MATLAB: How to calculate the inverse fourier transform in matlab

inverse fourier transform

Hi. I have to calculate the inverse fourier transform of the function F in may code and compare with the original function f. The code is
w0=15; %frequencia da fonte
w=linspace(1,150,150); %vetor da frequencia
deltaw=w(2)-w(1);
t=linspace(0,30,150); %vetor do tempo
alpha=0.1; %coeficiente de atenuação de sinal sísmico
for nt=1:length(t)
  if t(nt)>=0.0
      H(nt)=1.0; %H(t) é a função de Heaviside
  end
  if t(nt)<0.0
      H(nt)=0.0;
  end
  f(nt)=H(nt)*(exp(1)^(-alpha*t(nt)))*sin((pi/180)*w0*t(nt));
end
for nw=1:length(w)
  F(nw)=alpha/(alpha^(2)+(w(nw)+(pi/180)*w0)^(2));
end
A=(i*t'*w);
B=exp(A);
Ftempo=(1/(2*pi))*deltaw*(F*B.');
plot(t,f,t,real(Ftempo))
But the graphic is not good. What I have to do?

Best Answer

hi Marcia,
Are you trying to compute the inverse Fourier Transform of the Heaviside function and compare it with Heaviside function?
you can try this code in which Fast Fourier Transform is computed using loops not built in fft function :
 w0=15; %frequencia da fonte
w=linspace(1,150,150); %vetor da frequencia
deltaw=w(2)-w(1);
t=linspace(-10,30,150); %vetor do tempo
alpha=0.1; %coeficiente de atenuação de sinal sísmico
 % HEAVIVISE FUNCTION H,  F(H)=z  and F^1(z)=ZZ
 for nt=1:length(t)
    if t(nt)<0.0
      H(nt)=0.00; %H(t) é a função de Heaviside
    elseif t(nt)==0
        H(nt)=0.5;
    elseif t(nt)>0.0
      H(nt)=1.00;
    end
end
 figure, plot(t,H,'LineWidth',1.9), axis([-10 30 -1 2]), title(' Heaviside function H(x)'), grid on ,
 % Fourier Transform,  without using FFT
 N=length(H);
 nfft=N;
 z=zeros(1,nfft);
 Sum=0;
 for k=1:nfft
     for jj=1:N
         Sum=Sum+H(jj)*exp(-2*pi*j*(jj-1)*(k-1)/nfft);
     end
 z(k)=Sum;
 Sum=0;% Reset

 end
 figure, plot(w, abs(z),'LineWidth',1.9), title(' Fourier Transform of F[H(x)]'), grid on
 % Inverse FOURIER Transform
  ZZ=zeros(1,nfft);
 Sum=0;
 for k=1:nfft
     for jj=1:N
         Sum=Sum+z(jj)*exp(2*pi*j*(jj-1)*(k-1)/nfft);
     end
 ZZ(k)=Sum;
 Sum=0;% Reset
 end
 ZZ=ZZ/N;
 figure, plot(t, real(ZZ),'LineWidth',1.9), title(' Inverse Fourier Transform F^{-1}[F[H(x)]]=H(x)'), grid on
 axis([-10 30 -1 2])
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