# 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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### 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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1 vote
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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 ...
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### 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. ...
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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 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 generate wideband Gaussian white noise

I want to generate correlated complex white Gaussian noise signals in MATLAB. What I do is that I take complex Gaussian random variables with unit-variance and multiply them with the desired input ...
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### What is the outcome of applying a derivative on X and Y for an image? and Other Gaussian Questions

I've been diving into smoothing kernels and I came up with a lot of questions that I haven't been able to find in the internet. If you can I'd appreciate the help :) (Capitals and bold were used for ...
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### Are scipy second-order Gaussian derivatives correct?

For an edge detection algorithm, I need to compute second-order derivatives of an image, and I do this with use of Gaussian derivatives. I assumed that the ...
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### n independent, normal, random variable distribution

There is 2 time-series signal and we have to compare the distribution of them. I have heard there is a theory that says for n independent, normal, random variables of a series with many members, the ...
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### Why the value of Gaussian curve drop to 1/19 at 2 standard deviation?

Taken from Guide to DSP where it says: ... at two ... standard deviations from the mean, the value of the Gaussian curve has dropped to about 1/19 ... It seems to be a straight forward calculation ...
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### How to write a complex symmetric gaussian signal [closed]

In my work I need to use this signal of complex symmetric gaussian noise signal represented as $w$. But I don't know exactly how to represent it
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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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### Verifying if noise is gaussian in non-time series data

I'm trying to figure out if the noise in my experiments is gaussian or not. I don't have time series data. I first configure my system and then run some software application's and measure the average ...
1 vote
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### Ideally Lowpass-filtered White Gaussian Noise: question about a derivation of variance and covariance

Consider white gaussian noise $\omega(t)$ that has passed through and ideal lowpass filter with bandwidth $B$. This filter has the impulse response $$h(t) = 2B\text{sinc}(2Bt)$$ Sampling the filter ...
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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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### why GMSK use a gaussian filter instead of raised cosine filter?

I'm wondering why GMSK use a gaussian filter instead of raised cosine filter as a pulse shaping filter? Is there special reason?
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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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### Finding optimal decision threshold for binary comm system

I'm trying to solve the following exercise: Given a system that transmits bit $b$ with probability $p_b$ and $-b$ with $p_{-b}$ and the transmission is degraded by AWGN $N(0,\sigma^2)$. What is the ...
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### Having problems with understanding the meaning of PSD for colored Gaussian noise

After reading two articles on signal processing stack exchange: On coloured Gaussian noise How the white and colored noise differ in time domain I do understand that variance do not change over ...
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### 1st and 2nd Gaussian derivatives for edge detection

I have a project about edge detection, I made research on internet about filters and read many articles but there is an article talked about using Sobel and Gaussian derivatives then it mentioned &...
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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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### Relation between Gaussian derivatives and Gausian-windowed Cosine function

I am doing some research on UWB radars which transmit a pulse given by: $$g(t) = p(t) cos(2\pi f_{c}t) = A e^{(-\frac{t^{2}}{2\tau ^{2}})} cos(2\pi f_{c}t)$$ In some other papers, the transmitted ...
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### gaussian window for designing filters in DSP

I understand that we do not use rectangular window as a window in filter design because of the ringing/gibbs artifacts due to the sidelobes of the resulting sinc function in the time domain. ...
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### Fractional Bandwidth of a Gaussian Amplitude Modulated Signal

a gaussian modulated sinusoidal signal may be expressed as $$x(t)=A\cdot e^{(j2\pi ft)}\cdot e^{\left[-\frac{1}{2\sigma^{2}}\cdot(t-t_{0})^{2}\right]}$$ Let's consider the case in which the gaussian ...
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### What is the frequency of the Gaussian white noise model in control systems?

The design of control systems, particularly for SISO systems, is made convenient by tools such as Bode plots and the corresponding Nyquist stability criterion. These concepts allow engineers to design ...
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### Variance of Integral of a real white Gaussian Noise Process

In this question, is the answer not equal to infinity ? Answer is mentioned as 6. But my doubt is cant we think of it like a linear combination of many independent random variables each having ...
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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{...
1 vote
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### White gaussian noise analysis deduction

I´m stuck in a deduction analysis of the variance of a gaussian white noise signal in a "integrate-and-dump detector" of a baseband data transmission receiver, where $n(t)$ is white noise ...
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### Why do we need to construct Gaussian pyramid using SIFT detector

I am learning about SIFT detection and descriptor. I am slightly unsure about why a Gaussian pyramid is built for the image. I do understand that within each octave, we are applying the Difference of ...
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### The Effect of the Standard Deviation ($\sigma$) of a Gaussian Kernel when Smoothing a Gradients Image

I am trying to understand why smoothing an image with a gaussian kernel of different sigma values and then computing the gradients of the smoothed image leads to "thicker" trails. In the ...
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### Derivation of the LMMSE (Linear Minimum Mean Squared Error) Estimate and the MMSE Under Gaussian Prior

I am learning estimation theory through Steven M. Kay - Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory. In 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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### Is white noise WSS by nature or not?

I want to know what is the difference between white noise and WSS white noise. is there any difference between them or they're equal? and what about white Gaussian Noise?
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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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### Laplacian of Gaussian operator

This might be a silly question. I was reading about the Laplacian of Gaussian (LoG) operator and got confused about the alternative equivelant ways we can make use of it. Let's assume we have a 2D ...
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### Need assistance from MATLAB point of view [closed]

In my work there are three entities i.e, Tag , reader and RF source. In which for a single bit (0 or 1) from tag towards reader there are 40 consecutive complex gaussian signals at reader . How to ...
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