Implementing the Z-transform definition of the NDFT algorithm in Matlab

Question

I would like to implement the following z-transform equation in MatLab to calculate the 1-D Non-Uniform Discrete Fourier Transform (NDFT):

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X(z) is the z-transform of x[n], where x[n] is a horizontal 1-D vector that contains my unevenly spaced samples.

The z-transform is defined as a summation from n= 0 to n = infinity.

This definition is from n = 0 to n = N-1.

I have tried to implement ztrans, but isn't this definition for n = 0 to n = infinity?

Can anyone point me in the right direction into implementing this in Matlab?

score 0 · Answer 1 · answered Jun 17 '15 at 18:48

0

Using the definitions you provided this is a problem of making sure you do the matrix algebra correctly.

function X = NDFT(x, z)
    [n, Z] = meshgrid(0:length(x)-1, z);
    D = Z.^n;
    X = D*x;
end

answered Jun 17 '15 at 18:48

user1543042

Makes sense, but how do I take into account that D is a matrix of Z-transforms with different indices ? Do I need to add the command ztrans somewhere ? – James Jun 18 '15 at 06:30
If `z` is a scalar `D` is a vector, if `z` is a vector `D` is a matrix. – user1543042 Jun 18 '15 at 11:17
I know that - I'm asking about z-transforms- z is the z-transform - how do I take that into account in matlab ? – James Jun 18 '15 at 12:21

1 Answers1