Questions tagged [gaussian]

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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 ...
0 votes
1 answer
133 views

When to zero-mean a signal?

I have two sets of signals. The first is a noisy sinewave, which I zero-mean before taking the FFT since I need to find the amplitude. The other is essentially noise with a gaussian distribution. I'm ...
1 vote
1 answer
71 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. ...
0 votes
0 answers
39 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 $XY.$?
0 votes
0 answers
30 views

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}}^{-...
3 votes
1 answer
94 views

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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0 answers
27 views

Affine transformation on circularly symmetric Gaussian distribution

Assume the complex random vector $\mathbf{y} \in \mathbb{C}^N$ is circularly symmetric distributed i.e. $\mathbf{y} \sim \mathcal{CN}(\mathbf{0},\mathbf{R})$ $$ p_{\mathbf{y}}(\mathbf{y})=\pi^{-N}\...
-1 votes
1 answer
174 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[...
6 votes
2 answers
3k views

How Is Laplacian of Gaussian (LoG) Implemented as Four 1D Convolutions?

I am trying to understand the four 1D convolution operations involved in implementation of Laplacian of Gaussian(LoG). I have read the answers to What Is the ...
1 vote
1 answer
85 views

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 ...
0 votes
2 answers
53 views

The notation to express a datum filtered by arbitrary 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 ...
2 votes
1 answer
408 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 ...
5 votes
2 answers
4k views

Parameters of Gaussian Kernel in the Context of Image Convolution

Hi Everyone i am new at image processing. I copy code from this website, I have image $600 \times 480$ gray scale. What will be the value of standard deviation or $\sigma$? What will be the value of ...
-1 votes
1 answer
387 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 ...
5 votes
2 answers
16k views

How to Calculate Gaussian Kernel for a Small Support Size?

How to calculate the values of Gaussian kernel? I think I understand the principle of it weighting the center pixel as the means, and those around it according to the $\sigma$ but what would each ...
4 votes
1 answer
1k views

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 ...
-1 votes
1 answer
46 views

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 ...
12 votes
2 answers
7k views

Why should an image be blurred using a Gaussian Kernel before downsampling?

I recently read that before downsampling an image, it should be blurred using a Gaussian Kernel. This way, the downsampled image is better than just picking a single pixel out of a NxN block or ...
2 votes
1 answer
38 views

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 ...
2 votes
1 answer
85 views

How to add noise with given autocorrelation to signal in Matlab?

My question is a mix of signal processing and Matlab coding. I have an FIR filter with added noise $w_n$ $$x_n=\sum_{m=0}^{N_h-1}h_mg_{n-m}+w_n.$$ Now the noise $w_n$ has the autocorrelation $$E[...
2 votes
1 answer
284 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 ...
5 votes
2 answers
2k views

Common Use Cases for 2D Non Separable Convolution Filters

In the image processing world, I've noticed that a lot of the popular convolution filters are separable. Here's a quick list of common separable filters: Sobel Gaussian blur Box filter (all ones, for ...
2 votes
3 answers
183 views

How to find the output mean and autocorrelation of a non-linear system

I need help with this question. I am sure this is the right StackExchange forum for this type of question. Consider a nonlinear device such that the output is $Y(t) = aX^2(t)$, where the input X(t) ...
2 votes
4 answers
3k views

filter coefficients to know high pass and low pass filter

Looked on few questions already there in dsp.stackexchange and couldn't get the direct answer. Basically I have a kernel of a gaussian separable filter. ...
0 votes
1 answer
100 views

Standard deviation of Morlet wavelet's Fourier transform

MATLAB has the complex Morlet Wavelet in the following form: $$\psi(t) = \frac{1}{\sqrt{\pi f_b}}e^{\frac{-t^2}{f_b}}e^{j2\pi f_ct}$$ I arrived at its Fourier transform as shown below (another ...
1 vote
1 answer
271 views

Filter by 2D Gaussian Kernel in MATLAB

I have written a function that implements a gaussian filter. I use fft2 to transform my image and my filter to 2d fourier transform. Then I multiply them and then ...
21 votes
6 answers
28k views

How to Generate Band Limited Gaussian White Noise in MATLAB?

In some papers, I read that the additive noise is band limited Gaussian white. How can I simulate this type of noise use MATLAB?
4 votes
2 answers
2k views

PSD of complex white gaussian noise

It may be a really simple question, but I'm not sure about this one: Given a complex white Gaussian noise process with iid real and imaginary parts and a double sided power spectral density of $N_0/2$...
6 votes
1 answer
1k views

Why Does 2D FFT of Gaussian Looks More Sharper than Gaussian Itself?

I am trying to understand why 2D FFT is done on a Gaussian process in a particular code. From my understanding from these posts: https://www.researchgate.net/post/...
2 votes
0 answers
161 views

Does a "chirp"-like generalization of the Gabor or Morlet wavelets definitions exist in the lit somewhere?

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\} \...
5 votes
1 answer
2k views

How Does the RMS of White Noise Change with Sampling Frequency?

There is an analog system which includes the continuous-time linear equalizer (CTLE). With some .noise analysis the power-spectral density (PSD) of the noise in that system is provided. So let's not ...
1 vote
2 answers
618 views

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 ...
4 votes
1 answer
441 views

Constructing a Gaussian kernel in the frequency domain

I'm currently learning about Fourier transform, but find the differences between spatial domain and frequency domain a bit confusing at times. Let's say I would like to perform convolution of an image ...
0 votes
1 answer
32 views

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 ...
0 votes
0 answers
34 views

Modern method for feature Gaussianization

Suppose non-negative feature vectors $X = [x_0, x_1, ..., x_{N-1}]$. Existing methods include: BoxCox Lambert Iterative, rotations Log-median: $$ \hat X[n, p] = \log \left(1 + \frac{X[n, p]}{C \mu[p]...
0 votes
2 answers
503 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 ...
-1 votes
2 answers
54 views

How is the distribution of the received signal affected if the transmitted signal is changed from complex Gaussian to PSK

Suppose the received signal is $y(n) = h_0s(n)+w(n)$----(1) Where $h_0, s(n), w(n)$ all are distributed as zero mean complex Gaussian. Thus I know that $y(n)$ will also have the same distribution. If $...
0 votes
1 answer
31 views

understanding the distribution of received signal

In one of the research paper following equations are given : $y(n) = h_0s(n)+w(n),d = 0$ $y(n) = h_1s(n)+w(n),d = 1$ where $n$ ranges from $1$ to $N$ and $h_0,h_1$ are wireless channel assumed as $\...
1 vote
1 answer
1k views

Uniform quantizer for gaussian input signal

I have a gaussian signal $x$ with zero mean and unit variance. I am quantizing it by using a uniform quantizer of step size $q$ calculated by $$q = \frac{x_\mathrm{max} - x_\mathrm{min}}{2^{M_\mathrm{...
2 votes
2 answers
574 views

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 ...
-1 votes
1 answer
52 views

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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0 answers
48 views

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 ...
0 votes
1 answer
132 views

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 ...
5 votes
1 answer
228 views

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 $\sqrt{\rho n}$ (...
4 votes
1 answer
3k views

Generate Complex White Gaussian Noise in MATLAB

In the followinf code I am trying to generate a Complex Gaussian Noise: ...
0 votes
0 answers
76 views

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 ...
1 vote
2 answers
241 views

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?
0 votes
0 answers
29 views

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!!
2 votes
1 answer
185 views

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 ...
27 votes
4 answers
86k views

Gaussian Blur - Standard Deviation, Radius and Kernel Size

I've implemented a gaussian blur fragment shader in GLSL. I understand the main concepts behind all of it: convolution, separation of x and y using linearity, multiple passes to increase radius... I ...

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