# 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 ...
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
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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 $XY.$?
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}}^{-...
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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 &...
27 views

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### 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
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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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 ...
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 ...
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 ...
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### 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
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 ...
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 ...
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 ...
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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 ...
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
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 ...
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 ...
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 $\sqrt{\rho n}$ (...
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### Generate Complex White Gaussian Noise in MATLAB

In the followinf code I am trying to generate a Complex Gaussian Noise: ...
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
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?
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!!