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Questions tagged [gaussian]

The gaussian function, an exponential function with a negative square of the argument in the exponent, is interesting in signal processing because the Fourier Transform of a gaussian function is also a gaussian function.

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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 ...
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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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Transform coding gain of two channel Haar Wavelet transform (first stage)

Question My interpretation Work I'm attempting to do this in MATLAB. I know that for discrete Random Processes going into an LTI system the autocorrelation function of the output is $R_y[n] =...
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Brownian noise is integration of gaussian or uniform white noise?

On this wikipedia page it is written that Brown noise can be produced by integrating white noise What kind of white noise is meant? The Gaussian or uniform white noise?
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Parameters of Gaussian Kernel in the Context of Image Convolution

Hi Everyone i am new at image processing. I copy code from Code with C - Gaussian Filter Generation in C++, I have image $600 \times 480$ gray scale. What will be the value of standard deviation or $\...
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10 votes
3 answers
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Capacity of AWGN channel

I am confused understanding basic concepts of communication over AWGN channels. I know the capacity of a discrete time AWGN channel is: $$C=\frac{1}{2}\log_2\left(1+\frac{S}{N}\right)$$ and it is ...
Mah's user avatar
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Parameters of Butterworth filter that approximates the amplitude response of a Gaussian filter?

For a given narrowband Gaussian filter with a specific central frequency and filter width, I need corners of a bandpass Butterworth filter whose amplitude response is close enough to the Gaussian ...
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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 ...
Ria George's user avatar
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2 answers
1k views

bandwidth limited pulse,what window function is it?

I want to know what kind of shape a multiple cycle sine wave pulse ( or maybe the correct term is burst ) should have to have the narrowest bandwidth possible at given pulse width. In the laser ...
Sweeper's user avatar
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Value of power spectral density $N_0$ or effect of scaling bandwidth to SNR

I want to compare performance over AWGN channel of two systems that are exactly identical but their bandwidth. I will talk only about baseband system for sake of simplicity. For more details about ...
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Is there any way to measure of Gaussian-ness?

I have some sampled data that has $1/f$ noise in it, with departures from the mean. These are long term departures. I could use something like a median filter but the window length would be longer ...
Voltage Spike's user avatar
6 votes
1 answer
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Convolution of Two Kernels [OpenCV]

I've been completely stuck on a portion of my assignment for a few days now. After plenty of searching around, I have been unsuccessful in discovering information that leads me to the correct solution....
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What should be the output of the pdf for multivariate normal distrubition?

Let's think we have a multivariate normal distribution with $$\mathbf x_1=\begin{bmatrix}x_{11}\\x_{12}\end{bmatrix},\quad \mathbf x_2=\begin{bmatrix}x_{21}\\x_{22}\end{bmatrix},\quad\mathbf m=\begin{...
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Additive White Gaussian Noise (AWGN) 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 ...
Alexander Reshytko's user avatar
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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 ...
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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. In some fields, it is called ...
Laurent Duval's user avatar
3 votes
2 answers
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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 ...
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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 ...
Karthik Swaminathan's user avatar
2 votes
2 answers
288 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 ...
Laurent Duval's user avatar
2 votes
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142 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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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 ...
Raj's user avatar
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2 votes
1 answer
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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 ...
Fred's user avatar
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1 vote
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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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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 ...
Jogging Song's user avatar
1 vote
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409 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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1 answer
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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 ...
physioConfusio's user avatar
5 votes
1 answer
259 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 ...
DSP_user's user avatar
2 votes
2 answers
1k 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 ...
Jogging Song's user avatar
6 votes
1 answer
7k 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 ...
DVG's user avatar
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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 ...
Guilherme Gaspar's user avatar
5 votes
1 answer
1k 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 \...
a concerned citizen's user avatar
2 votes
1 answer
595 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 ...
sambajetson's user avatar
1 vote
1 answer
1k 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( ...
user2350366's user avatar
2 votes
3 answers
850 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 ...
gfole's user avatar
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2 votes
3 answers
2k 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. ...
Lolo's user avatar
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4 votes
1 answer
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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 ...
Television's user avatar
3 votes
2 answers
152 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 ...
sideband's user avatar
3 votes
1 answer
3k 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 ...
Libor's user avatar
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6 votes
1 answer
699 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 ...
The Dude's user avatar
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0 votes
1 answer
241 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 ...
Ajith's user avatar
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10 votes
2 answers
16k 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 ...
eecs's user avatar
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1 vote
1 answer
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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 ...
Tab's user avatar
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2 votes
2 answers
17k 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 <...
zahraesb's user avatar
  • 135
0 votes
1 answer
35 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 =...
jakeoung's user avatar
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1 vote
0 answers
54 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 ...
MUH's user avatar
  • 111
2 votes
1 answer
150 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\...
John's user avatar
  • 585
3 votes
1 answer
154 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 ...
Ali's user avatar
  • 153
2 votes
1 answer
1k 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 $$ \...
Lupus's user avatar
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1 vote
0 answers
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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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