Questions tagged [gaussian]

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Standard deviation of Gaussian corresponding to perfect low pass filter [1,1]

For a time discrete signal, the rect-filter (for 1D signal [1,1]) is a perfect low pass filter. I was wondering, what is the best gaussian approximation of this filter? For a current problem, I ...
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5answers
22k views

noise of zero mean and variance?

It might be a very silly question, however I'm facing problem with it. Now, the Gaussian noise is a signal with zero mean and variance. I understand what the mean and the variance mean however, I'm ...
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0answers
96 views

What is SNR of Signal with Additive White Gaussian Noise [duplicate]

Calculating the power of AWGN should be equal to infinity as PSD is constant and its integration is infinity over all frequencies. Hence for any signal with finite power mixed with AWGN, SNR should ...
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520 views

Constant amplitude, uniform phase - what's the distribution of the complex signal then?

The well-known relationships for zero-mean circularly-symmetric complex Gaussian $z = a + jb = |z| \exp(j\varphi)$ signals are the amplitudes $|z| = \sqrt{a^2 + b^2}$ are Rayleigh-distributed the ...
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1answer
2k views

How to generate AWGN with given power spectral density

I am a little unsure about the generation of a additive white Gaussian noise, so I would appreciate to hear from you if I`m doing it correctly. My goal is to generate the time-domain noise ...
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0answers
56 views

Thresholding for Movement Classification

I have an application which creates a Gaussian model of the background based on consecutive frame difference and auto-generates a threshold for separating no-changes to movements. The application ...
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0answers
64 views

Is a Stationary VAR Process with Zero Mean Gaussian Innovations a Gaussian Stationary Process?

Consider the stationary VAR process $${\bf X}_t = \sum_{\tau = 1}^{L} A_\tau {\bf X}_{t-\tau} +{\bf \epsilon}_t$$ If the innovations $\epsilon_t \sim MVN({\bf 0},\Sigma)$ then is ${\bf X}_t$ a ...
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1answer
131 views

frequency components of discrete Gaussian-windowed signal

When we are do a discrete Gabor transform on a 1D signal, we apply a Gaussian window on a segment of the signal. However, due to the tapering ends of the Gaussian window, the magnitude of the data ...
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2answers
246 views

Calculating information loss in a signal after smoothing?

I have a signal. I applied Gaussian smoothing to it and then for baseline reduction I appied Tophat filter to the smoothed version. This is the original signal: This is the final signal: I read ...
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1answer
196 views

Highpass filter applied to noise

Suppose the input signal is represented as $$y=x+w$$ where $x$ is the signal to be estimated and $w$ is AWGN. I design a high pass filter $H$. What does $$H^{T}Hw$$ represent? Will it be just AWGN but ...
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0answers
62 views

Fitting VAR Process with Generalised Gaussian Noise

Consider the $m$-dimensional VAR process $${\bf x}_t = \sum_{l=1}^{P} A_l{\bf x}_{t-l} + {\bf e}_t$$ where the componenets of ${\bf e}_t$ are spatially and temporally independent and follow a ...
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3answers
4k views

Which sigma to use for edge detection

I know that in many edge detection algorithm the first step is choosing a scale to work on. We actually operate on the chosen scale by applying a gaussian blur on the original image. I wanted to ...
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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 ...
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2answers
264 views

Situations where complexity is too big to exceed linearity and gaussianity

I'm studing about Kalman Filter and Particle Filter in multiple target tracking in computer vision (tracking pedestrians). Reading sientific papers I'm colliding with a lot of sentences like: The ...
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3answers
46k 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 ...
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1answer
7k 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 ...
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1answer
894 views

gaussian kernel and bionomial coefficients

The following image is from robert collins' ppt from http://www.cse.psu.edu/~rcollins/CSE486/ How to calculate sigma ? It shows [1 4 6 4 1] is corresponding to sigma=1. I learned that usually 3*...
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2answers
5k 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 ...
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5answers
22k views

How to Generate Band Limited Gaussian White Noise?

In some papers, I read that the additive noise is band limited Gaussian white. How can I simulate this type of noise use Matlab?
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1answer
809 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&...
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1answer
83 views

Is there a need of Point interpolation before proceeding for gaussian smoothing of an incomplete distribution?

Suppose there is a distribution that has values sampled on the interval 1-25 with corresponding sample values that have to be smoothed. For example: ...
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1answer
629 views

Estimating number for iterations for gaussian smoothing

I have some data sets on which I applied Gaussian smoothing using [1 4 6 4 1] kernel. In my program I iterated this kernel 50 times on the data sets. But only a few ...
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3answers
2k 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, ...
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2answers
241 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 ...
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2answers
3k 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 ...
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1answer
5k views

Determine the optimum receiver and the corresponding $P_{eM}$ for an AWGN channel

I have a source that emits $M$ equiprobable messages, which are assigned signals $s_1, \dots,s_M,$ that are equidistant by $a$. That is, if we plot the $s_k$ signals in a horizontal axis they are dots ...
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1answer
14k 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 ...
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0answers
137 views

Compensate for standard deviation loss

I am not sure if this question will be a little off-topic on this forum, that I will give it a try anyway, since it implies signal process arguments. By using ...
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1answer
1k 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 ...
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1answer
602 views

How to Obtain Mathematically High Frequency and Low Frequency Component Separately Using Bilateral Filter?

I have asked this question before in the sense that what does a high frequency and low frequency component signify in a image and i got satisfactory answers now i want to know that how i can get high ...
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5answers
8k 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 ...
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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 ...
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1answer
110 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, ...
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2answers
7k 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....
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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 ...
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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 ...