# Questions tagged [gaussian]

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### 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 $\sqrt{\rho n}$ (...
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### 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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### Finding the error in the total integrated intensity of a fitted 2D Gaussian

I have been trying to fit signals to a 2D Gaussian function, and while I have bene able to use sciKit-image's curve_fit function to find the covariance matrix for ...
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### 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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### What Is a Weighted Local Histogram?

I'm reading through a couple of academic papers, and this terms often comes up "local weighted histogram". An example of quote is the following: First, cumulative histograms are built for every ...
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### Creating realization of 2D Gaussian field in Fourier space

I want to generate a 2D Gaussian field with dimensions $L\times L$ with $N^2$ cells each of size $l = L/N$. I'm doing this by producing a realization of this field in Fourier space by producing ...
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I have asked this at the Math SE also. Predicating this on the definition of the continuous Fourier Transform preferred by most electrical engineers: $$X(f) \triangleq \mathscr{F} \Big\{ x(t) \Big\}... 0answers 160 views ### Binomial Approximation of Gaussian Distribution It is said that we may use the binomial coefficients ( a layer from Pascal's triangle) to approximate the 1-D Gaussian kernel with certain \sigma, where \frac{n}{4} = \sigma and n is the index ... 1answer 255 views ### Interpreting zero-mean Gaussian noise in the context of Kalman Filters Consider an object moving in 2D space with constant speed v_x,v_y. If its acceleration is modelled as zero-mean Gaussian  a_x \sim N(0,\sigma_{a_x}^2) and  a_y \sim N(0,\sigma_{a_y}^2) within ... 0answers 78 views ### Help Understanding Radial Gaussian Filter I am currently reading through Mueller's "Fundamentals of Music Processing" and I am trying to understand audio segmentation through the use of self-similarity matrices. Currently, my matrix looks ... 0answers 39 views ### variance of filtered polynomial Consider the following system: What is the variance of y, \mathbb{E}(y^2) ? (EDIT: I know input signal has infinite power but will be made bandlimited by H. Both H and G are simple ... 0answers 378 views ### Gaussian Mixture Model-UBM based for image recognition Scenario: Open set recognition: Unknown individuals may appear on scene (CCTV). Gallery = 10 individuals with a mug-shot image per individual. Approach: Gaussian Mixture Model-UBM based Use video ... 0answers 37 views ### Analytical expression for salient Blob detection in scale space I am working on exact mathematical expression which can be obtained in image processing tasks.(I do not know much about image processing but my work is more mathmatical) In Gaussian scale space, we ... 0answers 1k views ### What does the output of Gaussian Mixture Model (GMM) represents in a HMM-GMM based speech recognition application? Till now I know that- first the speech is converted frames and feature vectors are calculated for each frame using MFCC. And while training the Acoustic model- HMM model is generate for each phoneme ... 0answers 71 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 ... 0answers 134 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: ... 0answers 57 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 ... 0answers 69 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$$If the innovations \epsilon_t \sim MVN({\bf 0},\Sigma) then is {\bf X}_t a ... 0answers 62 views ### Fitting VAR Process with Generalised Gaussian Noise Consider the m-dimensional VAR process$${\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 ... 0answers 8 views ### How to get sigma of gaussian from accelerometer noise ug/sqrt(HZ) I'm trying to model an accelerometer with gaussian noise in my application. The actual accelerometer has the following specs: ... 0answers 26 views ### Determine Gaussian distribution parameters from the signal-to-noise ratio Is there a straightforward formula for determining the mean and standard deviation of the gaussian distribution followed by noise applied on an image, knowing the signal-to-noise ratio between the ... 0answers 14 views ### Is splitting single white gaussian noise samples-stream in multiple sample-streams still gaussian noises? Suppose I have a random generator that generates gaussian distributed samples (mean = 0, variance = sigma) at a rate of 4*N samples per second. I want to generate 4 different streams from this ... 0answers 19 views ### How would I modify a squared-exponential covariance kernel to be periodic? I want to create a Gaussian process that resembles one generated by an exponential kernel (smooth and with a lot of variance) with a single caveat: I need the final value to be the same as the initial ... 0answers 17 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_{... 0answers 95 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 ... 0answers 25 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 ... 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 ... 0answers 41 views ### additive white Gaussian noise -ask fsk psk i want to simulate a system that uses ask,fsk ,psk in Matlab with additive Gaussian noise for each mode . figure shows the system propti and Eb/N0=6db my question is how to calculate the standard ... 0answers 46 views ### How do I narrow the frequency from a time domain Gaussian signal? I'm trying to get a frequency domain Gaussian signal that starts from 180.045 THz and ends in 180.65 THz. This is the matlab code I used to get the FFT of time domain Gaussian signal: ... 0answers 9 views ### How to warp and enlarge the center of an image? I am trying to smoothly enlarge the center part of an image. The Skimage code that I use need an inverse map that specifies location of input pixels that will occur at the output pixel location. If I ... 0answers 64 views ### Use of gauspuls command in matlab, unable to broad signal at frequency spectrum I have a doubt in the gauspuls command in matlab, i entered a fbr(fractional bandwidth of 1.5,ie. bandwidth= 0.75Mhz ) but as i plot the signal in the frequency spectrum using fft. i dont see the ... 0answers 29 views ### I want to create a signal in time domain using gauspuls command in Matlab, and plot the same in freq domain to check? I have got a code from (www.simsonic.fr) which takes input as fractional BW, time and centre frequency, and gives in phase pulse and envelope as output. But my concern is how can I check if the signal ... 0answers 107 views ### I want to plot a gaussian pulse in MATLAB in the frequency domain, with its centre at the highest value I have tried one way but i am getting 2 peaks at the edges as shown in the picture. I have used 1 part of my code for the signal generation where i used the gauspuls command (reference: www.simsonic.... 0answers 58 views ### Should I increase the mean or the variance of Gaussian noise? I am new in DSP. I am currently working with a project and I want to try which algorithm works better given different image noises. To test it out, I have been using the Gaussian noise in images. ... 0answers 39 views ### Autocorrelation function and product of summations Let u[k] be a white gaussian noise with variance \sigma^2 and y[k]=\sum\limits_{i=0}^q b_i u[k-i], that is a moving average model. I am trying to compute the autocorrelation function of y[k]: ... 0answers 50 views ### What is meant by labels in 'gaussian shaped labels (reference attached)'? I am trying to understand MATLAB code and it uses a line like: ... 0answers 69 views ### How to calculate the variance of noise when an image is downsampled? I have a noisy image for which I know the noise variance. (Basically I created noisy image by adding noise). Now, I'm downsampling this noisy image. How does the noise variance change? Is it possible ... 0answers 36 views ### Voice classification I'm working to prepare research article for my project. While preparing for it, I've gone through the topics like Gaussian mixture model and Fourier transform for voice classification problems. I've ... 0answers 151 views ### issue with the MFCC and GMM for audio recognition i am working on a project related to audio events recognition in real time like a door bell, baby crying, footstep, I have 9 categories of sound events so the first step i did was getting many wav ... 0answers 293 views ### frequency spectrum of a sampled signal, PSD and power discussion Before I go into my question, I first want to review the basics of sampling a signal and at the same time I build the basics of my questions so that they make more sense. I know I have asked couple of ... 1answer 131 views ### Approximating a Gaussian Process Suppose that \theta_t is an exogenous variable with known Gaussian process. Next, suppose that for any index i\in [0,1],$$ a_{i,t} = (1-\beta)\mathbb E[\theta_t|\mathcal I_{i,t}]+\beta \mathbb E[...
My goal is to create a noise model so that the PSNR of the noisy image compared to the original is some pre-defined constant $\alpha$. This means the mean squared-error will also be a constant. My ...