Linked Questions

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1answer
214 views

how we can prove that the Variance of (white Gussian noise) is average power of the noise? [duplicate]

White Gaussian Noise PSD is fixed No/2. So how we can investigate that noise variance is average power of the noise?
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0answers
122 views

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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0answers
97 views

What is SNR of Signal with Additive White Gaussian Noise [duplicate]

Calculating the power of AWGN should be equal to infinity as PSD is constant and its integration is infinity over all frequencies. Hence for any signal with finite power mixed with AWGN, SNR should ...
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2answers
3k views

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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2answers
3k views

White noise vs. delta pulse and Ultraviolet catastrofe

Everybody explains that white noise has all frequencies equally strong. But, this immediately means that Ultraviolet catastrofe inevitably happens if power > 0 stays constant at any frequency and, ...
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2answers
3k views

What can we deduce about variance when we are given the noise spectral density?

Given the noise spectral density ${N_0\over 2} = a$, what can be deduced about the variance? In the case of a two-symbol canal(/cable), and when $T_0 = 1$. Is it that, $\sigma_X^2 = {N_0 \over 2} *...
2
votes
2answers
2k views

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 ...
1
vote
1answer
641 views

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(...
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1answer
753 views

What's the Intuitive Description of Circular Symmetric Complex Zero Mean White Gaussian Noise?

Suppose we have an added discrete noise signal defined as: $$y[n]=x[n]+w[n], $$ where $w$ is zero mean white Gaussian noise. Question: When we say white noise, is it sufficient to say that it is ...
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1answer
881 views

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 ...
0
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1answer
544 views

Evaluation of Autocorrelation and Power Spectral Density of white noise through a filter

So say there's a filter with an impulse response of $h(t) = (0.8)^t u(t)$. I'd like to pass white noise through this and figure out the autocorrelation and power spectral density of the output. I'm ...
1
vote
1answer
512 views

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 ...
1
vote
1answer
435 views

How to calculate the noise power for a non-stationary noise?

With stationary noise we have constant mean and variance (let's assume it is Gaussian noise). My first question is, how is the noise power calculated and how it is related to the variance? Now, I ...
0
votes
2answers
230 views

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 ...
0
votes
1answer
161 views

Relation between constellation SNR and baseband SNR

Let's say I have an I/Q modulation, ie. QPSK. I can simulate an the effects of an AWGN channel by adding to my QPSK symbols the realizations of a complex normal. $\mathcal{CN}(0,\frac{1}{\mathrm{SNR}...

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