# Questions tagged [gaussian]

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### MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)

This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv If $v \sim CN(0,2\sigma^2_v)$ ...
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### Why does the Kalman filter remove only Gaussian noise?

What and where in the derivation of the Kalman filter is the assumption of Gaussian noise? Why and how does this assumption help?
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### Is there a mathematical method to determine if noise is Gaussian?

Is there a mathematical method to determine if a signal's noise is Gaussian? The only way I know so far is to analyze the histogram and layover a Gaussian distribution to visually determine if the ...
172 views

### What is stochastic differential equation and its need?

A white noise process can be simulated using the Matlab command randn(). The numbers will be drawn from a Normal distribution of zero mean and variance 1. Is the ...
508 views

### Discrepancy between Gaussian FFT and its Fourier Transform

I am trying to do the FFT of a Gaussian signal and comparing it to the theoretical Fourier transform. For infinitely small time step $dt$ and infinitely long signal length $T$, the 2 should become ...
1k views

### Correct way to add AWGN to a signal

I have a signal, S whose bandwidth is bw Hertz and is sampled at fs Hertz. To contaminate it with a noise corresponding to SNR <...
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### Interpreting zero-mean Gaussian noise in the context of Kalman Filters

Consider an object moving in 2D space with constant speed $v_x$,$v_y$. If its acceleration is modelled as zero-mean Gaussian $a_x \sim N(0,\sigma_{a_x}^2)$ and $a_y \sim N(0,\sigma_{a_y}^2)$ within ...
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### Why do we express complex noise as Gaussian distributed while the channel is Rayleigh distributed?

I have a confusion regarding the distribution of noise and channel fading. As we know channel fading is usually modeled with Rayleigh fading since it has Gaussian distributed real and imaginary ...
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### Deriving statistics of band limited Random Noise

The question is: Consider a continuous random number with a Gaussian distribution of mean $\mu$ and variance $\sigma$ . The RV is measured from time $t=-\infty$ to $t=\infty$. This time domain signal ...
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### Doubts and some confusion on variance for complex rv

This question is in continuation of the one asked here. Let's say that the measurement noise $w$ or any random variable is circularly Gaussian complex. If the imaginary and real components each has ...
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### Fourier transform of a Gaussian in Excel returns imaginary coefficients [duplicate]

I am using Fourier Analysis tool in Excel to transform a Gaussian $\exp(-x^2)$ on a uniform and symmetric grid of $x$ values. I am expecting the result to contain only real numbers (which should ...
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### Gaussian noise generation for a given SNR ?

I am trying to add a Gaussian noise, normal distributed to a signal I have simulated (sig_noiseFree), to get a noisy signal (sig_noisy). lease see the code. I wrote the function my self according to ...
343 views

### Gaussian filter looks pixelated

What does it mean when an image looks pixelated after a Gaussian filter (Multivariate Gaussian Distribution filter) is applied (in context of mu, Sigma, and the meshgrid created), and what parameters ...
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### Creating a noise model with a fixed PSNR

My goal is to create a noise model so that the PSNR of the noisy image compared to the original is some pre-defined constant $\alpha$. This means the mean squared-error will also be a constant. My ...
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