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Homework Answers
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elsewhere elsewhere 6. Convolution between two discrete time signals, #1 [n] and 12[n] is given by:...
Let x[n] and y[n] be periodic signals with common period N, and let z[n] = {...
Let x[n] and y[n] be periodic signals with common period N, and let z[n] = { x[r]y[n – r) r=<N> be their period convolution. Let z[n] = sin(7") and y[n] = { . 0 <n<3 4 <n <7 Asns? be two signals that are periodic with period 8. Find the Fourier series representation for the periodic convolution of these signals.
(a) Find the convolution of these two signals, and sketch the result.
Circular vs. Linear ConvolutionConsider sequences(x[0], x[1], x[2], x[3], x[4], x[5], x[6], x[7])=(1,1,1,1,0,0,0,0)and(h[0], h[1], h[2], h[3], h[4], h[5], h[6], h[7])=(1,2,3,4,3,2,1,0)where x[n]=0 for n ∉\{0, …, 7\} and h[n]=0 for n ∉\{0, ..., 7\}.(a) Find the convolution of these two signals, and sketch the result.(b) Find the 8-point circular convolution of these two signals, and sketch the result.(c) Assume that each of the signals has been zero padded up to a length 16. Find the 16 -point circular convolution of these two...
Solution required in MATLAB 1. Convolution and Discrete-Time Fourier Series (DTFS) (a) Generate a periodic signal r2[n]...
Solution required in MATLAB
1. Convolution and Discrete-Time Fourier Series (DTFS) (a) Generate a periodic signal r2[n] with the fundamental period N ralla-sin(2nn/ İ0) + sin(2m, 2 ) + sin(2nn/30) for 0 < n < N-1 Find the fundamental frequency Ω0-2, N, with the fundamental period N. (b) Generate a periodic signal h2[n] with the fundamental period N haln] = (1/2)", for 0 < n < N-1 (e) Using the com ftuction n Matab, compute the compvolution (d) Using the...
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)
Find the discrete-time Fourier Series for the following periodic signals: 3. 4 cos 2.4n n +...
Find the discrete-time Fourier Series for the following periodic signals: 3. 4 cos 2.4n n + 2 sin 3.2n n x[n] a. xn 0 12 15 6 b. xn 2N No 2N C.
my id is 1633168 Given the two signals x,(n) = [a , b, c) 1 x,(n)...
my id is 1633168
Given the two signals x,(n) = [a , b, c) 1 x,(n) = [ your ID number] RO 0 If y(n) = x;(n) * x2(n) [ convolution sum] and if you know that y(0)=3, y(1)= -5, y(2)=8, find y(5). Enter your answer
Find the convolution of the following two signals: X(t) ylt). Plot the resulting signal. 1. 0...
Find the convolution of the following two signals: X(t) ylt). Plot the resulting signal. 1. 0 x (t) y (t)
3) (25 points) Consider the following discrete-time aperiodic signals. x(n) 3 2 1 n x(n) 3...
3) (25 points) Consider the following discrete-time aperiodic signals. x(n) 3 2 1 n x(n) 3 2 1 -1 x(n) 6 4 2 a. (15 points) Compute the Fourier transform X(w). b. (5 points) Write down all the characteristics and properties of X(w). c. (5 points) Explain the limitations of X(w) if it should be compute using a microprocessor. What is the solution?
2.6 Let x(t) and y(t) be two periodic signals with period To, and let X, and...
2.6 Let x(t) and y(t) be two periodic signals with period To, and let X, and yn denote the Fourier series coefficients of these two signals. Show that 7. Le***0*n di = § 00 2.7 Show that for all periodic physical signals that have finite power, the coefficients of the Fourier series expansion x,, tend to zero as n → .
Name: UIN: Course No 4. (20 points, 5 points each) Two finite length signals, nijej and rlel are given Let y(n] be the linear convolution of a ej and lal (a) Detemine yin) (b) Ifwe execute the fol...
Name: UIN: Course No 4. (20 points, 5 points each) Two finite length signals, nijej and rlel are given Let y(n] be the linear convolution of a ej and lal (a) Detemine yin) (b) Ifwe execute the following Matlab script to get yiin what is ynn List all values in y(n) p-ifftfh,8).h,8)),8)% (hint: 8-point circular convolution) (c) Ifwe execute the following Matlab script to get yinl what is ylm? List all values in yin n- ifhiiff,10)ffhc,10)),10)(hint: 10-point circular convolution) Write...
Let x[n] and y[n] be periodic signals with common period N, and let z[n] = { x[r]y[n – r) r=<N> be their period convolution. Let z[n] = sin(7") and y[n] = { . 0 <n<3 4 <n <7 Asns? be two signals that are periodic with period 8. Find the Fourier series representation for the periodic convolution of these signals.
Solution required in MATLAB
1. Convolution and Discrete-Time Fourier Series (DTFS) (a) Generate a periodic signal r2[n] with the fundamental period N ralla-sin(2nn/ İ0) + sin(2m, 2 ) + sin(2nn/30) for 0 < n < N-1 Find the fundamental frequency Ω0-2, N, with the fundamental period N. (b) Generate a periodic signal h2[n] with the fundamental period N haln] = (1/2)", for 0 < n < N-1 (e) Using the com ftuction n Matab, compute the compvolution (d) Using the...
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)
Find the discrete-time Fourier Series for the following periodic signals: 3. 4 cos 2.4n n + 2 sin 3.2n n x[n] a. xn 0 12 15 6 b. xn 2N No 2N C.
my id is 1633168
Given the two signals x,(n) = [a , b, c) 1 x,(n) = [ your ID number] RO 0 If y(n) = x;(n) * x2(n) [ convolution sum] and if you know that y(0)=3, y(1)= -5, y(2)=8, find y(5). Enter your answer
Find the convolution of the following two signals: X(t) ylt). Plot the resulting signal. 1. 0 x (t) y (t)
3) (25 points) Consider the following discrete-time aperiodic signals. x(n) 3 2 1 n x(n) 3 2 1 -1 x(n) 6 4 2 a. (15 points) Compute the Fourier transform X(w). b. (5 points) Write down all the characteristics and properties of X(w). c. (5 points) Explain the limitations of X(w) if it should be compute using a microprocessor. What is the solution?
2.6 Let x(t) and y(t) be two periodic signals with period To, and let X, and yn denote the Fourier series coefficients of these two signals. Show that 7. Le***0*n di = § 00 2.7 Show that for all periodic physical signals that have finite power, the coefficients of the Fourier series expansion x,, tend to zero as n → .
Name: UIN: Course No 4. (20 points, 5 points each) Two finite length signals, nijej and rlel are given Let y(n] be the linear convolution of a ej and lal (a) Detemine yin) (b) Ifwe execute the following Matlab script to get yiin what is ynn List all values in y(n) p-ifftfh,8).h,8)),8)% (hint: 8-point circular convolution) (c) Ifwe execute the following Matlab script to get yinl what is ylm? List all values in yin n- ifhiiff,10)ffhc,10)),10)(hint: 10-point circular convolution) Write...
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