Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 ?

share|improve this question
    
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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.