the 4-point DFT of X(k) for x(n)-1-5 4-7-2].
shown that the discrete Pourier transform(DFT) of a time-varying process h(4) for (k = 0, 1, 2, . .. ,N-1), is give...
shown that the discrete Pourier transform(DFT) of a time-varying process h(4) for (k = 0, 1, 2, . .. ,N-1), is given by N-1 Choosing N-8 carry out the Cooley-Tukey formulation of FFT by following the steps below. (a) Write the expressions for DFT H, in terms of hite) and the inverse DFT h(te) in terms of H, for N 8 (b) Define W-ca/N and rewrite (a) using W (c) Express (b) in matrix form. (d) Express n and k...
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.
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)
Problem 3 20 points Let f[n]- 1,2,1,0 Use MATLAB to compute the DFT F[k] and turn in the some comments and inclilcle the answer % Compute DFT from FFT x-[1 2 1 0] N-length(x) F-fft(x,N)
Problem 3 20 points Let f[n]- 1,2,1,0 Use MATLAB to compute the DFT F[k] and turn in the some comments and inclilcle the answer % Compute DFT from FFT x-[1 2 1 0] N-length(x) F-fft(x,N)
Digital processing signals
For SYSTEM 4", characterized by: y(n) x(n) - x(n-2) + 0.2 y(n-1)-0.04 y(n-2) a) Draw its block diagram b) b.1 - Obtain its transfer function H(z) b.2-Calculate and PLOT | H(e*)l, for θ 0, π/4. π/2. 3π/4, and π. Obtain and plot its poles and zeros, in the z-plane c)
Suppose the sequence x(n) = 5 * n-15, n-0,-. . , 16 is the input to the filter with the impulse response h(n) = (2,5,1). (a) Compute the output y/i(n) using MATLAB. ] help (numbers). b) Use the overlap-save method to compute the filter output using MATLAB. Suppose L 5 new data points are employed in each block. Use MATLAB function ovrlpsav ] help (numbers). What is the filter size? help (numbers). What is the block size (the size of...
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...
signal & system cours
Signals and Systeme Q2 b) Given two signals x1(n)=[-1 2 0 -2 l) and x3[n] = [5 -4 0 4 -51 (5 Marks) Prove that sum of two signals is an odd signal. Prove that the product of two signals is an even signal. 1) 1 Signals and Systems Q5 b) How can you derive the Discrete-Time Fourier transform from the z-transform? (5 marks)
Problem 4. The goal of this problem is to compute y(n)-x(n)'h(n) when xin)- (2, 0, 1) and h(n)- 1, 34) Find the length of yin) Use the "brute-force" table method presented in class to determine y(n) Show all work to earn credit. Your answer should be: yn) (2 2 5 9 3 4) a. b. Problem 5. Repeat the previous problem but now using the signals given by: x(n) - 1.1,1 1, 1) and h(n)- u 2, 1). Be y...
Prob.1.(6pts) Compute the 4-point i) (3pts) DFT for x(n)-l-5 4-7 -2] ii) (3pts) IDFT for X(k)-1-10 2-j6 -14 2+j6] Prob. 2. (5pts) i) (3pts)Derive the 4-point DIT (Decimation-InTime) FFT and draw its signal-flow graph representation. ii) (2pts) Using the signal-flow graph representations of the 4-point DIF FFT, calculate the 4-point DFT of X(k) for x(n)-1-5 4-7-2].
shown that the discrete Pourier transform(DFT) of a time-varying process h(4) for (k = 0, 1, 2, . .. ,N-1), is given by N-1 Choosing N-8 carry out the Cooley-Tukey formulation of FFT by following the steps below. (a) Write the expressions for DFT H, in terms of hite) and the inverse DFT h(te) in terms of H, for N 8 (b) Define W-ca/N and rewrite (a) using W (c) Express (b) in matrix form. (d) Express n and k...
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.
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