- 4 + 4, cost 20172) +EB, sine Write a m Matlab file to implement the Fourier Series of function f(x) = x on interval (-

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4 4 Cost 20172 Eb Sine Write A M Matlab File To Implement The Fourier Series Of Function F X X On Interval 1 (75.51 KiB) Viewed 40 times

- 4 + 4, cost 20172) +EB, sine Write a m Matlab file to implement the Fourier Series of function f(x) = x on interval (-1.7). Requirements: 2ηπχ 2nex 1. In the Fourier Series formula ''(x) = +4.cos - -), compute only first 20 2. T items. [In the class the example only summed the first 8 items.] 2. Compute 20 approximated functions: 4 2n2x 2nx 5)+B, sin [contain only 1st term of each summation) 2 T T 4. 2nex [contain first 2 terms of each summation] Y = S(x) = +ΣΑ, cost 2 т T 2;= f(x) = + 4, cosa 2ητα -Σ8, since - 4+ 2ηπχ, Vzo n = S(x) = 4 + 34,cosa 2nfix, +36 ) ΣΑ ΣΒ, sint- 2плх т + 2nex T (contain first 20 terms of each summation] 3. Compute 20 absolute errors between y = S(x) = x and each of 20 functions above. That is, 2n2x 2nxx 4 cos 5+B sint T T 2n2x 2плх, +ΣΒ, sint- T T e- es + X + , cosa - - - cs = 4 + 34.cos 2mpx + 3B . sina 2mpx - x 2ηπχ eo 2nex T 4. Plot (1) Create a figure in which there are two x-y planes aligned vertically. [Use subplot() to create such a figure. See the example I ever gave in the class] (2) Top x-y plane: plot 20 curves defined by y; = S(x), Y; = S(x)....930 = %.(x). The title is "Approximation of Fourier Series", x_label is x, y label is Fourier Series. (3) Bottom x-y plane plot 20 curves of absolute errors by e (x) ,e.(x) ...(x). The title is "Absolute error of Fourier Series",x label is x,y label is Absolute error.