Scaling Problem with IFFT after operating in the Fourier domain.

Hi all,

I've encountered a scaling problem when doing the IFFT.

In this code, the DFT a slope matirx of a surface function is used to reconstruct the function. A slew of operations are required in the Fourier domain before IDFT to get reconstructed surface matirx.

However, the resulting reconstructed surface is scaled by a factor. I am unable to determine any scaling standard that is suitable.

Here, the code in 1D is as follows:

%----Determination of Sampling period/space, Length of matrix etc.-------% dX = 0.64; % Sampling distance/period -mm L = 25; %Physical Length of Specimen -mm M =floor(L/dX); % Length of matrix x = (0:M)*dX; % space vector N = size(x,2); % vector size of x/phi df=1/(dX*N); % frequency q=0:M; % x/phi Matrix Coordinahtes (starting frm 0) %-------Surface function, slope matrix and FFTs------------------% phi=sin(x); % given surface function, phi - 1D Fphi=fft(phi); % DFT of phi [Sx]=gradient(phi,dX); % Slope matrix FSx=(fft(Sx)); % DFT of slope %----Operations to form IDFT of surface (in Fourier domain)------% phiup= ((exp(1i*-2*pi.*q./N)-1).*FSx ); phido=1./(2*((sin(pi.*q./N)).^2 )); phifi=phiup.*phido; phifi(1)=0; %eliminates infinite/NaN value %Make matrix conjugate symmetric% for k=2:floor(N/2) phifi(N-k+2)= real(phifi(k))-1i*imag(phifi(k));end %------IDFT,final reconstructed matrix--------% phiRe=(ifft(phifi)); %----------------PLOTS------------------- % figure; subplot(2,2,1);plot(x,real(phiRe),'r',x,phi,'b'); %8 title('Reconstructed phase, comparison'); subplot(2,2,2);plot(x,abs(phifi),'r',x,abs(Fphi),'b'); title('alpha/DFT phase (abs), comparison'); subplot(2,2,3);plot(x,real(phifi),'r',x,real(Fphi),'b'); %7 title('alpha/DFT phase (real), comparison'); subplot(2,2,4);plot(x,imag(phifi),'r',x ,imag(Fphi),'b'); title('alpha/DFT phase (imag), comparison');legend('Reconstructed','Actual'); The resultant plot gives phiRe with a scaling of around 3. However, I need to establish a standard for Scaling. How should i scale it correctly?

I need to understand this well as it will be applied for a 2D case too. THANKS!