Questions tagged [gaussian]

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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
65 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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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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2answers
250 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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2answers
122 views

MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)

This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv If $v \sim CN(0,2\sigma^2_v)$ ...
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2answers
5k views

How to Calculate Gaussian Kernel for a Small Support Size?

How to calculate the values of Gaussian kernel? I think I understand the principle of it weighting the center pixel as the means, and those around it according to the $\sigma$ but what would each ...
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5answers
23k 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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1answer
831 views

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 ...
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2answers
2k 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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2answers
265 views

Optimum Filter Signal Detection for Non AWGN Channels

I have been reading this question and it confirms that the matched filter is the maximum-likelihood receiver in the presence of additive white Gaussian noise. So in the AWGN channel it maximizes the ...
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1answer
182 views

What is stochastic differential equation and its need?

A white noise process can be simulated using the Matlab command randn(). The numbers will be drawn from a Normal distribution of zero mean and variance 1. Is the ...
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1answer
728 views

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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2answers
365 views

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 ...
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1answer
205 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 ...
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1answer
20 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 =...
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2answers
943 views

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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1answer
597 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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1answer
74 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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1answer
924 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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1answer
14 views

How good is the Leech lattice for AWGN coding or MSE quantization of Gaussian sources?

Anyone know where to find graphs showing how well it works vs other schemes? thanks
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1answer
132 views

Relation between constellation SNR and baseband SNR

Let's say I have an I/Q modulation, ie. QPSK. I can simulate an the effects of an AWGN channel by adding to my QPSK symbols the realizations of a complex normal. $\mathcal{CN}(0,\frac{1}{\mathrm{SNR}...
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1answer
90 views

Fast Recursive 1D Signal Smoothing - IIR / Auto Regressive Implementation of Gaussian Smoothing

I have just begun to dive into the field of signal processing, but there is the need to program a digital filter, that has to smooth a realtime signal from a sensor device. As far as I know, in my ...
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1answer
66 views

SIFT About Difference-of-Gaussian function extrema?

How to get formula (2) by formula(1)?
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1answer
801 views

How Does the RMS of White Noise Change with Sampling Frequency?

There is an analog system which includes the continuous-time linear equalizer (CTLE). With some .noise analysis the power-spectral density (PSD) of the noise in that system is provided. So let's not ...
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1answer
44 views

Play with a Gaussian random set in the frequency domain to obtain desired effect in the time-domain

Please assume we have a set of 100 random numbers obeying Gaussian PDF in time-domain. Let's index them 1-100. Within a time-accurate simulation, I apply four operations on this dynamic set every ...
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1answer
38 views

From Uniform to 2D gaussian

I have a 2D uniform distribution. I would like to assign probability-weights in the distribution, according to the standard deviation to convert the distribution into a 2D gaussian. I know how to do ...
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1answer
213 views

$\tt awgn$ and $\tt wgn$ functions in MATLAB always output the same signal, no matter what I input as SNR

I'm very new to all of this. Right now I'm just trying to add a bunch of different noises to an input signal and see how they affect my signal. This is the current output of my code: ...
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1answer
240 views

Fourier transform of a Gaussian in Excel returns imaginary coefficients [duplicate]

I am using Fourier Analysis tool in Excel to transform a Gaussian $\exp(-x^2)$ on a uniform and symmetric grid of $x$ values. I am expecting the result to contain only real numbers (which should ...
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2answers
364 views

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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2answers
2k views

Parameters of Gaussian Kernel in the Context of Image Convolution

Hi Everyone i am new at image processing. I copy code from this website, I have image $600 \times 480$ gray scale. What will be the value of standard deviation or $\sigma$? What will be the value of ...
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1answer
208 views

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 ...
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1answer
301 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 ...
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2answers
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
366 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
484 views

Gaussian wavelet generation of a given frequency

How can I generate a Gaussian wavelet (time domain) with a given central frequency. I mean, if I take the Fourier Transform then its spectrum should be around that given central frequency. For ...
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1answer
479 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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2answers
81 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
190 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
566 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
101 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
1k views

Applying Gaussian Blur in Frequency Domain

Please see second update I'm trying to implement gaussian blur in frequency domain using c#. Those are steps that I'm doing: Load bitmap. Split bitmap into separate color channels. Convert every ...
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1answer
415 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
53 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
134 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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1answer
952 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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0answers
8 views

Problem implementing KL expansion with square-exponential kernel: output just looks like Gaussian

I am trying to implement the Karhunen Loeve expansion for a 1-D Gaussian random field with a square-exponential kernel. Specifically, I know that a Gaussian process has a KL expansion $\hat{U}=\sum_{...
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0answers
93 views

Audio experiment with intermodulation by multiplying two analytic signals

1) First, I describe intended processing with a basic case: Let's say on left channel I have a sin wave with frequency F1, and constant amplitude A1. Then on right channel a sin wave with frequency ...
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1answer
50 views

Low-Pass FIR that keeps all values positive

Let's say, that I want to low-pass the norm (hence positive values) of an analytic signal (related to Hilbert transform). This allows me to perform experiments with the envelope of audio. For low-...
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0answers
24 views

Acoustic features

I am working on an automatic sound recognition project. I found that the LDA performs better than the SVMs. Does this mean that the acoustic features are Gaussian distributed? Also, is this the ...
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0answers
7 views

How to normalize data by mapping data points from one mixture of multivariate normal distributions to another

Problem description I am trying to normalize multivariate time series data. The individual data sets (spectrograms from temporal EEG) comes from sources that differ widely in their noise ...