# Questions tagged [gaussian]

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### 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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### 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 ...
125 views

### What's the expression of the noise for a RF signal?

I am confused about how to give the expression of noise. Can someone tell me if my equations are correct? If the received RF signal is expressed as: where If I want to add a AWGN, can I give the ...
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### SIFT About Difference-of-Gaussian function extrema?

How to get formula (2) by formula(1)?
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### Gaussian noise generation for a given SNR ?

I am trying to add a Gaussian noise, normal distributed to a signal I have simulated (sig_noiseFree), to get a noisy signal (sig_noisy). lease see the code. I wrote the function my self according to ...
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### What are the advantages and disadvantages separability of Gaussian 2D filter?

I know separability of a Gaussian filter enhances the computational complexity from $\mathcal{O}(L^2*N*M) \to \mathcal{O}((L*N*M)$. How this really reflect on my program? I suppose the number of for ...
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### Power spectrum of downsampled image

I am not sure if this is the right stackexchange community for this question, but here goes. I am generating a Gaussian Random Field (GRF) of a pre-defined power spectrum. In the image below, the ...
6k views

### Which IIR filters approximate a Gaussian filter?

So it recently dawned on me that Bessel filters, despite being listed along with the other common types, are really an oddball that belongs in a different "class", and I'm trying to learn more about ...
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### 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 ...
386 views

### Optimum Filter Signal Detection for Non AWGN Channels

I have been reading this question and it confirms that the matched filter is the maximum-likelihood receiver in the presence of additive white Gaussian noise. So in the AWGN channel it maximizes the ...
367 views

### 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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### 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 ...
1k views

### How Does Gaussian Blur Affect Image Variance

I am trying to find a way to analytically estimate how the noise (or variance in pixel values) will be affected for a zero-frequency image of random noise after applying a Gaussian blur. In more ...
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### Applying Gaussian Blur in Frequency Domain

Please see second update I'm trying to implement gaussian blur in frequency domain using c#. Those are steps that I'm doing: Load bitmap. Split bitmap into separate color channels. Convert every ...
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### 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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### issue with the MFCC and GMM for audio recognition

i am working on a project related to audio events recognition in real time like a door bell, baby crying, footstep, I have 9 categories of sound events so the first step i did was getting many wav ...
126 views

### Why Does the Odd Multiple of $\frac{\pi}{4}$ on Gaussian Cause Loss in Repeatability Under Image Rotations?

I couldn't figure out below paragraph on SURF paper and hope that someone can help me to understand it. Why image rotations around odd multiples of $\frac{\pi}{4}$ lead to a loss of repeatability? ...
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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 ...
108 views

### What is SNR of Signal with Additive White Gaussian Noise [duplicate]

Calculating the power of AWGN should be equal to infinity as PSD is constant and its integration is infinity over all frequencies. Hence for any signal with finite power mixed with AWGN, SNR should ...
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### What is a $BT$ (Bandwidth-Time) product with reference to modulation?

I would like to know what does Bandwidth-Time product mean. I understand that Bandwidth ($B$) = 1/Symbol Time ($T$), hence $BT = 1$. But how can it vary? What is its significance? e.g. When we say ...
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### Is it a good idea to whiten a colored noise in order to apply formulas for AWGN?

I have posted a question before regarding the detection of a signal under colored Gaussian noise: Energy detection in presence of colored Gaussian noise Theoretical formulas for setting the detection ...
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### From Uniform to 2D gaussian

I have a 2D uniform distribution. I would like to assign probability-weights in the distribution, according to the standard deviation to convert the distribution into a 2D gaussian. I know how to do ...
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### Determine the optimum receiver and the corresponding $P_{eM}$ for an AWGN channel

I have a source that emits $M$ equiprobable messages, which are assigned signals $s_1, \dots,s_M,$ that are equidistant by $a$. That is, if we plot the $s_k$ signals in a horizontal axis they are dots ...
163 views

### 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} \...
164 views

### MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)

This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv If $v \sim CN(0,2\sigma^2_v)$ ...
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### Ramp function as derivative in frequency domain?

It is said that to get Laplacian of Gaussian in frequency domain, we may multiply the Fourier transform of Gaussian with two differentiating ramp function (1 ramp gives 1 order of derivative). The ...
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### $\tt awgn$ and $\tt wgn$ functions in MATLAB always output the same signal, no matter what I input as SNR

I'm very new to all of this. Right now I'm just trying to add a bunch of different noises to an input signal and see how they affect my signal. This is the current output of my code: ...
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### 2D Gaussian Seperation into 1D Gaussian components

I have been reading this http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm and I am having trouble to perform the seperability. So I kinda did it in paper. Lets say y Gaussian function is G(X,Y), ...
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### Intuitive understanding of scale-space extrema detection

Can someone explain intuitively why local maxima and minima in the scale-space domain make for good keypoints? I understand using LoG or DoG zero-crossing points to identify spacial variations, i.e. ...
102 views

### Dimensional analysis of integrated white noise process

This question is somewhat related to this post. Let us consider we have a white noise current source $i_n(t)$, with a variance $\sigma_i^2$, and mean, $\mu_n=0$. Assume that this current is passed ...