Non-uniformly sampled transfer function data

[bot19]

I have non-uniformly sampled transfer function data (magnitude only) in the range of 100kHz and 200MHz. Using this transfer function, I would like to calculate output from specific input.

Question :

1. To obtain phase of the transfer function from the magnitude data, I am trying to use Hilbert transform.
   
   (1) Phase = - imag( Hilbert( log ( TF_magnitude ) ) );
   
   Is above line of code right? I found the below equation for calculating the minimum phase.
   
   (2) θ(ω)=−H[ln(G(ω))]
   
   I do not know why (1) use imag function.
2. I do not have the transfer function data under 100kHz, especially 0Hz. In this case, should I extrapolate the data under 100kHz? or insert 0? insert mean value? Does this make a big difference in output?
3. The sampling period of the transfer function is not linear, but uniform in log-scale. To make this linear, I tried to interpolate this using cubic-spline. But as the figure below, the transfer function does not have any regularity.

Therefore, I am trying to extract input data that is corresponding to transfer function data, calculate the output, and then interpolate the output for linear spaced output points. Does it matter if I work this way?​

In addition, should I make the output (or the transfer function) linear to perform IFFT in MATLAB?​

As I am poor at English, I am not sure my thoughts are conveyed.. but I hope so. Any help would be appreciate.

 

[nilesh_pat]

Answer :1. The line of code you provided is correct, however you need to be careful about the order of operations. You should take the log of the magnitude data first, and then use the Hilbert transform to calculate the phase. 2. You may be able to extrapolate the data under 100kHz if you have enough data points to do so, however it is not recommended as you may introduce errors into your calculations. It would be best to insert 0 or the mean value in this case. 3. Interpolating the transfer function using a cubic spline is a valid approach, but it may introduce errors into your calculations. You can try to extract input data that is corresponding to the transfer function data, calculate the output, and then interpolate the output for linear spaced output points. This will help reduce any errors introduced by the interpolation.4. In order to perform IFFT in MATLAB, you will need to make the output (or the transfer function) linear.