Rational fit of complex data with complex 'x'

Hi, I want to do a rational curve fit of a complex data y(x)= N(x)/D(x) where variable x is also complex. I have tried cftool, rationalfit but they support only real x. Would you please help?

[Walter Roberson]

I am not clear here as to what are the knowns and what are unknown and what the expected outputs are? Are N and D function handles?

Are you trying to find two integer-valued but complex functions N and D such that N(x)/D(x) approximates y(x) ?

[Walter Roberson]

Have you considered using System Identification techniques from the Control System Toolbox?

[RFSignal]

Not yet. ARMA looks interesting to me.

[Walter Roberson]

https://www.mathworks.com/help/ident/gs/about-system-identification.html

[Joao Nizer]

It has been a while, but did you have any progress on that @RFSignal?

I'm trying to do the same, except that my y(x) maps to a real number. I've implemented an fminsearch() algorithm to try finding the complex coefficients. But it has been a little difficult for some specific input data.

Answer 1

[RFSignal]

Hi, The knowns are y and x. Both of them are complex data set. The unknowns are the co-efficients p1, p2,...pn and q1, q2,...qn for the rational function y(x)= (p1 + p2.x^2 + ..pn.x^n )/(q1 + q2.x^2 + ..qn.x^n ). In other words I want to do a rational curve fit.

[Walter Roberson]

Is the number of coefficients the same for numerator and denominator?

[RFSignal]

yes

Answer 2

[RFSignal]

One more point, the co-efficients p1, p2....q1, q2 are also complex.