Linked Questions

11 votes
2 answers
6k 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, ...
abc's user avatar
  • 269
4 votes
2 answers
1k 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 ...
Probably's user avatar
  • 107
4 votes
1 answer
3k 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 ...
shampar's user avatar
  • 328
3 votes
2 answers
5k 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 ...
Rikeijin's user avatar
  • 189
2 votes
2 answers
6k 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} *...
Chris's user avatar
  • 123
2 votes
2 answers
4k 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, ...
Val's user avatar
  • 1
2 votes
2 answers
411 views

Discrete-time sampling of filtered white noise

I am trying to understand how I can relate a discrete-time random process to a continuous-time random process sampled at discrete times. Suppose I have a noise source $N_\tau(t)$ which is derived ...
Jason S's user avatar
  • 1,059
2 votes
1 answer
689 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}...
xvan's user avatar
  • 23
2 votes
1 answer
370 views

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 ...
Raksha's user avatar
  • 23
2 votes
1 answer
493 views

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 ...
Ba5o's user avatar
  • 61
2 votes
0 answers
154 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.
kaka's user avatar
  • 213
1 vote
1 answer
132 views

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?
Remy's user avatar
  • 13
1 vote
1 answer
871 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(...
bigredx24x's user avatar
1 vote
1 answer
1k 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 ...
Keegs's user avatar
  • 310
1 vote
0 answers
44 views

$E(X(t)X(t))=\sigma^2\delta(\tau)$ 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^...
Antoine's user avatar
  • 11

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