21 questions linked to/from Variance of White Gaussian Noise
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### Effect of windowing on noise

I understand that truncating a signal in time 'smears' the frequency response depending on the window chosen. In general, the shorter the signal duration, the more 'flattened' the frequency response, ...
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### Understanding PSD: Why Does Power at High Frequencies Affect Low Frequencies?

I'm trying to wrap my head around power spectral density on a conceptual level, but I am having some difficulty. Suppose I have a communication system where I am receiving and sampling white Gaussian ...
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### How Does the RMS of White Noise Change with Sampling Frequency?

There is an analog system which includes the continuous-time linear equalizer (CTLE). With some .noise analysis the power-spectral density (PSD) of the noise in that system is provided. So let's not ...
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### Definition of average power?

There are two kind of average power I encountered in random signal class and textbook: definition 1: average power =$$E[|x(t)|^2]=R_{xx}(0)=\int^\infty_{-\infty} S_{xx}(f)\,df$$ definition 2: average ...
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### Variance of a signal

How to calculate the variance of noise samples modeled as follows: $n_a(t)$ is a Gaussian zero-mean white noise process with (two-sided) power spectral density $\frac{N_0}{2}$. $n_a(t)$ is passed ...
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### Why I don't get the right PSD

I need to model a noise with a given PSD. To do this, I am starting from a white gaussian noise (WGN) and feed with the WGN a transfer function, which will act like a filter. In fact,it's easy to ...
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### White Gaussian Noise: a reality or fantasy? [duplicate]

White noise has infinite variance, whereas Gaussian random variable must have some finite-variance to exist. How do two disjoint phenomena co-exist? Help will be highly appreciated.
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1 vote
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### Why level of noise can be magnified twice through each numerical differentiation?

I was reading a paper and saw this is mentioned there, but I cannot figure out how this can analytically be proven?
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1 vote
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### Expectation of product of Filtered White Gaussian Noise

Assume I have a random process $X(t)$ that is white gaussian noise with psd $S(f)$. Now, let's filter that noise through a LPF of bandwidth $B$. How would I evaluate the following expression: E[S(...
1 vote
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### Why does increasing FFT length (narrowing bandwidth) not decrease Noise Power per bin?

I was under the impression that zero-mean white guassian noise had a constant Power Spectral Density which means that smaller bandwidths should decrease the power in that band. I'm getting surprising ...
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### $E(X(t)X(t))=\sigma^2\delta(\tau)$ or $E(X(t)X(t))=\sigma^2$
(Question already asked on Math StackExchange) Let's say we have a white noise process $x(t)$ such that: $E(X(t)X(t+\tau))=N\delta(\tau)$ $E(X(t))=0$ In particular, with $\tau=0$, \$E(X(t)X(t))=E(X^...