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Homework Help: MATLAB user defined inverse fourier transform

  1. Jun 10, 2010 #1
    Hi i am stuck with a program in MATLAB to find the time domain impulse response of a system from its continuous transfer function in the frequency domain.

    Here is the program-
    delt=1.5625e-9; %definition of delta t(sampling time).To be taken sufficiently small depending upon the time constant of the original signal.

    delomg=1/(N*delt); % Kept sufficiently small to prevent repetition of curves in the plot due to aliasing .

    komg=[-100*pi/(delt):delomg:100*pi/(delt)]; %matrix containing the omegas over which the summation is done.Should be sufficiently large to cover all the frequencies present the original signal.

    s=sqrt(-1)*komg; %definition of s=jw

    transfer_func_image= 1 -(s.*r1*(c1+c2) +1)./(s.^2.*r1.*r2.*c1.*c2 + s.*(r1*c1 + r2*c2+ r1*c2) +1);

    h_image_dirac=zeros(1,N); %initialisation of the h_image matrix for better speed

    for n=1:N % first sample at t=0
    sumint_image = sum(transfer_func_image.*exp(s.*t).*delomg);

    This program defines a transfer function in terms of s.
    The last part of the program starting from for n= 1:N , then integrates the transfer function by multiplying the transfer function vector with exp(j*omega*t) and summing the vector obtained after multiplying it with delomg.This duplicates the formula of laplace transform for the special case where the real part of s =0 and is thus effectively inverse fourier transform.

    The problem is the program is not giving the right result.If i find the value of the transfer function above at 2Meg, it is of the order of 10^-4
    but if i use this program to obtain the impulse response and then convolve that with a sine wave at 2meg the answer is of the order of 100 and not 10^-4.

    Where am i going wrong?This program works fine for another transfer function which i have tested.

    please help.

    thanks a lot.Please contact me if the problem is not clear.any help wud be appreciated.It is really important.
  2. jcsd
  3. Jun 12, 2010 #2
    Your transfer function is a biquad filter. To get an impulse response, the transfer function has to be applied to an impulse. I'm not sure if I understand the question right, but you could convert the transfer function to discrete form (the Z-domain), and then get an impulse response. This is often done by using the "bilinear transform".
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