System frequency response via fft
3 views (last 30 days)
Show older comments
Dear all,
I am trying to determine system response with given input and output and using the system response to determine an other pair of input for a given output.
Mathematically,
System frequency response F(h)=(F(y1))/(F(x1))
where F Fourier transform
h system response
x1 top hat input
y1 system output, assumed guassian
y2 required output, top hat
x2 input to be determined
F(x2)=(F(y2))/(F(h))=(F(y2).F(x1))/(F(y1))
x2=ifft((F(y2).F(x1))/(F(y1)))
I am doing fourier transform using fft and getting strange x2 curve. Not sure what I am doing wrong.I am using the following code. Many thanks for the anticipated response.
close all
% sampling size
step_num = 100;
% x range to define the curves
x_max = 50;
x_margin = 20;
% sampling frequency
fs = step_num/(x_max+x_margin);
fx = (0:step_num-1)/step_num*fs;
% x linespace
x = linspace(0,x_max+x_margin,step_num);
% x1 top hat profile
x1 = x<=x_max; % x1 is one for Ex less than x_max and zero afterwards
x1_f = (fft(x1,step_num)/step_num);
% y1 guassian
y1 = exp(-(0.05*x).^2);
% fourier conversion
y1_f = (fft(y1,step_num)/step_num);
% y2 req: top hat profile
y2 = x<=x_max; % x1 is one for Ex less than x_max and zero afterwards
y2_f = (fft(y2,step_num)/step_num);
% determining fourier of required input
x2_f = (y2_f).*(x1_f)./(y1_f);
x2 = real(ifft(x2_f));
% curve plot
figure
plot(x,x2,'Color','green','LineWidth',2);
hold on
plot(x,x1,'Color','black','LineWidth',2);
plot(x,y1,'Color','blue','LineWidth',2);
xlabel('Radial coordinate','fontsize',12);
ylabel('Intensity','fontsize',12);
legend('Required input x2','Input x1','Output y1')
axis([0 70 0 1.1])
0 Comments
Answers (0)
See Also
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!