# Relations between complex functions satisfying a specific condition

What is the relation between the following two complex functions:

$$g(\theta)=\sum_n x[n]\ y[n]\ e^{in\theta}$$

and

$$f(\theta)=\sum_n \left(x[n]\pm i\sqrt{1-x[n]^2}\right)\ y[n]\ e^{in\theta}$$

where $\theta$ ranges from $-\pi$ to $\pi$ and $x[n]$ is real and smaller than 1 and $y[n]$ is in general complex ? Can we find a single equation that relates the two functions ?

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Is $|x[n]|<1$..? – Ron Gordon Feb 22 '13 at 16:44
@rlgordonma yes! – Tarek Feb 22 '13 at 16:47
I don't know of any nonlinear transformation on the Fourier side that can be expressed explicitly in terms of functions. So the answer to "can we find..." is: in all likelihood, no. – user53153 Feb 23 '13 at 5:02