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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.

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Gaussian Pulse shaping filter

I need expert advice on implementation of Gaussian Pulse Shaping filter for generating GMSK signal in further steps. I have implemented as follows, Can anyone confirm that the Pulse would be shaped as ...
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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 ...
mads grønbeck's user avatar
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Regarding SINR (Signal to Interference Plus Noise Ratio) in wireless communication

I am working on a research paper related to wireless communication, wherein I am facing some doubt while writing expression of SINR (which is a ratio of Signal variance in numerator to Interference ...
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Narrowband Gaussian Noise

Could anyone lead me on the right path on where I could get more information in regards to a narrowband Gaussian signal can be modeled as: $$ X(t)\cos(2\pi f t)+Y(t)\sin(2\pi f t) $$ where $X(t)$ and $...
SignalToBeLearnt's user avatar
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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 ...
Leon's user avatar
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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 ...
Jokerp's user avatar
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How to mask part of signal?

I am trying to implement masking in 1D signal data, I saw in one paper that they are masking 70% of the signal as in the figure below: In another study, they have mentioned that the mask part is ...
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$i^{\text{th}}$-dimensional autocorrelation function

I am referring to the work of Stephen A. Billings on "Identification of a class of nonlinear systems using correlation analysis" from the year 1978, where it is mentioned that the $i^{\text{...
Neuling's user avatar
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ADC response inversion to Gaussian noise

Assuming the input to an ADC is a Gaussian white noise signal, and being a bit idealistic in all senses, is there a theoretical expression that links input power to output power which can be inverted, ...
Albert's user avatar
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ADC bias, noise and number of bits under Gaussian signals

I'm digitizing a zero-mean complex Gaussian white noise signal with certain variance, through independent I/Q baseband sampling (two ADCs). The noise variance (power) depends on the thermal emission/...
Albert's user avatar
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6 votes
2 answers
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Discrete Fourier Transform of the Gaussian

Cross-posted from here I encountered the following question in a Digital Image Processing examination: Find the 2D DFT of $\frac{1}{2 \pi \sigma^2} e^{-\frac{(x - x_0)^2 + (y - y_0)^2}{2 \sigma^2}}$ ...
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Finding mean, autocorrelation, and power spectrum of $y[n]=(x∗h)[n]$ where $x[n]$ is zero mean white gaussian noise

If given $x[n]$ is zero mean white Gaussian noise with variance $\sigma_x^2$, and a filter with a known impulse response $h[n]$, how would I find the mean, autocorrelation, and power spectrum of $y[n] ...
Mark Boccelli's user avatar
1 vote
1 answer
158 views

What's the distribution of the DFT of a real-valued, zero-mean, normally distributed random vector?

Suppose $X$ is a real-valued N-dimensional Gaussian vector, $X \sim \mathcal{N}(\mathbf{0}, C_X)$. The discrete Fourier transform can be obtained by left-multiplying with the unitary DFT matrix, i.e. $...
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Approximating variable-length coding by "aggregating" fixed-length coding

Consider the problem where I want to quantize a univariate standard Gaussian with two bits, and the objective is to minimize MSE reconstruction loss. According to these slides, the Lloyd algorithm and ...
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Decomposing Gaussian Diffraction Pattern

I was recommended to post this question here from the physics stack exchange. I have the following diffraction pattern produced by a fabry-perot etalon. The red represents the center of that pattern. ...
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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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Generating time-domain noise from PSD

I have a question regarding generating a time-domain noise from the power spectral density (PSD), this was addressed in this question (How to generate time-series from a given one-sided PSD?) but I ...
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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 ...
SNIreaPER's user avatar
1 vote
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Which probability density functions to use in a likelihood ratio test for the radar detection problem?

I am trying to understand the radar detection problem in the form of the generalized likelihood ratio test and am having a little trouble with understanding the noise distributions. Perhaps this will ...
Jim's user avatar
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How to evaluate pairwise error probability and detection in presence of gaussian noise?

I am reading Digital Communication Systems by Simon Haykin and I am stuck at one point. Consider a two-dimensional signal space that has a message constellation of four points, given by $s_1,s_2,s_3,...
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Spectral power density of thermal noise

In telecommunications the received signal $y(t)$ of a receiver is equal to $x(t)S+n(t)$ where $x(t)$ is the sent signal of the sender , $S$ is a constant which describes the total attenuation of the ...
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Approximating fractional-octave Gaussian smoothing with non-causal variable-width IIR filters

I am trying to implement fractional-octave smoothing of amplitude response data with approximated Gaussian filters, as briefly discussed in this AES paper. Unfortunately, no implementation details are ...
butch_warns's user avatar
2 votes
2 answers
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Contradiction when simulating WGN

To my knowledge, white Gaussian noise (WGN) is defined as a process with a correlation function: $$ R[k]=\sigma^2 \delta[k] $$ and whose symbols are distributed according to $N(0,\sigma^2)$. Naturally,...
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Gaussian filter: Plotting DTFT and DFT (by hand) from the continuous-time impulsive response

I am trying to make an algorithm that plots out the Discrete-Time Fourier Transform (DTFT) and the Discrete Fourier Transform (DFT) of the Gaussian filter. The impulsive response and its transfer ...
Juliana Xavier's user avatar
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1 answer
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Can a time signal be modeled as a multivariate Gaussian distribution?

Suppose I have several groups of signal measurements, each containing multiple replicates, and I know that within each group the signal "shape" is approximately the same but with variance/...
Dennie's user avatar
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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 ...
guidolard's user avatar
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1 answer
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Real-time convolution with Gaussian noise

I have a brain activity simulator that is capable of receiving various stimuli. Both generated signals and input stimulus are causal: a single sample is created every time step. I use a sinusoidal ...
Daniel Polyakov's user avatar
3 votes
1 answer
367 views

Choosing sigma values for Gaussian blurring on an anisotropic image

I have an anisotropic image that is anisotropic both in terms of number of voxels and also in terms of voxel resolution. ...
Harsha Y's user avatar
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3 answers
128 views

The Effect of the Finite Radius of Gaussian Kernel

Page 168 of Digital Image Processing, Global Edition says: we know that the values of a Gaussian function at a distance larger than 3𝜎 from the mean are small enough that they can be ignored. If we ...
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Is f/fL a high pass filter where fL is a low-pass version of f?

Let there be a signal f and its low pass filtered signal be fL. Then what can we say about the spectrum of f/fL ? To be specific I am obtaining fL simply using gaussian blurring in the spatial domain. ...
Mohit Lamba's user avatar
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Inverting the normalized Gaussian to get a kernel window radius

I am seeking to compute a kernel radius to use with my gaussian convolution filter, and inspired by https://stackoverflow.com/a/68050503/, I came up with: $$r=\sqrt{-2\sigma^2\ln\left( \epsilon\sigma\...
multiscale's user avatar
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One-sided bandwidth of the Gaussian filter

As defined in the CCSDS (section 3.1.2), the impulse response of the Gaussian filter is given by $$ h(t) = \frac{1}{\sigma T \sqrt{2\pi}}e^{-\frac{t^2}{2\sigma^2T^2}} $$ where $$ \sigma = \frac{\sqrt{\...
Rubem Pacelli's user avatar
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188 views

Downsample (aggregate) raster by a non-integer factor, using a Gaussian filter kernel

The task is to downsample (aggregate) a raster from 100m pixel size to 460m. The aggregation should be performed using a Gaussian filter. To better understand the task, I am following the paper ‘The ...
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Finding the average probability of error for a transmission system using this signal constellation [duplicate]

We have a signal constellation with decision regions given in the figure below and symbols are equally likely to be transmitted. Now we have to find the average probability of error for a ...
TM1's user avatar
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4 votes
2 answers
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ICA and Gaussianity: A Misleading Example in the Book Konstantinos Koutroumbas, Sergios Theodoridis - Pattern Recognition

A book reports that ICA cannot be used if the independent components of the analyzed data are Gaussian (at most one can be Gaussian, but no other). However, in the same book, the following example is ...
volperossa's user avatar
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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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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?
wrek's user avatar
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Where does the following expression for stationary Gaussian Noise come from: $\langle \tilde{n}(f)\tilde{n}(f')\rangle = \delta(f-f')\frac{1}{2}S_n$?

First, the definitions: Definition (Gaussian process) A random process $X(t)$ is a Gaussian process if for all time points, $t_1,\ldots,t_n$ the random variables $X(t_1 ),\ldots,X(t_n)$ have a ...
DetectorNoise007's user avatar
4 votes
1 answer
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Classifying samples from complex Gaussian distributions

Assume we are trying to classify a sample $X$ as coming from one of two distributions: $$ \mathcal{CN}(\mu, \sigma^2) \\ \mathcal{CN}(\nu, \sigma^2), $$ where $\mathcal{CN}$ denotes a (circularly ...
Sami's user avatar
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1 answer
196 views

Confusion about KL divergence between complex Gaussians

The KL divergence between two real-valued Gaussian distributions with means $\mu_1$ and $\mu_2$ and common variance $\sigma^2$ is well known to be: $$ D_{\text{KL}}\left(\mathcal{N}(\mu_1, \sigma^2) \...
Sami's user avatar
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2 answers
529 views

Understanding y=Hx+n equation in detail?

Consider a wireless communication system having $t$ transmitting antennas and $r$ receiving antennas. Then, the received signal is given by $y = \mathbb{H}x+n \tag{1}$ where $\mathbb{H}$ is a $r \...
chaaru's user avatar
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Bounding Detection and Estimation by SNR in Gaussian Channel

Assume the following problem: A deterministic signal $X$ whose magnitude is known to satisfy $0 \leq \Vert X \Vert_2 < \Delta$ for some known constant $\Delta$ is transmitted through a Gaussian ...
Sami's user avatar
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1 answer
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In this question, what does μ stand for?

Let $X_i$ ($i=1,\ldots,N$) be random variables describing an unknown constant signal $S$ and a noise $n_i$. $$X_i = \mu_i S + n_i$$ In this question what does "$\mu$" stand for? Also, can I ...
Terklton's user avatar
3 votes
1 answer
220 views

Why resizing an image smoothed by Gaussian by factor of 2 also increase sigma by factor of 2

In the paper about SIFT algorithm (Distinctive Image Features from Scale-Invariant Keypoints) it says at the end of section 3.3: We double the size of the input image using linear interpolation prior ...
dorzv's user avatar
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3 votes
2 answers
822 views

Metric for image sharpness?

Suppose I have a blurry image: a photo convolved with a gaussian blur kernel of unknown sigma. I would want to deconvolve the blurry image using several gaussian kernels (with different sigmas). Is ...
ArekBulski's user avatar
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0 answers
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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, ...
average_discrete_math_enjoyer's user avatar
2 votes
0 answers
56 views

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 ...
Hazman's user avatar
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1 vote
1 answer
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FFT of a gaussian signal in Python

I've been trying to get the FFT of a gaussian in Python. When I use the following parameters, the FFT goes hand in hand with the theoretical FT of the gaussian, but if I increase $\sigma$ they rapidly ...
JIVP's user avatar
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3 votes
1 answer
609 views

Gaussian filter: The best parameters for an implementation

Gaussian filter' range is [-inf +inf], but we truncate it for a GMSK modulation implementation. I have defined the truncated length tr_lg= 1. ...
FrimHart64's user avatar
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0 answers
58 views

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 $XY.$?
Jaimin Shah's user avatar

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