Questions tagged [gaussian]

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145 views

Why Does 2D FFT of Gaussian Looks More Sharper than Gaussian Itself?

I am trying to understand why 2D FFT is done on a Gaussian process in a particular code. From my understanding from these posts: https://www.researchgate.net/post/...
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1answer
884 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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2answers
802 views

carrier frequency difference

Papers use wireless device-dependent radio-metrics as fingerprints. A radio-metric is a component of radio signal, amplitude, frequency and bandwidth. Each device creates a unique set of radio-metrics ...
2
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1answer
65 views

ARMA Model - DSP

I'm taking a DSP course and we're being introduced to the whole probability/stats side of DSP and I'm just confused on things like the ARMA models. These things don't seem intuitive to me at all. ...
2
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1answer
236 views

Matched Filter of Gaussian Signal

How can we evaluate the matched filter's impulse response of a Gaussian function $x(t) = \exp(-\frac{t^2}{2})$. As far as we know, for a signal of finite duration $T$, the impulse response of it's ...
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1answer
58 views

Does a collection of Gaussian random variables necessarily constitute a Gaussian Process?

If $\{X(t)\}$ is a Gaussian Process then the random variables $X(t_k)$ where $k = 1,2,3...n$, are jointly Gaussian. If each random variable $X(t)$ is a Gaussian variable, then will the random ...
2
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1answer
3k 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 ...
2
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3answers
348 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 ...
2
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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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1answer
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. ...
2
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1answer
220 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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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. ...
2
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1answer
3k views

What is correlation kernel and compare with gaussian kernel

I read a paper that said about correlation kernel that defined: $$W(x-y)=(α/1+d(|y − x|))$$ where $α = (\int(1+d(y − x)dy)^{-1}$, $(d(|y − x|))$ is spatial Euclidean distance from the central pixel. ...
2
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1answer
117 views

Why Does the Odd Multiple of $ \frac{\pi}{4} $ on Gaussian Cause Loss in Repeatability Under Image Rotations?

I couldn't figure out below paragraph on SURF paper and hope that someone can help me to understand it. Why image rotations around odd multiples of $\frac{\pi}{4}$ lead to a loss of repeatability? ...
2
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1answer
65 views

Are There Common Values of Standard Deviation for Gaussian Noise of an Image?

For example, it occurs to me that there might be a standard deviation value of Gaussian noise in which the human eye could no longer distinguish an object because the standard deviation is very high ...
2
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1answer
147 views

What's the relationship between the parameters of this noise generator and the gaussian curve it produces in the frequency domain?

This algorithm produces a sequence $y$ having a magnitude spectrum that resembles a normal distribution, peaking at frequency $\omega$: $$b[n]=(1-\sigma)b[n-1]+\frac{\sigma}{\omega} C$$ $$p[n]=p[n-1]+...
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2answers
620 views

Fitting a gaussian image using opencv

I'm reading through the opencv documentation and some questions in SO but it doesn't seem to provide this information. I've an image $I(x,y)$ and I want to find a gaussian function $f_{\mu,\Sigma}(x,...
2
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1answer
82 views

Dimensional analysis of integrated white noise process

This question is somewhat related to this post. Let us consider we have a white noise current source $i_n(t)$, with a variance $\sigma_i^2$, and mean, $\mu_n=0$. Assume that this current is passed ...
2
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1answer
421 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, ...
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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. ...
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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
267 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 ...
2
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1answer
196 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. ...
2
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0answers
160 views

Noise PSD and sampling rate relation

Let's consider generating samples of a random process like white Gaussian noise (AWGN). Let's assume I am generating $N$ samples of AWGN with variance $\sigma ^2$ in MATLAB by using randn() funtion i....
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0answers
136 views

Gaussian filter convolution giving unexpected results

I am trying to smooth a time series signal with a Gaussian filter and then differentiate the signal (this is for an application for edge detection). A nice property of convolution is: $$ \frac{d}{dx} \...
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0answers
57 views

Detection over AWGN analysis disagrees with Monte Carlo simulation

I have a fixed vector $\mathbf{s} \in \{\pm1\}^m$ and a random vector $\mathbf{d} \in \{\pm1\}^m$. I send either $\mathbf{x} = \mathbf{x_1} = [\mathbf{s}\space\mathbf{d}]$ or $\mathbf{x} = \mathbf{...
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2answers
724 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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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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2answers
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 ...
2
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1answer
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 ...
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2answers
100 views

Is it a good idea to whiten a colored noise in order to apply formulas for AWGN?

I have posted a question before regarding the detection of a signal under colored Gaussian noise: Energy detection in presence of colored Gaussian noise Theoretical formulas for setting the detection ...
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1answer
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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3answers
326 views

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 ...
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2answers
889 views

How Is Laplacian of Gaussian (LoG) Implemented as Four 1D Convolutions?

I am trying to understand the four 1D convolution operations involved in implementation of Laplacian of Gaussian(LoG). I have read this answer and I am also reading ...
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2answers
202 views

How to approximate gaussian kernel for image blur

From wiki, a $3 \times3$ gaussian kernel is approximated as: $$\frac{1}{16}\begin{bmatrix}1&2&1\\2&4&2\\1&2&1 \end{bmatrix}.$$ Applying this kernel in an image equals to ...
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1answer
655 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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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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2answers
285 views

imshow command for Gaussian function

I'm trying to plot 2D gaussian function using "imshow" in MATLAB. However I could not see any white points in image. I tried to change sampling values and limits of x and y values. In addition to this,...
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1answer
184 views

Is there a clever way to implement cascaded moving average filters?

I'd like to effeciently approximate a gaussian filter's step response using cascaded moving average filters. I know about recursive moving average, but is there some clever algorithm to cascade them ...
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1answer
499 views

Gaussian window and standard deviation

I am trying to figure out how to use the matlab gausswin function which constructs a Gaussian window for $N$ samples with a given standard deviation $\sigma$. The function is defined by ...
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2answers
95 views

Derivation of $ R_{N(t)}(\tau) $ from its $f_{N(t)}(\eta)$

How can we prove the auto-correlation function of white gaussian noise $\{ R_{N(t)}(\tau) \}$ is $\frac{N_0}{2} \delta(\tau)$ from its p.d.f in equation below? $$ f_{N(t)}(\eta)=\frac{1}{\sqrt{2 \pi \...
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2answers
303 views

Why does second order Gaussian called Laplacian Gaussian?

We usually use Laplacian of Gaussian as the filter for edge detection or blob detection. But the filter itself is essentially a second order Gaussian. So why do we call it Laplacian of Gaussian? Is ...
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2answers
702 views

What is DC level in white gaussian noise?

Am studying unbiased estimators and keep seeing this term "DC Level". What is the expansion of DC and what is a DC Level? Even the Wikipedia page on WGN says nothing about it.
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2answers
289 views

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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1answer
88 views

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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1answer
59 views

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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1answer
57 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
85 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
1k views

How Does Gaussian Blur Affect Image Variance

I am trying to find a way to analytically estimate how the noise (or variance in pixel values) will be affected for a zero-frequency image of random noise after applying a Gaussian blur. In more ...
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1answer
1k views

Downsampling and Gaussian filtering in the context of scale space pyramids

In the context of scale space image pyramids using Gaussian filters I noticed that it's common to downsample the image after blurring with $\sigma = 2*\sigma_{init}$ . My question is: What is the ...