Normalized Autocorrelation of two signals

In summary, the conversation is about obtaining the Autocorrelation function of two signals and wanting to know how to normalize it. The person asking for help has tried using the formula for Autocorrelation on a period of 2pi and has found their answer, but is unsure about normalizing the function. They clarify that the signals are comprised of two sinusoidal components and ask for clarification on how to form an autocorrelation between different functions. The expert suggests scaling the function by making sure Rx(at t=0) is equal to 1.
  • #1
baby_1
159
15

Homework Statement


I obtain Autocorrelation function of two signal:
VRsnk.png

as
G4GHV.png

Homework Equations


[/B]

The Attempt at a Solution


[/B]
I want to know what is Normalized Autocorrelation of above equation?

Thanks
 
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  • #2
baby_1 said:

Homework Statement


I obtain Autocorrelation function of two signal:
VRsnk.png

as
G4GHV.png

Homework Equations


[/B]

The Attempt at a Solution


[/B]
I want to know what is Normalized Autocorrelation of above equation?

Thanks
What have you tried so far?
 
  • #3
Thanks for your response
I don't know I did right or it should be something else
6637266300_1470977277.png

or
3369574900_1470977277.png

or
...?
 
  • #4
baby_1 said:
Thanks for your response
I don't know I did right or it should be something else
6637266300_1470977277.png

or
3369574900_1470977277.png

or
...?
Sorry if this is a dumb question, but how can you form an autocorrelation between different functions? Can you show your detailed work?
 
  • #5
Probably a signal comprised of 2 sinusoidal components.
 
  • #6
Thanks for your response
I used https://en.wikipedia.org/wiki/Autocorrelation on a period of (2pi)
I found out my answer. when we want to normalized our autocorrelation function we should pay attention to Rx(at t=0)=1 to scale the function.
 

Related to Normalized Autocorrelation of two signals

What is normalized autocorrelation?

Normalized autocorrelation is a statistical method used to measure the similarity between two signals. It calculates the correlation coefficient between the two signals, which represents the strength and direction of their relationship.

How is normalized autocorrelation calculated?

The formula for normalized autocorrelation involves taking the covariance of the two signals and dividing it by the product of their standard deviations. This results in a value between -1 and 1, with higher values indicating a stronger correlation.

What is the significance of normalized autocorrelation?

Normalized autocorrelation is commonly used in signal processing and time series analysis to determine if there is a repeating pattern or relationship between two signals. It can also be used to identify the time delay between two signals.

What is the difference between normalized autocorrelation and standard autocorrelation?

The main difference is that normalized autocorrelation takes into account the scale and magnitude of the signals, while standard autocorrelation does not. This makes normalized autocorrelation more useful for comparing signals with different scales.

What are the limitations of normalized autocorrelation?

Normalized autocorrelation assumes that the signals are stationary and have a linear relationship. It may also give misleading results if the signals have a high level of noise. Additionally, it may not capture more complex relationships between signals, such as non-linear or time-varying relationships.

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