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Questions tagged [gaussian]

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389 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 ...
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0answers
78 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 ...
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1answer
938 views

Complex normal Gaussian noise

I would like to create complex normal Gaussian noise with dimensions $(M,N)$. The noise should be zero mean and the variance should be equal to one. How can I do so?
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0answers
494 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 ...
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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 ...
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1answer
667 views

Poles of an analog Gaussian filter

I am trying to calculate the poles of an analog Gaussian filter. Its characteristic function, $e^{-\log(2)x^2}$, can be expanded into MacLaurin series: $$2^{-x^2} = e^{-\log(2)x^2} = \lim_{N \to \...
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1answer
144 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 ...
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0answers
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 ...
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1answer
233 views

Mutual information of $ \infty $-PAM

I'm trying to compute using matlab the mutual information for an $ \infty $-PAM input (the limit of a very dense PAM constellation) for a range of snr and I got stuck. I'm working with a real-valued ...
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1answer
125 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 ...
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0answers
378 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 ...
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1answer
48 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 ...
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1answer
397 views

Difference of Gaussian filter but using Gaussian CDFs not PDFs

A very common filter in signal / image processing is the Laplacian of Gaussian filter, and its approximation, the difference of gaussians filter. The DoG filter is the difference of 2 Gaussian PDFs ...
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1answer
714 views

Does the Wiener–Khinchin-Einstein theorem hold for non-Gaussian processes? If so are there any assumptions?

The Wiener–Khinchin-Einstein theorem states that the auto-correlation $(r_{xx}(\tau))$ and spectral density $(S(f))$ are Fourier duals, i.e. $$r_{xx}(\tau) = \int^{+\infty}_{-\infty} S(f) \exp\left( ...
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3answers
397 views

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 ...
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1answer
109 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 ...
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1answer
769 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 ...
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2answers
136 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 ...
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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 ...
2
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1answer
289 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 ...
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1answer
221 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 ...
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1answer
41 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 ...
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1answer
216 views

What is the most efficient way to perform Gaussian blurs for varying sizes of Gaussian kernels in an image?

I have detected corner points of images using Harris corner detector in GLSL and now, I intend on using Fast Retina Keypoint(FREAK) as keypoint descriptor to later match the keypoints between images. ...
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1answer
23 views

Derivative of equation containing Gaussian filtered image

Let $w$ be our image. For example, consider the following with the vectorized $w$: $$ E(w) = \frac 12 \|Aw+b\|_2^2 $$ I know the optimal condition of the above equation: $$ \nabla_wE = A^TA\hat w + b =...
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1answer
133 views

How can I implement image widowing in my image in Java?

My initial image is a medical image and my main objective is finding directionality. The original size of my image was 8X8 and I have rescaled the image to 32X32 to increase my accuracy. My input ...
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0answers
37 views

Analytical expression for salient Blob detection in scale space

I am working on exact mathematical expression which can be obtained in image processing tasks.(I do not know much about image processing but my work is more mathmatical) In Gaussian scale space, we ...
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1answer
75 views

Which is correct representation for function of variable?

I have a function as $$E=\int_\Omega -\log\big( p_i(x)\big) dx$$ where $p_i(x)$ is density distribution which estimated by Parzen window method. $$p_i(x)=\frac{1}{\Omega_i} \int_{\Omega_i}K_\sigma\...
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0answers
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 ...
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2answers
966 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 ...
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2answers
319 views

equations to calculate coefficients of recursive IIR Gaussian blur filter

I am reading the implementation of IIR Gaussian blur filter from this link. In the source code, the coefficients are generated by the following code ...
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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 $n$ ...
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2answers
3k 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.
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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?
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1answer
396 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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1answer
2k 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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1answer
518 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 ...
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1answer
968 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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2answers
3k views

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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1answer
660 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 ...
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4answers
2k views

filter coefficients to know high pass and low pass filter

Looked on few questions already there in dsp.stackexchange and couldn't get the direct answer. Basically I have a kernel of a gaussian separable filter. ...
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1answer
802 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. ...
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0answers
71 views

Curve fitting to distorted Gaussian

I have to measure the distance between two pulse trains, each of which looks like a slightly long tailed Gaussian distribution. Is there a relatively easy curve fitting method for this? I can do it ...
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1answer
58 views

How to derive the $\log$ of fraction of two Gaussian distribution

I am designing a function $A(x)$ that map $x\to \{0,1\}$. The function $A$ can be expressed as $$A(x)=\begin{cases} 1 \text{ if $p_1(x) \ge p_2(x)$}\\ 0 \text{ otherwises} \end{cases} $$ where $p_1$...
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1answer
94 views

What is the equivalent smoothing function to running the same Gaussian 8 times?

Suppose there is an image which is to be smoothed by convolving it with a Gaussian kernel with standard deviation $\sigma$. If the image is then smoothed with this kernel 8 consecutive times, is the ...
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1answer
643 views

Uniform quantizer for gaussian input signal

I have a gaussian signal $x$ with zero mean and unit variance. I am quantizing it by using a uniform quantizer of step size $q$ calculated by $$q = \frac{x_\mathrm{max} - x_\mathrm{min}}{2^{M_\mathrm{...
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2answers
788 views

Gaussian noise generator algorithm trouble

I stumbled upon the following algorithm for Gaussian noise generation and I just can't figure out how this is supposed to work at all. The algorithm is as follows: First of all: $j = \arg\min_i (q_1 ...
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2answers
83 views

How does gaussian convution stacking work?

If I first convolve an image with a Gaussian filter with σ = 1, and then convolve the output of that image with a Gaussian with σ = 2 Does this give the same effect as convolving the original image ...
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1answer
139 views

Multiscale Shape and Detail Enhancement from Multi-light Image Collections

I have been working on a practical implementation in Matlab of the algorithm Raanan Fattal suggested in the following paper. I couldn't understand the meaning of eq. 11 on page 5: g is a gaussian, ...
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1answer
196 views

Gaussian in matlab

I have written a function that implements a gaussian filter. I use fft2 to transform my image and my filter to 2d fourier transform. Then I multiply them and then use ifft2. The resulting image is ...
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1answer
466 views

Complex Gaussian Channel + AWGN noise

If I define a channel to have complex Gaussian coefficients, do I still need to add noise to the signal passing through this channel using the command "awgn" or would that be redundant?