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July 19th, 2008 admin

Is narrow band random noise really flowing Rayleigh Distribution?

Sci THANK YOU.
What is different between
Narrow band “fading noise”
& —————-”random noise”
I can ‘t find it in many text books

James,

A random noise has a bell-shaped symmetrical distribution of instantaneous power on two sides of its mean power. A fading noise does not have a symmetrical distribution. Rather its distribution has a longer tail on the far end of the low-power side of the mean. This tail represents the probability of finding the fading (extremely low power) instances.

Of the two foundation RF test equipment, the spectrum analyzer when not connected displays a random noise floor. In contrast, a scalar network analyzer when not connected displays a fading noise floor.

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A narrowing down of the bandwidth of a random noise does NOT cause its time domain power pdf to change from Gaussian to Rayleigh. Occasional deep fading of instantaneous power in time domain is typically seen in muticarrier RF that cancel one another in the medium. A technically precision rephrasing, hence, should be either (1) “a narrow band FADING noise has a Rayleigh distribution,” or (2) “a narrow band RANDOM noise has a family of Gaussian pdf’s that have the mean tracing a sinc function making the composite pdf a Gaussian that has a larger variance but with a kurtosis (the variance of the variance) equal the variance of the all-band noise’s pdf.”

If you trace the instantaneous movement of power of an ideal all-band random white noise it, by definition, must have a uniform distribution of power in frequency, and a Gaussian distribution of power in time.

If you reduce the band width to make the random noise narrow band, the rectangular window frequency shaping function causes a sinc shaping function in time domain. This sinc window shapes the mean of the instantaneous power in time domain. However, this sinc shaping does nothing to cause the occasional deep fades that are characteristic of a Rayleigh pdf.

The Narrow – The Banded