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\fWrite a MATLAB script that does the following: When the signal g ( t ) goes through a filter h ( t ) where the frequency domain definition of the filter is: 5 @ . @ S 20 H(@) = 0. elsewhere the results in a time domain output signal: m( t). (a) Using convolution theorem, calculate the frequency domain output signal M (w). Plot the magnitude and phase of M(w) in a 2x1 subplot for the interval W=-31. 4:0.01:31.4. (b) Evaluate m( t ) using the definition of Inverse Fourier Transformation. Plot Re(m(t) ) and Im(m( t) ) in a 2x1 subplot for the interval t=-100:0. 1: 100. Where g(t) is defined as: 8 (1) = ]G(w) du and G(@) is defined as: 2, 5 5 @ $10 G(w) = 0, elsewherePlease help write a MATLAB script for #3. 1. A time domain real-signal x ( t ) has a Fourier Transform property of x (w ) = X* (-W). Consider the following frequency domain description of a signal G ( W) : G(W)= 2, 5 5 w S10 0, elsewhere (a) Evaluate g (t ) using the definition of Inverse Fourier Transformation 8(1)= JG(we do Plot G(w), Re(g(t) ), and Im(g(t) ) in a 3x1 subplot for the interval W=-31. 4:0. 01:31 . 4 and t=-100:0. 1: 100. (b) Now consider Y ( W) =G(@-5 ) . Plot Y (w), Re (y (t) ), and Im(y (t) ) in a 3x1 subplot with the same intervals. (c) Are g ( t ) and y ( t ) real-signal or complex signal? 2. When the signal g ( t ) goes through a filter h ( t ) where the frequency domain definition of the filter is: H(@) = 5 0 , w S 20 0, elsewhere the results in a time domain output signal: m(t). (a) Using convolution theorem, calculate the frequency domain output signal M (w). Plot the magnitude and phase of M(w ) in a 2x1 subplot for the interval W=-31 . 4:0. 01:31.4. (b) Evaluate m( t ) using the definition of Inverse Fourier Transformation. Plot Re(m( t) ) and Im(m( t ) ) in a 2x1 subplot for the interval t=-100:0. 1 : 100.3. Calculate the energy of the output signal m( t ) for the time range t=-100:0. 1: 100. Also evaluate the energy of the output signal in frequency domain using Parseval's theorem (use the frequency range W=31 . 4:0. 01:31.4).\fScalar Operations and Order of Operations 2.3 Create MATLAB" code to perform the following calculations: 52 5+3 Figure P2.4(a) 5-6 V4+ 6 ( Hint: A square root is the same thing as a 1/2 power.) 6 #12 + 7-53+ 2 1 + 5-3/6 + 2 -4-1/5.5 Check your code by entering it into MATLAB and performing the calculations on your scientific calculator. 2.4 As you answer the following questions, consider the shapes shown in Figure P2.4. (a) The area of a circle is wr. Define ras 5, then find the area of a circle, using MATLAB . (b) The surface area of a sphere is 4wr. Find the surface area of a sphere with a radius of 10 ft. (c) The volume of a sphere is 4/3#r. Find the volume of a sphere with a radius of 2 ft. Figure P2.5 (a-c) 2.5 As you answer the following questions, consider the shape shown in Figure P2.5. (a) The area of a square is the edge length squared (A = edge?). Define the edge length as 5, then find the area of a square, using MATLAB" (b) The surface area of a cube is 6 times the edge length squared Figure P2.6 (SA = 6 X edge ). Find the surface area of a cube with edge length 10. The geometry of a barbell can (c) The volume of a cube is the edge length cubed ( V = edge ). Find the be modeled as two spheres volume of a cube with edge length 12.1. Use MATLAB to compute the following expressions: ( Double check your answers with a calculator] in a. *= 3(15 - 33) - 2475 12 14+16 7265 5 log.(1500) 590 0 b. V= - 137-69 c. sin() hint: the whole sine function is squared d. sit-a hint: only the value inside the sine function is squared a e - + 3.47 log( 14) + 1287\f4) MATLAB: Write a Matlab program to calculate the following questions, (Modified version of the problem in Probability and Statistics for Computer Scientists - Example 5.14 (Shared computer]). A supercomputer is shared by 600 independent subscribers. Each day, each subscriber uses the facility with probability 0.301. The number of tasks sent by each active user has Geometric distribution with parameter 0.15, and each task takes a Gamma(10, 3) distributed computer time (in minutes). Tasks are processed consecutively. (ANSWER TO THIS QUESTION IS NOT REQUIRED TO BE HANDWRITTEN a) What is the probability that all the tasks will be processed, that is, the total requested computer time is less than 60 hours? Estimate this probability, attaining the margin of error +0.01 with probability 0.99. (20 points) b) Create a graph for "the total requested computer time less than" vs "probability of the total requested computer time less than given value graph for 400, 500, 600 and 700 independent subscribers. Do not forget to put title, x axis and y axis labels similar to the figure given below. Also include screenshot of Matlab and source code in your report. (20 points) He blit Yew lment Pooh Deanop Window Heip Total Time vs Probability-Unit D. ULUSAR Probable 100 Total Time Less Than Ml