Questions tagged [gaussian]

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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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360 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
3k 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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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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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
487 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
623 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
1k 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
791 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
833 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
76 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
59 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
102 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
778 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
894 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
112 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
205 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
491 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?
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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....
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1answer
6k views

Question about Difference of Gaussian (DoG) algorithm

I am recently learning about Computer Vision and I am having a trouble understanding Difference of Gaussian (DoG) algorithm. I get how the algorithm works in high level idea, but I am trying to ...
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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 ...
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1answer
625 views

FFT function of Gaussian pulse

I need gaussian pulse fft. I set the sigma of gaussian pulse 1e-10 and define the gaussian function in time and use the fft. as you know the amplitude of should be unit in frequency domain. but my ...
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1answer
1k views

Why/How a Gaussian Channel is both band-limited and Power limited?

All physical channels are band-limited, such that, X(f) = 0 for |f| > W A Gaussian Channel is limited in both power and bandwidth. For this reason we encounter phrases, such as, "A band-limited ...
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1answer
116 views

Can we decompose a correlated random variable into correlated plus uncorrelated?

Assume a random sequence $ Y_k = X_k \cdot H_k + W_k $ where $X_k$ is a deterministic quantity, $H_k$ is a correlated random sequence, $W_k$ is Additive White Gaussian random sequence. Can we ...
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1answer
444 views

Is there a closed form expression for noise other than white noise?

For white noise, where the PSD is constant, we can model that as a simple Gaussian. Is there any way to model the probability density function of other types of noise (pink noise, red noise, blue ...
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1answer
77 views

What type of sensors have complex Gaussian noise?

What type of sensors have complex Gaussian noise? Do strain gauges also exhibit such noise?
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0answers
135 views

Effect of Gaussian Smoothing to mean image intensity

I am implementing Perona-Malik Diffusion in using the formulas: Creating image at time k+1 using equation This is my implementation: ...
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1answer
47 views

How to determine stopband of discrete Gaussian, stdev sigma, support N

I would like to analyse a gaussian smoothing kernel with a set standard deviation and support (let's say, in MATLAB, fspecial('gaussian', [5 1], 1.3) so sigma is 1.3 and support is 5) in the DTFT ...
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0answers
59 views

Relation between Gaussian and Savitsky-Golay kernels

I would like to make a mathematical comparison between two methods in my field. One smooths with a Gaussian filter, and one smooths using a second-order Savitsky-Golay filter. Let's say the window ...
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2answers
305 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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2answers
900 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 ...
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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 ...
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1answer
317 views

Spacing between gaussian windows for STFT

I'm computing discrete short time Fourier transform. Data is split into overlapping chunks and gaussian window is used for each chunk. However, I'm not sure how much overlap there should be between ...
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2answers
4k 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 ...
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1answer
56 views

Different results for seperable filtering v/s direct filtering on 2-D image in MATLAB

I compared the difference between seperable and direct filtering for MATLAB's cameraman image. The difference is huge. I would like to understand the reason for this. Code below. ...
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1answer
1k views

Fixed SNR with unitary noise variance

I've just one question : How can I write a model like y = x + w,( with w a white gaussian noise) with a fixed SNR and a noise variance equal to 1. What coefficient may I have before x ? Thanks !
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What is purpose of correlation kernel? IIs it high pass filter or low pass filter?

I am research about correlation kernel and I have some questions that need your help. Let see the pp. 3302-3303 in the paper: Changyang Li, et al., Robust Model for Segmenting Images With/Without ...
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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. ...
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1answer
753 views

Intuition behind the Gaussian Filter in Image Processing

I've been using a Gaussian Filter and know how to use it but I don't understand the physical significance behind using the filter. We use it but why? What is the significance? I'm just starting out in ...
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1answer
675 views

Expectation of product of Filtered White Gaussian Noise

Assume I have a random process $X(t)$ that is white gaussian noise with psd $S(f)$. Now, let's filter that noise through a LPF of bandwidth $B$. How would I evaluate the following expression: $$E[S(...
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2answers
2k views

Computer Vision - Gaussian Pyramid, Scale Space and Pattern Matching

I am planning to implement a pattern matching algorithm using something like correlation as a matching metric. I know that the template I am going to use will, if present, have different sizes in the ...
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52 views

Localization of a Gaussian

Studying for an exam I'll have I ran into a question about computing the localization of a Gaussian Filter in 1D, but sadly I have no idea of what such localization is. Can you give me a hint? ...
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1answer
277 views

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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0answers
560 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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3answers
5k 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
135 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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0answers
58 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 ...