Questions tagged [gaussian]

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22
votes
3answers
60k 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 ...
16
votes
6answers
24k views

How to Generate Band Limited Gaussian White Noise in MATLAB?

In some papers, I read that the additive noise is band limited Gaussian white. How can I simulate this type of noise use MATLAB?
16
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3answers
6k views

How do I add AWGN to an I and Q representation of a signal?

I have a wireless communication system that I am simulating in Matlab. I am performing some watermarking through slightly adjusting the phase of the transmitted signal. My simulation takes the ...
15
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2answers
6k 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 ...
12
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2answers
8k views

What is the relationship between the sigma in the Laplacian of Gaussian and the two sigmas in the Difference of Gaussians?

I understand that a Laplacian-of-Gaussian filter can be approximated by a Difference-of-Gaussians filter, and that the ratio of the two sigmas for the latter should be 1:1.6 for the best approximation....
11
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5answers
9k views

Low-pass filter parameters for image downsampling

I need to downscale an image in a factor of $s_x$ horizontally and $s_y$ vertically ($s_x$, $s_y$ < $1$). I want to use a finite $n\times m$ low-pass filter before downsampling. How should I ...
10
votes
5answers
5k views

Why is random noise assumed to be normally distributed? [duplicate]

From residual in the linear regression to noise in signal processing are assumed to be normally distributed? By considering them as normally distributed we are kind of telling the pattern in the noise ...
9
votes
3answers
884 views

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 ...
9
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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.
8
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1answer
4k 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 ...
8
votes
2answers
9k 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 ...
8
votes
1answer
2k views

Is there a mathematical method to determine if noise is Gaussian?

Is there a mathematical method to determine if a signal's noise is Gaussian? The only way I know so far is to analyze the histogram and layover a Gaussian distribution to visually determine if the ...
8
votes
1answer
1k views

Is the discrete Gaussian kernel an eigenfunction of the DFT?

So the Gaussian function is an eigenfunction of the Fourier transform because it transforms into itself, right? But this isn't true for the sampled Gaussian in the DFT because the tails of the ...
7
votes
2answers
290 views

What is the difference between a simple gaussian filter and gaussian filter multiplied by its sum of it elements?

1 2 1 1 2 1 2 4 2 (A) (1/16) * 2 4 2 (B) 1 2 1 1 2 1 Both matrices are the same ...
7
votes
1answer
2k views

Choice of Gaussian kernel parameters when lowpass filtering before image resampling?

I need to decimate a signal by a factor of q. More specifically my signal is a 3D "image": $\ I(x_i,y_j,z_k)$, which I need to downsample by a factor of two in the z direction. I want to do lowpass ...
5
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2answers
3k views

Why should an image be blurred using a Gaussian Kernel before downsampling?

I recently read that before downsampling an image, it should be blurred using a Gaussian Kernel. This way, the downsampled image is better than just picking a single pixel out of a NxN block or ...
5
votes
1answer
2k 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 ...
5
votes
2answers
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 ...
5
votes
2answers
5k views

Gaussian Filter Close to Image Border

When applying Gaussian filters close to the borders of an image, algorithms usually zero-pad or replicate/mirror/wrap the borders. This is not good enough for my case, so I wonder if there is ...
5
votes
1answer
111 views

Is there a transformation filter to decode light signal through Glass Bricks?

A friend is doing renovations and getting his entire ground-floor street-side wall replaced with glass bricks. I told him that with all those bricks giving similar distorted views of the same room, ...
5
votes
1answer
1k views

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....
5
votes
0answers
181 views

Distribution of the output of AWGN channel

$$\mathbf{Y}=\mathbf{X}+\mathbf{W}$$ $\mathbf{X}$ is input, an $n$-dimension equiprobable vector in a finite subset of complex space $\mathcal{A}^n \subset \mathbb{C}^n$ with norm $\sqrt{\rho n}$ (...
4
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5answers
2k views

Why Does the Kalman Filter Remove Only Gaussian Noise?

What and where in the derivation of the Kalman filter is the assumption of Gaussian noise? Why and how does this assumption help?
4
votes
2answers
4k 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 ...
4
votes
1answer
1k 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: ...
4
votes
1answer
1k 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?
4
votes
2answers
343 views

STFT calculation with Gaussian Window

$$ f(t)=\exp(jat^2) \,\,\, and \,\,\, g(t)\,\,is\,\, a\,\, Gaussian\,\, Window:$$ $$ g(t)= \left (πσ^2\right)^{\frac{-1}{4}}\exp\left (\frac{-t^2}{2σ^2} \right ) , \,\,\,\,\,\,\left \|g(t) \right \|...
4
votes
1answer
153 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 ...
4
votes
1answer
143 views

2D Multi Scale Dot Enhancement Filter based on Gaussian Filter and Hessian Matrix

I'm trying to implement an algorithm that enhance dot and line like structures based on Hessian matrix, the algorithm uses Gaussian filter with different scales before calculating the hessian matrix ...
4
votes
1answer
326 views

Zero padding effect on a FFT of gaussian noise

I have a gaussian noise $\nu(t)$ with variance $\sigma^2$. After a FFT I get $X(\omega)$. If now I do the IFFT on the $X(\omega)$ can I say that the result is still a gaussian noise of variance $\...
4
votes
1answer
3k 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 ...
4
votes
1answer
140 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 ...
4
votes
1answer
388 views

Shannon capacity with distribution different from Gaussian

If I understand correctly, in AWGN channel, for a given SNR, there is a code for $M$ input codeword $\mathbf{X}_{i, 1 \leq i \leq M}$ that $$\lim_{n \to \infty} R=\lim_{n \to \infty}\frac{\log(M)}{n} ...
4
votes
1answer
915 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 ...
3
votes
3answers
3k views

Gaussian random generator

I have quite a straight-forward question. What I aim for is the generation of a certain set of random numbers with a normal distribution (mu = 0, ...
3
votes
2answers
123 views

Signal with Complex Gaussian noise

If I have: $$ y = x_r+jx_i + n_r +j n_i$$ with $n_r$ and $n_i$ Gaussian with mean 0 and variance $\sigma^2$, what is the pdf of the envelope |y| and phase(y)? Is it still Rayleigh-distributed and ...
3
votes
2answers
2k 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 ...
3
votes
1answer
8k views

What is use of a gaussian filter over histogram?

I am working in the field of digital image processing and currently i am reading this paper and I have two questions about it.... After applying a gaussian filter to a histogram, will the pixel ...
3
votes
1answer
417 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/...
3
votes
1answer
849 views

Determine Parameters of gaussian distribution to fit a certain Image-Filter

I'd like to know what the parameters for the two-dimensional gaussian distributions are, which create this (I think) quite common image-processing filter: $$ h_\sigma(x,y)= \left[ \matrix { 1&2&...
3
votes
1answer
160 views

Higher-order moment of output of LTI system

Assume a very simple LTI system. Assume $x$ is white Gaussian i.i.d. with variance $\sigma^2$. The output variance is straightforward to obtain. For example, for a continuous-time system: $$\mbox{...
3
votes
1answer
15k views

Fit data to Gaussian distribution

I want some data to fit the corresponding Gaussian distribution. The data is meant to be Gaussian already, but for some filtering reasons, they will not perfectly match the prescribed and expected ...
3
votes
1answer
318 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....
3
votes
1answer
808 views

Discrepancy between Gaussian FFT and its Fourier Transform

I am trying to do the FFT of a Gaussian signal and comparing it to the theoretical Fourier transform. For infinitely small time step $dt$ and infinitely long signal length $T$, the 2 should become ...
3
votes
2answers
257 views

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 ...
3
votes
1answer
770 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 \...
3
votes
1answer
179 views

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

$Z(t) = A\cos(\omega t+\theta)$ where $A$~$\mathcal N(0,\sigma ^2) $ and $\theta $~$\mathcal U(0,2\pi)$ are independent. I'm trying to figure out if $Z(t)$ is a Gaussian random process and whether it ...
3
votes
1answer
162 views

Multi Scale 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: \begin{equation}\...
3
votes
1answer
331 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 ...
3
votes
1answer
258 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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