Average of the power spectrum of Poisson noise

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Thread starter arcTomato
Start date Oct 31, 2020
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Average Noise Poisson Power Power spectrum Spectrum

In summary, the power spectrum of Poisson noise is a measure of the frequency distribution of the power of a signal affected by Poisson noise. The average of the power spectrum can be calculated by taking the average of the power spectral density values at each frequency. It provides an estimate of the noise level in a signal, with a higher average indicating a higher noise level and a lower average indicating a lower noise level. Poisson noise affects the power spectrum by introducing random fluctuations that increase the power at high frequencies and decrease the power at low frequencies, resulting in a characteristic "hump" shape. The length of the signal can also affect the average of the power spectrum, with longer signals providing a more accurate estimate of the noise level.

Oct 31, 2020

arcTomato

TL;DR Summary: Poisson distribution

I am learning about noise that follows a Poisson distribution. When I do a Fourier transform of the data with only Poisson noise to get the power spectrum, what is the average value of the power spectrum?

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Nov 2, 2020

marcusl

Science Advisor

Gold Member

You can find it by using the Fourier energy theorem (often called Plancherel's or Parseval's theorem).

1. What is the average of the power spectrum of Poisson noise?

The average of the power spectrum of Poisson noise is the average power or intensity of the signal over a range of frequencies. In other words, it is the average amount of energy at each frequency in the signal.

2. How is the average of the power spectrum of Poisson noise calculated?

The average of the power spectrum of Poisson noise is calculated by taking the squared magnitude of the Fourier transform of the signal and averaging it over a range of frequencies. This can be done using mathematical formulas or software programs.

3. What is the significance of the average of the power spectrum of Poisson noise?

The average of the power spectrum of Poisson noise is significant because it provides information about the distribution of energy in a signal at different frequencies. This can be useful in analyzing and understanding the characteristics of the signal.

4. How does Poisson noise affect the average of the power spectrum?

Poisson noise is a type of random noise that can affect the average of the power spectrum by adding variations in the signal's intensity at different frequencies. This can result in a higher or lower average power spectrum depending on the level of noise present.

5. Can the average of the power spectrum of Poisson noise be used to filter out noise?

Yes, the average of the power spectrum of Poisson noise can be used to filter out noise by identifying the frequency components with the highest energy and removing them from the signal. However, this method may not be effective for all types of noise and may also remove important signal information.