# Questions tagged [gaussian]

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### 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 ...
1answer
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 ...
1answer
422 views

### Gaussian weighted distance between pixel amplitudes: motivations and sources?

In several image processing papers, and for instance in Random Walks for Image Segmentation (2006) by Leo Grady, changes in image intensities are turned into edge weights. This applies to graphs too, ...
2answers
202 views

### Equivalent of Fourier transform for Gaussians?

I have a long signal (million of samples) containing a lot of Gaussian peaks, whose standard deviation is random and about $5$ to $50$ samples wide. Sometimes, these peaks overlap, but not often. The ...
2answers
352 views

### Hardware implementation of Gaussian noise generator

I am implementing a GNG using Verilog. The implementation is based on the IEEE paper "Hardware Architecture of a Gaussian Noise Generator Based on the Inversion Method". In this, i could not ...
2answers
134 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 ...
0answers
73 views

### Help Understanding Radial Gaussian Filter

I am currently reading through Mueller's "Fundamentals of Music Processing" and I am trying to understand audio segmentation through the use of self-similarity matrices. Currently, my matrix looks ...
0answers
450 views

### Image reconstruction using Laplace pyramid

Given a sub-sampled Image $P_n$ belonging to layer $n$, a Gaussian kernel $G$ and a Laplace Layer $L_{n-1}$ of layer $n-1$, my efforts to create $P_{n-1}$ of previous layer $n-1$ have failed. This ...
1answer
4k views

### How to convert a low-pass Gaussian filter to a high pass filter

I have the following code for a applying a Gaussian filter to an image. From what I understand this is a low pass filter. Now I have to convert this into a high-pass filter, and from what we were told ...
0answers
39 views

### variance of filtered polynomial

Consider the following system: What is the variance of $y$, $\mathbb{E}(y^2)$ ? (EDIT: I know input signal has infinite power but will be made bandlimited by $H$. Both $H$ and $G$ are simple ...
1answer
198 views

### Band Limit in Gaussian Pyramid

In the paper The Laplacian Pyramid as a Compact Image Code, it says The pyramid algorithm reduces the filter band limit by an octave from level to level. How is the conclusion drawn? Is this related ...
0answers
369 views

### Gaussian Mixture Model-UBM based for image recognition

Scenario: Open set recognition: Unknown individuals may appear on scene (CCTV). Gallery = 10 individuals with a mug-shot image per individual. Approach: Gaussian Mixture Model-UBM based Use video ...
1answer
47 views

### Beginner level: deconvolving Gaussian noise to find initial PDF

noob question. An initial process has an unknown pdf, P(X), which is then subjected to additive Gaussian noise. Repeated sampling of the sum is performed so that $y=x+noise$ is repeatedly ...
1answer
118 views

### Does delta-sigma ADC also reduce Gaussian noise on input signal to ADC or just quantization noise?

The motive for posing this questions arises from a difference of analysis between a colleague an myself. Our general environment is in the construction of an analog front-end which takes in signals ...
1answer
287 views

### interpretation of histogram in statistical image processing

I am learning statistical image processing by myself. In papers and books, it always show the histogram of original images and gradients as the following image shows. The histograms of images vary ...
1answer
2k views

### Difference between Gaussian and moving average filters for peak detection and doppler shift detection?

Consider having a signal in the time domain, and you want to smooth the signal. Moving average and Gaussian filters that are used. How do you choose which is used for what? What are the conditions ...
2answers
356 views

### What is the relation between noise (AWGN) variance and number of antennas?

I'm working in two Matlab scripts trying to simulate a MIMO system using OFDM (downlink) and SC-FDE (uplink). My question is: for different numbers of transmit and receive antennas, what is the ...
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607 views

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### Why is my laser beam intensity profile not Gaussian?

I am kind of new to laser physics and signal processing, I hope I am in the right place to ask this question. I am also sorry for my not-great English. I have been asked to study the transverse ...
3answers
1k views

### Intuitive understanding of scale-space extrema detection

Can someone explain intuitively why local maxima and minima in the scale-space domain make for good keypoints? I understand using LoG or DoG zero-crossing points to identify spacial variations, i.e. ...
1answer
678 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 ...
2answers
133 views

### If noise is your signal, what is your noise?

Consider the following contrived situation. Imagine a Gaussian white noise process $x[t]$, with bandwidth $Δf$, with PSD equal to some quantity $A$ which you would like to measure. So the way to ...
1answer
2k views

### Gaussian Pyramid - How is Subsampling Rate Related to Sigma?

I found a gaussian pyramid implementation in a MOPS paper (feature detection). They use sampling rate $s=2$ and $\sigma=1$ - i.e. to generate a new level of the pyramid, the current level is smoothed ...
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268 views

### Decorrelating Stationary Colored Gaussian Noise — Effect On The Desired Signal

So given stationary colored gaussian noise $\mathbf{n}$, I know that I can decorrelate it by first finding it's autocorrelation $R_{nn}$ and performing $R^{-\frac{1}{2}}_{nn} \mathbf{n}$. In ...
1answer
191 views

### What is the value of the standard deviation $\sigma$? [closed]

I am using the following formula to add the additive Gaussian noise. noise= (x/255)*(randn(size(image))), where x is the ...
2answers
7k 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 ...
1answer
39 views

### Difference in following random proccess

Let just say I understand the first process that is white noise, Process 1: If $x(n)$ is a Gaussian random variable and a process is formed from a sequence of $x(n)$ and all random variables are ...
2answers
10k views

### generating white gaussian noise in matlab using two different functions

I want to know the difference between the two Gaussian noises generated below? Which one is white and how can i make the other one white? y=wgn(1,10000,0) and <...
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20 views

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108 views

### Resources on Non-Gaussian Channels

I understand why most of the classic textbooks only consider Additive White Gaussian Noise channels in digital data transmission. Unfortunately in my case noise is not Gaussian and it might even be ...
1answer
690 views

### Determinant of Hessian approximation (SURF)

I have a question regarding formula in SURF article by Bay et al. Theory Given a point $p=(x,y)$ in an image $I$, the Hessian matrix $\mathcal{H}$ in $x$ at scale $\sigma$ is defined as follows  \...
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1k views

### What does the output of Gaussian Mixture Model (GMM) represents in a HMM-GMM based speech recognition application?

Till now I know that- first the speech is converted frames and feature vectors are calculated for each frame using MFCC. And while training the Acoustic model- HMM model is generate for each phoneme ...
2answers
928 views

### Finding Argmax in MATLAB [closed]

I have a Gaussian random variable $z$, whose mean $\mu$ and variance $\sigma^2$ are functions of two variables $x$ and $y$. Is there any way in MATLAB so that I can find the values of $x$ and $y$ for ...
1answer
2k views

### What does it mean by “Adding Gaussian Noise to a 2D Image”? [duplicate]

As far as I understand, Suppose, we have a 2D image of pixel resolution 200 x 300. That means, the image has 60000 pixels in it. Now, we would generate $n$ random values and add those values to $n$ ...
2answers
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.
2answers
26 views

### Is there any transformation to exploit the sparsity of a Gaussian Wave?

I am looking for a transformation in which the gaussian wave when transformed with a particular analysis function would make the energy contents be mostly present only in a short band of frequencies?
1answer
1k views

### 2D Gaussian Seperation into 1D Gaussian components

I have been reading this http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm and I am having trouble to perform the seperability. So I kinda did it in paper. Lets say y Gaussian function is G(X,Y), ...
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346 views

### Double Integrating Gaussian Noise

My question has to do with integrating gaussian noise. Let us assume we have samples of discrete gaussian white noise with mean $\mu = 0$ and variance $\sigma_{th}^2$. These noise samples are passed ...
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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. ...
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476 views

### Gaussian wavelet generation of a given frequency

How can I generate a Gaussian wavelet (time domain) with a given central frequency. I mean, if I take the Fourier Transform then its spectrum should be around that given central frequency. For ...
1answer
135 views

### Is $A\cos(\omega t+\theta)$ a Gaussian random process?

$Z(t) = A\cos(\omega t+\theta)$ where $A$~$N(0,\sigma ^2)$ and $\theta$~$(0,2\pi)$ are independent. I'm trying to figure out if $Z(t)$ is a Gaussian random process and whether it is strict sense ...
1answer
829 views

### Gaussian filter in terms of pixel radius

So I'm writing an app that blurs and downscales large quantities of images, but all the image processing libraries I've come across define gaussian blurs in terms of sigma and kernel size rather than ...
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### what is a Gaussian signal?

I am learning Wiener filtering for 2D images by myself. From one book, it reads It should be noted that the study of the more general problem of signal denoising dates back to at least Norbert Wiener ...
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623 views

### Implementing a 1-D Kalman Filter Regression, Missing the smoothing action (getting the opposite)

I am implementing the 1D Kalman Filter in Python on a fundamentally noisy set of measurement data, and I should be observing a large amount of smoothing...but, instead, my Kalman Filter is doing the ...
1answer
471 views

### How do I calculate the autocorrelation of a train pulse having only the pdf?

I have a pulse train of a fixed period, but a random amplitude following a Gaussian distribution $(\mu=0,\sigma=1)$. I know how to work with a random period or delay, but how do I proceed to calculate ...
1answer
770 views

### How to make a 2D gaussian Blur terms?

I want to make a 2D gaussian Blur coeffients. Now I am making 1D gaussian Blur term as following. ...