21 questions linked to/from Variance of White Gaussian Noise
880 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?
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.
• 213
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 ...
• 111
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, ...
• 269
6k views

• 23
1 vote
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 ...
• 310
732 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
415 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 ...
• 1,059
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 ...
• 61
371 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 ...
• 23
1 vote
565 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 ...
• 13
1 vote
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?
• 13
1 vote
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 ...
• 61
1 vote
### $E(X(t)X(t))=\sigma^2\delta(\tau)$ 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^...