Why the Poisson noise level is set to 2 after applying Leahy norm

This can be seen in the equation provided, where the Poisson noise level is equal to 2 divided by the number of photons times the squared amplitude. This ensures that the power spectrum is normalized to a value of 2. It is not possible to expand the equation further to adjust the Poisson noise level to a different value. In summary, the Poisson noise level in Leahy normalization is set to 2 for normalization purposes in high energy astrophysics.
  • #1
arcTomato
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TL;DR Summary
Why the Poisson noise level is set to 2 after applying Leahy normalization
I am studying about power spectrum analysis in high energy astrophysics.
I cannot understand why the Poisson noise level is set to 2 after applying Leahy normalization.
$$P_{j}=2 /_{N \mathrm{ph}}\left|a_{j}\right|^{2}$$
The above is the equation for leahy norm, Can I expand the equation from here to require that the Poisson noise level is 2?

Thank you.
 
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  • #2
Leahy normalization is a technique used in X-ray astronomy to normalize the power spectrum of a source so that it can be directly compared with other sources and models. The Poisson noise level is set to 2 because the variance of the Poisson noise is equal to the mean value, and since the expectation value of the power spectrum is unity, the variance of the power spectrum is equal to two. This means that for a given power spectrum, the Leahy normalization will set the Poisson noise level to two.
 

1. Why is the Poisson noise level set to 2 after applying Leahy norm?

The Poisson noise level is set to 2 after applying Leahy norm because it is a commonly used normalization technique in X-ray astronomy. It is based on the assumption that the observed data follows a Poisson distribution, which is a common distribution for counting data. By setting the noise level to 2, it allows for a more accurate representation of the data and can help to reduce systematic errors.

2. What is the significance of setting the noise level to 2 in the Leahy norm?

The significance of setting the noise level to 2 in the Leahy norm is that it helps to remove any background noise or systematic errors from the data. This normalization technique is often used in X-ray astronomy to improve the signal-to-noise ratio of the data and make it easier to detect any underlying patterns or signals.

3. How does setting the noise level to 2 affect the data in the Leahy norm?

Setting the noise level to 2 in the Leahy norm does not change the data itself, but rather it rescales the data to a more appropriate level for analysis. This normalization technique helps to remove any background noise and improve the overall quality of the data, making it easier to interpret and analyze.

4. Are there any alternatives to setting the noise level to 2 in the Leahy norm?

Yes, there are alternative normalization techniques that can be used instead of setting the noise level to 2 in the Leahy norm. Some common alternatives include the RMS normalization and the standard deviation normalization. These techniques may be more suitable for certain types of data or research goals, so it is important to carefully consider which normalization method is most appropriate for a given study.

5. Can the noise level be set to a value other than 2 in the Leahy norm?

Yes, the noise level can be set to a value other than 2 in the Leahy norm. However, a value of 2 is commonly used because it has been found to provide the best results for most X-ray data. In some cases, a different value may be more appropriate, but it is important to carefully consider the implications and potential effects on the data before choosing a different noise level.

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