Autocorrelation function of the output of the nonlinear device

[baby_1]

Hello
for an input signal with a noise we have

and for obtain Power spectural density we use autocorrelation function

where hkm is

but I need to know what is autocorrelation function for different inputs with different frequencies? such as

Any help will appericate

 

[FactChecker]

The autocorrelation should be linear. You should see the separate autocorrelation spikes for the w₁ and w₂ frequencies.

 

[baby_1]

Thanks FactChecker
It means we can write autocorrelation function as this form?

but I think in above equation we consider noise for each input signal and it seems we calculate noise twice

 

[FactChecker]

Thanks FactChecker
It means we can write autocorrelation function as this form?

but I think in above equation we consider noise for each input signal and it seems we calculate noise twice

I was assuming that the only noise is n(t), and that it has 0 autocorrelations.

 

[baby_1]

Thanks FactChecker for your help
Could you recommend good literature that cover autocorrelation formula for non-linear device?

 

[FactChecker]

Thanks FactChecker for your help
Could you recommend good literature that cover autocorrelation formula for non-linear device?

I'm not clear on why you say this is nonlinear. Although the signals of your example are periodic, they are added in a linear way. The periodic nature of the inputs does not make it nonlinear.

If you sample a time series of the output, a very general model and technique that I think would apply is the Auto-Regressive Integrated Moving Average (ARIMA) model and the Box-Jenkins method.