Linked Questions

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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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}...
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^...
1 vote
0 answers
150 views

Noise Shape Digital Filter

My objective is to build a noise shape filter from a given transfer function (in one case) and from a given PSD (for another case). Checking my precedent questions you can see that this argument is ...
0 votes
1 answer
1k 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 ...
0 votes
0 answers
127 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 ...
0 votes
1 answer
877 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?
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 ...
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 ...
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?

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