%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % fourier_series.m % % Euler Method Example % % Created by : Brenden Epps, bepps@mit.edu, 28 February 2007 % % 2.23 - Hydrofoils & Propellers % % % % All rights reserved % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear, close all, clc, set(0,'DefaultFigureWindowStyle','docked') set(0,'defaultaxesfontsize',14); linewidth = 1.5; %%%%%%%%%%%%% Fourier Series example %%%%%%%%%%%%%%%%%%%%%%%%% % % Find the Fourier series representation for f(x) = x on x=[-pi,pi]. % (i.e. saw-tooth wave) % % f(x) = 1/2 a_0 + sum(a_n*cos(nx)+b_n*sin(nx)) %%% solve for a single value of delta_t %%% X = -pi:0.01:pi; figure plot(X,X,'k','LineWidth',linewidth), xlabel('x','Fontsize',14), ylabel('f(x)','Fontsize',14), title('f(x)','Fontsize',16) hold on; a_0 = 0; f = (1/2)*a_0; for n = 1:20 a(n) = 0; b(n) = 2*(-1)^(n+1)/n; f = f + a(n)*cos(n*X) + b(n)*sin(n*X); plot(X,f,'r') pause end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % t = 0:0.001:0.6; % x = sin(2*pi*50*t)+sin(2*pi*120*t); % y = x + 2*randn(size(t)); % plot(1000*t(1:50),y(1:50)) % title('Signal Corrupted with Zero-Mean Random Noise') % xlabel('time (milliseconds)') % % Y = fft(y,512); % % Pyy = Y.* conj(Y) / 512; % % f = 1000*(0:256)/512; % plot(f,Pyy(1:257)) % title('Frequency content of y') % xlabel('frequency (Hz)')