how can i compute the inverse fourier transform of the heaviside function without use the ifft, if in this case i have the function in the frequency domain and one time vector and a frequency vector that I would like to plot my function?

The code that I have is:

w0=15; %frequencia da fonte
w=linspace(1,150,150); %vetor da frequencia
t=linspace(-10,30,150); %vetor do tempo
alpha=0.1; %coeficiente de atenuação de sinal sísmico 

% HEAVISIDE 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])

But, in my case, I don't have the function in time domain to compare. I have only the function in the frequency domain. I need help, please.