Autocorrelation function of the output of the nonlinear device

In summary, the conversation discusses the use of autocorrelation function to obtain power spectral density for input signals with noise. The autocorrelation should be linear and there should be separate spikes for different frequencies. The individual autocorrelation spikes are not affected by the periodic nature of the inputs. The Auto-Regressive Integrated Moving Average (ARIMA) model and the Box-Jenkins method are recommended for studying the autocorrelation formula for non-linear devices.
  • #1
baby_1
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Hello
for an input signal with a noise we have
6174589100_1470202354.png

and for obtain Power spectural density we use autocorrelation function
6302258400_1470202355.png

where hkm is
5460939900_1470202515.png


but I need to know what is autocorrelation function for different inputs with different frequencies? such as
1329197400_1470202724.png


Any help will appericate
 
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  • #2
The autocorrelation should be linear. You should see the separate autocorrelation spikes for the w1 and w2 frequencies.
 
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  • #3
Thanks FactChecker
It means we can write autocorrelation function as this form?
2752371800_1470301475.jpg

but I think in above equation we consider noise for each input signal and it seems we calculate noise twice
 
  • #4
baby_1 said:
Thanks FactChecker
It means we can write autocorrelation function as this form?
2752371800_1470301475.jpg

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.
 
  • #5
Thanks FactChecker for your help
Could you recommend good literature that cover autocorrelation formula for non-linear device?
 
  • #6
baby_1 said:
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.
 
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1. What is the Autocorrelation Function of the Output of a Nonlinear Device?

The Autocorrelation Function (ACF) of the output of a nonlinear device is a mathematical tool used to measure the similarity between a signal and a delayed version of itself. It is often used to analyze the presence of periodic patterns or cyclical behavior in a signal.

2. How is the Autocorrelation Function Calculated?

The Autocorrelation Function is calculated by multiplying a signal with a delayed version of itself and averaging the results over a certain time period. The result is a function that shows the similarity between the signal and the delayed version at different delay times.

3. What Does the Autocorrelation Function Tell Us About a Nonlinear Device's Output?

The Autocorrelation Function can provide insights into the periodicity and cyclical behavior of a signal and how it is affected by the nonlinear device. It can also reveal any correlations between the input and output signals, which can help in understanding the behavior of the device.

4. How is the Autocorrelation Function Used in Nonlinear Device Analysis?

The Autocorrelation Function is often used in nonlinear device analysis to identify any patterns or cycles in the output signal, as well as to measure the strength of any correlations between the input and output signals. It can also be used to compare the performance of different nonlinear devices.

5. How Can the Autocorrelation Function Help Improve Nonlinear Device Design?

The Autocorrelation Function can be used to optimize the design of a nonlinear device by identifying any periodic or cyclical behavior in the output signal. By understanding the correlations between the input and output signals, engineers can make adjustments to improve the device's performance and reduce any unwanted effects.

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