Fourier transform of impulse function

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friet
friet 2017년 2월 28일
댓글: Hira Asghar 2018년 2월 25일
I calculated the Fourier transform of a pulse function(figure 1) Using the fft function. However The fft result if kind of weird. Can anyone check if my code is right. //Thanks
clc
clear all
close all
t1=7.0e-08;
sigma=1e-08;
t=linspace(0,4.0000e-7,1000);
P=exp(-(t-t1).^2./sigma.^2);
P_FT=fft(P); %fourier transform of P
figure(1)
plot(t*10^6,P);
grid on
xlabel('time[\mus]')
ylabel('amplitude[a.u]')
figure(2)
plot(P_FT);
grid on
  댓글 수: 1
Hira Asghar
Hira Asghar 2018년 2월 25일
Can u explain your signal 'p'?

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채택된 답변

Star Strider
Star Strider 2017년 2월 28일
편집: Star Strider 2017년 2월 28일
The Fourier transform of an impulse function is uniformly 1 over all frequencies from -Inf to +Inf. You did not calculate an impulse function.
You calculated some sort of exponential function that will appear as an exponential function in the Fourier transform.
Your slightly modified code:
t1=7.0e-08;
sigma=1e-08;
L = 1000;
t=linspace(0,4.0000e-7,L);
Ts = mean(diff(t));
Fs = 1/Ts;
Fn = Fs/2;
P=exp(-(t-t1).^2./sigma.^2);
P_FT=fft(P)/L; %fourier transform of P
Fv = linspace(0, 1, fix(L/2)+1)*Fn; % Frequency Vector
Iv = 1:length(Fv); % Index Vector
figure(1)
plot(t*1E+6, P);
grid on
xlabel('time[\mus]')
ylabel('amplitude[a.u]')
figure(2)
plot(Fv, abs(P_FT(Iv))*2);
grid on
The correct representation of the Fourier transform of your signal is in figure(2).
  댓글 수: 2
Star Strider
Star Strider 2017년 2월 28일
I answered you in the email you sent. The essence of that being that you can use Laplace transforms to solve partial differential equations in time-domain and space-domain by converting them to ordinary differential equations in s-domain and space-domain. That is relatively straightforward with Laplace transforms but much more difficult with Fourier transforms, since they can involve complex frequency variables. Those are much more difficult to work with.
I do not understand the problem you want to solve.

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추가 답변(1개)

Walter Roberson
Walter Roberson 2017년 2월 28일
plot() with one argument that is complex-valued (hint!) plots real() of the parameter against imag() of the parameter.

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