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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. Determine the circular convolution of length-4 y[n] = x[n] 4 hin). (b) (6 points) Find the 4-point discrete Fourier transform (DFT) X[k], H[k], and Y[k]. (c) (2 points) Find the 4-point inverse DFT (IDFT) of Z[k] = {X[k]H[k].
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11. [5pts. Each] Let V = (1,-1,1), 12 =(2,1,3) and is =(-1,-1,2) be eigenvectors of the matrix A corresponding eigenvalue 4 = 2, =-2 and 1=3, respectively, and let v = (5.0,3) a. Express 1 as a linear combination of . 1, and is. b. Find Av.
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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1) A charge, g1, of -8 micro-coulombs is located at the origin, a charge, q2, of -5 micro-coulombs is located at x- 0 cm, y +8.6 cm, a charge, q3, of +8 micro-coulombs is located at...
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5. Let {h}n=o be a stochastic process and T be a random variable whose values are non-negative integers. Suppose that a random variable T is such that for each n the event (T 2 n) depends only on Yo, Y,...,Yn. Is T necessarily a Markov time with respect to (Y,)?
5. Let {h}n=o be a stochastic process and T be a random variable whose values...
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A charge, q1, of +10 micro-coulombs is located at x-o, y-8.8 cm, a charge q2 of -45 micro-coulombs is located at x-0, y -2 cm, an unknown charge of q3, is located at x-4.1 cm, y 0 cm, and a charge, q4, -7 micro- coulombs is located at x-...
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4. (a) let x[n] be a finite duration signal of duration N. Let y[n] = DFT(DFT(a[n])). All DFTs are N point DFTs. Find vinl in termas of rinl Prove all the properties you use in arriving at your result (b) Let an] and yIn] be sequences of duration N with...
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Question 39 1 pts A positively charged particle is moving to the right in the plane of this paper. A magnetic field points upward toward the top in the plane of this paper. The magnetic force on the charged points out of the screen toward you. upward in the plane of the screen. to the...
Please read the directions carefully and answer all questions. Read 1B, but do not answer it because I provided an answer that is correlated to 1C, so please just answer 1c. 1b) Suppose you work at a furniture or electronics store - name one potential benefit and one potential cost your customers may experience that could impact how they value your product. - I picked a furniture store. 1c) How might your firm (from part 1b) deliver value beyond an...
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Q3. Consider a causal LTI system whose input and output are related by the following differential equation: dy(t) +4y(t) x(t) dt and the input is x(t) cos(2Tut) sin(4t), find: (a) The transfer function of the system H(ja) (5 m) (5 m) (10 m) (5 m) (b) The impulse response of the system h(t) (c) The output y(t) (d) The power of y(t)