# Questions tagged [gaussian]

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22k views

### How to Generate Band Limited Gaussian White Noise?

In some papers, I read that the additive noise is band limited Gaussian white. How can I simulate this type of noise use Matlab?
2k views

### Why is Gaussian noise called so?

Can you please explain: why is a specific type of noise called "Gaussian noise"? Why is it relevant to call it Gaussian? Please, explain in layman's terms.
1k views

### what's gaussian noise look like?

I am using Matlab function imnoise to add gaussian noise to one image. However, it seems that adjacent samples of the noise is correlated. I am using matlab code below to add noise. ...
46k views

### Gaussian Blur - Standard Deviation, Radius and Kernel Size

I've implemented a gaussian blur fragment shader in GLSL. I understand the main concepts behind all of it: convolution, separation of x and y using linearity, multiple passes to increase radius... I ...
5k views

### Which IIR filters approximate a Gaussian filter?

So it recently dawned on me that Bessel filters, despite being listed along with the other common types, are really an oddball that belongs in a different "class", and I'm trying to learn more about ...
2k views

### Why does the separable filter reduce the cost of computing the operator?

A separable filter in image processing can be written as product of two more simple filters. Typically a 2-dimensional convolution operation is separated into 2 onedimensional filters. This reduces ...
3k views

### When should the sum of all elements of a gaussian kernel be zero?

I found an approximation of a 5x5 2D convolution kernel like this : Here, the sum of the elements is zero and this one was used for Laplacian of Gaussian! Another one here : This one has all ...
6k views

### What is a $BT$ (Bandwidth-Time) product with reference to modulation?

I would like to know what does Bandwidth-Time product mean. I understand that Bandwidth ($B$) = 1/Symbol Time ($T$), hence $BT = 1$. But how can it vary? What is its significance? e.g. When we say ...
1k views

### Common Use Cases for 2D Non Separable Convolution Filters

In the image processing world, I've noticed that a lot of the popular convolution filters are separable. Here's a quick list of common separable filters: Sobel Gaussian blur Box filter (all ones, for ...
4k views

### Standard Deviation in Gaussian Blur

I have a function that performs gaussian blur on image for some specific $\sigma$ (the standard deviation). It first computes kernel of size $\lceil 3\sigma \rceil$ and then performs convolution with ...
393 views

### Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary process in time (in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary ...
3k views

### Discrete approximation to Gaussian filter

One method of producing a discrete approximation kernel to a Gaussian filter of variance $\sigma^2$ is to assume a cutoff of $5\sigma$. This seems to suggest the following procedure: Create a uniform ...
7k views

### Horizontal banding (flickering) due to electronic rolling shutters

It is a well-known artifact that in CMOS cameras with electronic rolling shutter, horizontal banding (flickering), i.e. brightness intensity variations, are observed when the image is recorded under ...
114 views

### Conditions for symmetric and unimodal windows in both time and frequency domains

After a lecture on harmonic analysis and time/frequency methods, I reconsidered the Gaussian kernel, defined in continuous time. It is unimodal and symmetric, and its continuous Fourier transform is ...
699 views

### Confusion regarding pdf of circularly symmetric complex gaussian rv

Considering a random variable $x$ that takes in values from a complex domain. Its real and imaginary components are totally uncorrelated. I am following this link and also studying this document. In ...
635 views

### Relation between frequency spectrum and PDF of a random variable

I have a random variable that is being generated according to some probability distribution function (e.g. a Gaussian PDF). When looking at the frequency spectrum of the generated data does the ...
897 views

### How to generate random samples of Gaussian distribution directly in the frequency domain?

One can easily draw (pseudo-)random samples from a normal (Gaussian) distribution by using, say, NumPy: ...
586 views

7k views

### Simple fft to Gaussian pulse with MATLAB

trying simply to create femtosecond pulse in MATLAB exactly like in the attached image, the carrier frequency is around 374THz, and my sampling frequency is 10 times the carrier. The results of the ...
207 views

### Additive white Gaussian noise and undecimated DWT

One of the benefits of DWT is that it is an orthonormal transform. There are statements that the energy of noise component mainly concentrates on the high-frequency (detail) part and distributes ...
602 views

### How to Obtain Mathematically High Frequency and Low Frequency Component Separately Using Bilateral Filter?

I have asked this question before in the sense that what does a high frequency and low frequency component signify in a image and i got satisfactory answers now i want to know that how i can get high ...
616 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(...
215 views

### frequency spectrum of a sampled signal, PSD and power discussion

Before I go into my question, I first want to review the basics of sampling a signal and at the same time I build the basics of my questions so that they make more sense. I know I have asked couple of ...
875 views

### Fixed SNR with unitary noise variance

I've just one question : How can I write a model like y = x + w,( with w a white gaussian noise) with a fixed SNR and a noise variance equal to 1. What coefficient may I have before x ? Thanks !
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 $v \sim CN(0,2\sigma^2_v)$ ...