代做Mathematics、代写Matlab程序设计、代写amplitude spectrum、代做Matlab编程帮做R语言编程|调试

Methods of Applied Mathematics 1— Assignment 2SP2, 2018Due Date: 4:00 pm, 31 May, 2018.oooOoooPlease consult the Course Outline on the web page for this course for details of how to submityour assignment, and penalties for late presentation.Make sure to relate on the front page of your assignment any information about help given/receivedfor any of the questions you attempted, who received/gave help, and to reference any sources otherthan the notes and exercises for the course. You need to turn in your Matlab code (but you donot need to turn in the code in a disc). Cheers, Jorge.oooOooo1. Consider the signalf(t) = {0, t etsin t, t ≥ 0.(a) Draw a picture of this signal over a suitable range for t, and classify the signal asodd, even, or neither. (You may use MATLAB. If so, include your code.)(b) Find the Fourier Transform fb(α) for this signal. Simplify your answer.(c) Use MATLAB to draw the amplitude spectrum of f over an appropriate spectralrange. (That is, draw |fb(α)|.) [20 marks]2. Consider the signalf(t) = 13cos(3t) + 2 sin(6t) ? sin(8t).(a) What is the highest angular frequency present in this signal? What is the highestnumerical frequency present in this signal?(b) What is the Nyquist rate for this signal? Did you use the angular or the numericalfrequency?(c) If you sample this signal with sampling period T, which values of T may you chooseto be in accordance with the Nyquist rate? Choose and fix one such T.(d) After sampling you pass the sampled signal through a low-pass filter. Which thresholdM0 can be used in the low-pass filter?[3 marks each = 12 marks]3. Consider the time-limited signalf(t) =�0, t etsin t, π ≤ t ≤ π;0, t > π.(a) Use MATLAB to plot the signal for ?4 ≤ t ≤ 4.(b) Use MATLAB to plot the amplitude spectrum |fb(α)| over the range ?5 ≤ α ≤ 5.(c) We will arbitrarily pick M = 4, and try to use Shannon’s formula to sample andreconstruct f. By looking at the graph of |fb(α)| (or by magni代做Mathematics留学生作业、代写Matlab程序设计作业、代写amplitude spectrum作业、代做Mfying that graph), whatis the amplitude of the frequencies we are cutting out?(d) Fix M = 4, and treat it as the highest frequency in the signal f (although it reallyisn’t). What would be the Nyquist rate in this case? Which sampling period T wouldthen be appropriate? Choose a sampling period T, and fix it.(e) Choose an appropriate value M0 > 0 to serve as the low-pass filter threshold forthe sampled signal. What is the minimum value that M0 can have? What is themaximum value to avoid aliasing (in theory)? Choose your M0 and fix it.(f) Using the values of M0 and T chosen/obtained above, try to use Shannon’s SamplingFormula to reconstruct the signal f. (This is a MATLAB exercise.) Plot the reconstructedsignal by itself, then plot it superimposed over the original signal f. Includeyour code in your answer.[25 marks]4. Use the Laplace Transform method to solve the following differential equation problem:y′′(t) y(t) = sin(2t), y(0) = 0, y′(0) = 1.[15 marks]5. Use the z-transform method to solve the following difference equation:y[n + 2] = 2y[n + 1] + 8y[n], y[0] = 0, y[1] = 1.[15 marks]6. Suppose Φ is a uniform random variable on the interval [0, 2π].(a) What is the density f of Φ?(b) Use the formulaE[g(Φ)] = ∫ ∞∞g(x)f(x) dxto compute E[sin(3 + Φ)].(c) Compute E[ejΦ].[13 marks]Bonus Question. This is an Internet search bonus question. Let’s look at the stars. Thechemical composition of our sun (the one we see during the day) is given in this table:Element Hydrogen Helium Oxygen Carbon Nitrogen Silicon Magnesium Neon Iron SulphurMass % 71.0 27.1 0.97 0.40 0.096 0.099 0.076 0.058 0.014 0.040(Source: https://www.thoughtco.com/element-composition-of-sun-607581)How do we know this? Search the web and find an explanation based on the observedproperties of light emitted by our sun. Reference your sources carefully.This is a subjective question to mark. For full marks (5 marks at most), try to make yourexplanation as clear as possible.转自：http://ass.3daixie.com/2018121218788236.html