What is the variance of Gaussian white noise?

What is the variance of Gaussian white noise?

For Gaussian noise, this implies that the filtered white noise can be represented by a sequence of independent, zero-mean, Gaussian random variables with variance of σ2 = No W. Note that the variance of the samples and the rate at which they are taken are related by σ2 = Nofs/2.

Is uncertainty standard deviation or variance?

Uncertainty is measured with a variance or its square root, which is a standard deviation. The standard deviation of a statistic is also (and more commonly) called a standard error. Uncertainty emerges because of variability.

How is the autocorrelation of filtered white noise calculated?

For filtered white noise, we can write as a convolution of white noise and some impulse response : since for white noise . Thus, we have derived that the autocorrelation of filtered white noise is proportional to the autocorrelation of the impulse response times the variance of the driving white noise.

What kind of noise is a filtered white noise?

More generally, filtered white noisecan be termed colored noiseor correlated noise. As long as the filter is linear and time-invariant(LTI), and strictly stable (polesinside and not on the unit circle of the plane), its output will be a stationary “colored noise”.

When does a white noise sequence become correlated?

When a white-noise sequence is filtered, successive samples generally become correlated.7.8 Some of these filtered-white-noise signals have names: More generally, filtered white noise can be termed colored noise or correlated noise.

How to calculate the spectral density of white noise?

Suppose we have a discrete-time sequence x[t] which is stationary, zero mean, white noise with variance σ2. Then the autocorrelation of x is: Rxx[τ] = E[x[t]x[t + τ]] = {E[x[t]2], if τ = 0 0, otherwise = σ2δ[τ] where δ[τ] is the Kronecker delta.