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For thermal noise, its spectral density is given by N 0 = kT, where k is the Boltzmann constant in joules per kelvin (J/K), and T is the receiver system noise temperature in kelvins. The noise amplitude spectral density is the square root of the noise power spectral density, and is given in units such as volts per square root of hertz, V / H z ...
The real part of impedance, [()], is in general frequency dependent and so the Johnson–Nyquist noise is not white noise. The RMS noise voltage over a span of frequencies to can be found by taking the square root of integration of the power spectral density:
Thermal noise is approximately white, meaning that its power spectral density is nearly equal throughout the frequency spectrum. The amplitude of the signal has very nearly a Gaussian probability density function. A communication system affected by thermal noise is often modelled as an additive white Gaussian noise (AWGN) channel.
The sinusoidal output of an ideal oscillator is a Dirac delta function in the power spectral density centered at the frequency of the sinusoid. Such perfect spectral purity is not achievable in a practical oscillator. Spreading of the spectrum line caused by phase noise is characterized by the fundamental linewidth and the integral linewidth. [4]
If the noise has expected value of zero, as is common, the denominator is its variance, the square of its standard deviation σ N. The signal and the noise must be measured the same way, for example as voltages across the same impedance. Their root mean squares can alternatively be used according to:
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. [1] The term is used with this or similar meanings in many scientific and technical disciplines, including physics , acoustical engineering , telecommunications , and statistical forecasting .
However, shot noise is temperature and frequency independent, in contrast to Johnson–Nyquist noise, which is proportional to temperature, and flicker noise, with the spectral density decreasing with increasing frequency. Therefore, at high frequencies and low temperatures shot noise may become the dominant source of noise.
A measurement of the acceleration spectral density (ASD) is the usual way to specify random vibration. The root mean square acceleration (G rms) is the square root of the area under the ASD curve in the frequency domain.