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Intensity statistics of random signals in Gaussian noise
1Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas 78249, USA.
Summary
Gaussian noise affects random signal intensity statistics, transforming probability density via a Bessel transform. This method retrieves microwave transmission intensity statistics, even with noise at long delays.
Area of Science:
- Signal processing
- Statistical physics
- Probability theory
Background:
- Understanding signal intensity statistics is crucial in various scientific fields.
- Additive Gaussian noise is a common challenge in signal analysis.
- Phasor models are used to represent random signals.
Purpose of the Study:
- To develop a method for analyzing signal intensity statistics in the presence of Gaussian noise.
- To investigate the mathematical transformation induced by additive Gaussian noise.
- To apply the derived transformation to real-world signal analysis, such as microwave transmission.
Main Methods:
- Modeling random signals as a sum of a random signal and a random phasor.
- Applying additive Gaussian noise to the signal model.
- Deriving the resulting probability density function of signal intensity.
- Utilizing Bessel transforms to describe the noise-induced transformation.
- Analyzing microwave pulsed transmission data.
Main Results:
- Additive Gaussian noise results in a Bessel transform of the signal intensity's probability density.
- This transformation is applicable to mixtures of independent random signals, including complex-valued Gaussian processes.
- The method successfully retrieves intensity statistics of microwave pulsed transmission from Gaussian noise at long time delays.
Conclusions:
- The Bessel transform provides a powerful tool for understanding how Gaussian noise alters signal intensity statistics.
- The developed methodology offers a robust approach for signal analysis in noisy environments.
- This work has practical implications for analyzing complex signals like microwave transmissions.
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