Consider the function -1.0<xso x, (a) Find the Fourier series of the function f(x (b) Use any graphing software to plot the function f (x) (c) Graph the partial sums S (x) for N 1,2,3,5,10,20,50 in ONE graph (d) Analyse your results. END Consider the function -1.0
Consider the function -1.0xs0 0cxs2 x: 2 + 2x-x": 2: (x) = (a) Find the Fourier series of the function(x) (b) Use any graphing software to plot the function ,f(x). (c) Graph the partial sums S (x) for N 1,2,3,5,10,20,50 in ONE graph (d) Analyse your results. Consider the function -1.0xs0 0cxs2 x: 2 + 2x-x": 2: (x) = (a) Find the Fourier series of the function(x) (b) Use any graphing software to plot the function ,f(x). (c) Graph the...
11.1 and 11.2 Fourier Series Q1 Find the Fourier series of the given function f(x), which is assumed to have the period 2π. Show the details of your work. Sketch or graph the partial sums up to that including cos 5x and sin 5x. Note: Plot the partial sum using MATLAB. Hint: Make use of your knowledge of the line equation to find f(x) from the given graph. -π 0 11.1 and 11.2 Fourier Series Q1 Find the Fourier series...
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier coefficients for the function f(x)-9, 0, TL b. Use the computer to draw the Fourier sine series of f(x), for x E-15, 151, showing clearly all points of convergence. Also, show the graphs with the partial sums of the Fourier series using n = 5 and n = 20 terms. (1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier...
Please answer "b" only. %Example code function plotFS(m); %m = user provided number of terms desired in the Fourier series; %this code computes the Fourier series of the function %f(x)=0, for -pi<= x <0, % =cos(x) for 0<= x <pi %generate the interval from -pi to pi with step size h; h = pi/100; xx1=[-pi:h:0]; xx2=[0:h:pi]; xx = [xx1, xx2]; %generate the given function f so that it can be graphed ff = [zeros(size(xx1)), cos(xx2)]; %compute the first partial sum...
Consider the function y = x2 for x E (-7,7) . a) Show that the Fourier series of this function is n cos(nz) . b) (i) Sketch the first three partial sums on (-π, π) (ii) Sketch the function to which the series converges to on R . c) Use your Fourier series to prove that 2and1)"+1T2 12 2 2 Tu . d) Find the complex form of the Fourier series of r2. . e) Use Parseval's theorem to prove...
Find Fourier coefficients for the following function defined on x E [-π, π] Plot the original function and the first three partial sums of the Fourier series S1, S2, S3 on the same plot. Partial sum Sn is the sum of all contributions from the frequencies less than or equal to n, i.e. Sn(x) = a0+ Σ 1 (ak cos(kx) +br sin(kx)) Find Fourier coefficients for the following function defined on x E [-π, π] Plot the original function and...
k for 2 5. Consider the function f(x) = 37T 0 for 2 Hint: See examples of functions of a generic period t; James, 4th ed. pg. 581, Ex. 7.7 & 7.8 (a) State wether it has even or odd symmetry (b) Find the Fourier series representation for f. Plot graphs of the first three partial sums SI (c) Using the result in part (b), show that 1 + 1 +.. 7 4 k for 2 5. Consider the function...
12-21 FOURIER SERIES Find the Fourier series of the given function f(x), which is assumed to have the period 2T. Show the details of your work. Sketch or graph the partial sums up to that including cos 5x and sin 5x. 9. f(x) - 12-21 FOURIER SERIES Find the Fourier series of the given function f(x), which is assumed to have the period 2T. Show the details of your work. Sketch or graph the partial sums up to that including...
Please solve for part (b) and (c) thank you! 1. Consider the function f(x) = e-x defined on the interval 0 < x < 1. (a) Give an odd and an even extension of this function onto the interval -1 < x < 1. Your answer can be in the form of an expression, or as a clearly labelled graph. [2 marks] (b) Obtain the Fourier sine and cosine representation for the functions found above. Hint: use integration by parts....