Questions tagged [gaussian]
The gaussian function, an exponential function with a negative square of the argument in the exponent, is interesting in signal processing because the Fourier Transform of a gaussian function is also a gaussian function.
77 questions with no upvoted or accepted answers
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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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Horizontal banding (flickering) due to electronic rolling shutters
It is a well-known artifact that in CMOS cameras with electronic rolling shutter, horizontal banding (flickering), i.e. brightness intensity variations, are observed when the image is recorded under ...
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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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Time delay estimation for superimposed random signals sampled from a multivariate Gaussian mixture?
Suppose my signal model is:
$$
\mathbf{y} = D(\tau_1) \mathbf{x}_1 + D(\tau_2) \mathbf{x}_2
$$
where $D(\tau)$ is a delay matrix that shifts a signal by $\tau$ samples.
$\mathbf{x}_1$ and $\mathbf{x}...
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Detector for vector-valued signals
I'm trying to find the optimal probability of detection/false alarm for the following detection task. Given $N$ signal samples with $d$ dimensions (independent channels) each, assign the samples to ...
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How to achieve uniform gaussian profile? Beam profile has grainy/multimode pattern
Hi apologies in advance if this (optics & image-process) is not where I should post this question. Thanks for the help!
I'm required to make a jig that measures the divergence angle of a ...
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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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Gaussian filter convolution giving unexpected results
I am trying to smooth a time series signal with a Gaussian filter and then differentiate the signal (this is for an application for edge detection). A nice property of convolution is:
$$
\frac{d}{dx} \...
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Detection over AWGN analysis disagrees with Monte Carlo simulation
I have a fixed vector $\mathbf{s} \in \{\pm1\}^m$ and a random vector $\mathbf{d} \in \{\pm1\}^m$.
I send either $\mathbf{x} = \mathbf{x_1} = [\mathbf{s}\space\mathbf{d}]$ or $\mathbf{x} = \mathbf{...
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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 ...
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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 ...
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Comparison Between Average Kernel (Box Kernel) and Gaussian Kernel
In image processing, we have two kinds of major kernels that are average kernel and Gaussian kernel. For image segmentation, which is difference between average kernel and Gaussian kernel? I found ...
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Minimum Number of Base Accelerations Needed to Simulate Gaussian White Noise in Structural Dynamics?
I am currently working on a scientific paper where I subject a structure to base accelerations modeled as Gaussian white noise. I am relatively new to signal processing and would appreciate some ...
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How to implement scale-dependent Gaussian averaging using Morlet wavelet envelope in Python?
I'm trying to reproduce the scale-dependent Gaussian averaging of a time series as described in this paper: https://arxiv.org/pdf/1706.01126.pdf
The process involves performing a continuous wavelet ...
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Is it possible to reformulate a Kalman Filter as a Gaussian Markov Random Field?
The generic formulation of a KF uses a set of transitition equations, while the GMRF is typically specified through its mean and precision. However, a simple KF involves Gaussianity and Markov ...
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Can the standard deviation of the Gaussian window in a Gabor filter be made infinitesimally small?
My understanding is that the standard deviation of the Gaussian window in a Gabor filter dictates the temporal resolution.
Wouldn't it always be better then to make the window smaller, thus achieving ...
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Kalman Filter Under Non-Gaussian Noise
I know that Kalman filter is optimal filter under some assumption like process and measurement noise are Gaussian. But if the process and measurement noise is non-Gaussian, the estimation of the ...
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What could be the optimal filter given this situation?
I am using a camera and a Deep Neural Network to predict one angle. This network received as input the frame, and calculates the mean and the variance associated to the prediction (which is basically ...
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Generate skew-normal signal
Is there a simple way to generate a skew-normal shape? Shouldn't be perfect, I just need a rough approximation of it to test peak-detection algorithms.
I tried generating the signal according to the ...
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AWGN for a specific dBc
I have a square-ware signal with 1V peak-to-peak (alternating between -500 and +500mV, so its absolute value is a constant 500mV) and I would like to add to this an AWGN expressed in dBc ("decibels ...
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Gaussian Energy Broadening implementation to meet detector response
Respected Coding experts,
I am trying to perform Gaussian broadening on an energy spectrum. The final result should convert "specrum.png" to a similar form of "Exp.png". The method is explained in ...
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How to implement one dimensional low pass Gaussian filter with zero-phase shift?
I am trying to apply a low pass Gaussian filter on a signal and find the exact location of maximum/minimum in the resulting smoothed signal. I have to do it for a few values of sigma (Gaussian ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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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$$
If the innovations $\epsilon_t \sim MVN({\bf 0},\Sigma)$ then is ${\bf X}_t$ a ...
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Fitting VAR Process with Generalised Gaussian Noise
Consider the $m$-dimensional VAR process
$${\bf x}_t = \sum_{l=1}^{P} A_l{\bf x}_{t-l} + {\bf e}_t$$
where the componenets of ${\bf e}_t$ are spatially and temporally independent and follow a ...
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Gaussian blur with variable standard deviation
I'm trying to find fast ways to evaluate the following integral defined over points $\mathbf{x} \in \mathbb{R}^2$:
$$\Phi(\mathbf{x}) = \frac{1}{2\pi\sigma^2(\mathbf{x})}\int d^2y\, \exp\left(-\frac{|\...
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Amplitude error of STFT using gaussian window
I am implementing the STFT algorithm and I also need to find the amplitude accuracy and Probability of Intercept (POI).
The only reference I have been given for these factors is this formula
$$ E_{ZD,...
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The variance of a band-limited Gaussian process out of correlation filter
Let $X(t)$ be a real Gaussian process of bandwidth $W$ and spectral density $N_0/2$. Let $\phi(t)$ be a orthonormal (in $L_2$ sense) function with bandwidth $W$.
Consider the correlator output $\int_{-...
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Determining when a time series switches which of two Gaussians it samples from
I'm sampling from what should be an elliptical 2D Gaussian. However, one of the instruments in the setup seems to be switching between two values for the phase between synthesizers, which results in ...
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Why isn't the Gaussian blur kernel defined via the cdf?
A 1-D Gaussian blur kernel of size $2k + 1$ is defined as:
$$K = \text{Normalize}([G(-k), \ldots, G(0), \ldots, G(k)])$$
where
$${\displaystyle G(r) = {\frac {1}{\sqrt {2\pi \sigma ^{2}}}}e^{-{\frac {...
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GMSK Modulator Large sample Buffer size and high Bandwidth
I found good answers to my queries here Gaussian Pulse shaping filter and suggestion for NCO based GMSK modulator seems to be undersstandable. Thanks to Dan Boschen
, but when moving ahead to design ...
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Autocorrelation function of a Gaussian random signal
Im a beginner at signal processing and I've gotten the following question in an exercise:
"Write down the equation for a Gaussian probability density distribution and relate the different
...
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Kalman filter for multiple data sources, measurements from which have different characteristics of Gaussian noise
I am trying to use the Kalman filter for my task:
During the time, I receive data from different sensors. The state of the model may change over time according to the Const Velocity model, or the ...
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Remove additive-zero-mean-Gaussian noise
I have 5 values, and each value is corrupted by Additive-Zero-Mean-Gaussian Noise with variance = 0.05.
Each value is in the range from 0 to 1. Is there anyway for me to remove the noise?
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Probability of the rate of change of a filtered random process
I am given the following problem: I have a filter with impulse response $h(t) = e^{-10t}, t \leq 0$, and autocorrelation function of the input signal, which is WDS and Gaussian with median equal to 0, ...
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Pdf of product of two i.i.d random variable distributed as circular symmetric gaussian
What is a distribution of the product of two circular symmetric Gaussian random variables?
i.e $X ~ CN(0,1)$ and $Y ~ CN(0,1)$ then distribution of $XY.$?
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n-dimentional integral over Multivariate Gaussian
given the prior distribution of $\mathbf{a}=[a_1,\ldots,a_K]^T$ as
\begin{equation}
p_{\mathbf{a}}(\mathbf{a})= \frac{1}{\pi^K \det{\mathbf{R_{\mathbf{a}}}}} e^{\mathbf{a}^H \mathbf{R}_{\mathbf{a}}^{-...
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How to get an accurate edge value of gaussian scipy
i am new to this forum and I am not sure which topic I have to use. But I think my problem belongs to signal processing.
My problem is the following one. I try using filter to find the actual momentum ...
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Choose the right Sigma for Gaussian filter
I have the following problem: I have a time series with counted data. I now want to smooth it using a Gaussian low-pass filter. Is there a method to determine the sigma value? The window should have a ...
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when exposure time is longer, the Poisson noise become Gaussian
Can we have an explanation of why exposure time is longer, the Poisson noise become Gaussian?
Or any reference? Please provide a reference and I like to dig into more.
Thanks in advance!!
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How do you derive the new mean and variance when two gaussian functions are multiplied together?
I'm trying to understand the contents of this web-page which suggest that multiplying two Gaussian functions together produce a new Gaussian function with a new mean and variance.
Say I have the two ...
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What types of distributions (except the Gaussian) that follow for random jitter in a correlated signal?
For the simple case, let's consider the correlated signal $s$ with jitter (without noise) as follows:
\begin{align}
s(t, \theta_i) = \cos(2\pi f (t + \epsilon_t) + \phi + \theta_i), ~~ i=0,1, ...
\end{...
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Blind Estimation of Signal Parameters for Zero mean Normal distribution
Let $\mathbb{s}$ be zero mean with a normal distribution. Let one of the observed set of signals be given by $K\mathbb{s}$ and another by $L\mathbb{s^*}$, where $K$ and $L$ both are constants, and $\...
