Questions tagged [gaussian]

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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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58 views

Formula to calculate/generate gaussian noise?

What is the formula to calculate gaussian noise, given we have variance and mean? I am trying to search google for formula but i am unable to find any much relevant result. If for example i have mean ...
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15 views

Meaning of AWGN complex and real noise under BPSK Decision Scheme

I'm currently studying error correcting codes and decided to replicate some common Bit Error Rate curves under BPSK modulation. I initially had trouble to convert SNR to a Gaussian $\sigma$ because I ...
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Channel Impulse Response is zero mean Gaussian random variable?

In the Paper "Key Generation From Wireless Channels" the channel estimation is given as: $\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||S_B||^2}$, $\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||...
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15 views

The notation to express a datum filtered by arbitray number of one-dimensional filters?

I'm a pure novice in signal processing but I'm writing a paper that needs to be expressed in the SP way. The question is, I want to express an N-dimensional datum goes through N one-dimensional ...
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11 views

Spread out flux in 2D gaussian

I want to generate a 2D Gaussian model with flux spread out for a given radius. From theory, I found out that the total integrated flux of a Gaussian model. Now I want to image it such that total flux ...
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10 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: ...
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30 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 ...
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17 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 ...
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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 ...
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43 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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96 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
62 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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26 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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8 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 ...
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41 views

Time derivative of signal - effect on noise distribution

I have an angular velocity measurement that has a certain amount of ripple that yields an histogram shaped like a gaussian curve. I quantify that ripple using a standard deviation. I am interested in ...
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50 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 ...
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48 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: ...
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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 ...
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73 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 ...
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31 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 ...
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134 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....
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72 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. ...
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46 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 $y[k]$: ...
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57 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: ...
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87 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 ...
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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 ...
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1answer
252 views

Covariance matrix associated with random DC level in Gaussian noise

Given a signal $x[n] = A + w[n]$ where $A$ is a Gaussian random variable and $w[n]$ is Gaussian white noise, then the covariance matrix of the signal is given by $[C(\sigma^2_A)]_{ij}=E[x[i-1]x[j-...
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157 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 ...
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327 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 ...
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2answers
207 views

Ramp function as derivative in frequency domain?

It is said that to get Laplacian of Gaussian in frequency domain, we may multiply the Fourier transform of Gaussian with two differentiating ramp function (1 ramp gives 1 order of derivative). The ...
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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[...
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1answer
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How to determine variance/std deviation of Gaussian noise from measured data

If I have a signal measured in discrete time intervals of a process containing some signal and some Gaussian noise how do I go about measuring the variance of this noise [i.e. the $\sigma^2$ term in $\...
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1answer
236 views

Creating a noise model with a fixed PSNR

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 ...
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1answer
124 views

Transform coding gain of two channel Haar Wavelet transform (first stage)

Question My interpretation Work I'm attempting to do this in MATLAB. I know that for discrete Random Processes going into an LTI system the autocorrelation function of the output is $R_y[n] =...
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1answer
263 views

Parameters of Butterworth filter that approximates the amplitude response of a Gaussian filter?

For a given narrowband Gaussian filter with a specific central frequency and filter width, I need corners of a bandpass Butterworth filter whose amplitude response is close enough to the Gaussian ...
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2answers
783 views

bandwidth limited pulse,what window function is it?

I want to know what kind of shape a multiple cycle sine wave pulse ( or maybe the correct term is burst ) should have to have the narrowest bandwidth possible at given pulse width. In the laser ...
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1answer
351 views

What should be the output of the pdf for multivariate normal distrubition?

Let's think we have a multivariate normal distribution with $$\mathbf x_1=\begin{bmatrix}x_{11}\\x_{12}\end{bmatrix},\quad \mathbf x_2=\begin{bmatrix}x_{21}\\x_{22}\end{bmatrix},\quad\mathbf m=\begin{...
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541 views

Image reconstruction using Laplace pyramid

Given a sub-sampled Image $P_n$ belonging to layer $n$, a Gaussian kernel $G$ and a Laplace Layer $L_{n-1}$ of layer $n-1$, my efforts to create $P_{n-1}$ of previous layer $n-1$ have failed. This ...
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1answer
50 views

Beginner level: deconvolving Gaussian noise to find initial PDF

noob question. An initial process has an unknown pdf, P(X), which is then subjected to additive Gaussian noise. Repeated sampling of the sum is performed so that $y=x+noise$ is repeatedly ...
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2answers
381 views

What is the relation between noise (AWGN) variance and number of antennas?

I'm working in two Matlab scripts trying to simulate a MIMO system using OFDM (downlink) and SC-FDE (uplink). My question is: for different numbers of transmit and receive antennas, what is the ...
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1answer
2k views

2D Gaussian Seperation into 1D Gaussian components

I have been reading this http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm and I am having trouble to perform the seperability. So I kinda did it in paper. Lets say y Gaussian function is G(X,Y), ...
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1answer
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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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1answer
823 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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1answer
218 views

Plotting uniform and Gaussian random variables

I want to create uniform and Gaussian (normal) random variables in MATLAB via rand and randn syntax. And I would like to plot ...
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1answer
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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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57 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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153 views

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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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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103 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 ...