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Questions tagged [gaussian]

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How to calculate the variance of noise when an image is downsampled?

I have a noisy image for which I know the noise variance. (Basically I created noisy image by adding noise). Now, I'm downsampling this noisy image. How does the noise variance change? Is it possible ...
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1answer
37 views

Fast Recursive 1D Signal Smoothing - IIR / Auto Regressive Implementation of Gaussian Smoothing

I have just begun to dive into the field of signal processing, but there is the need to program a digital filter, that has to smooth a realtime signal from a sensor device. As far as I know, in my ...
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0answers
22 views

Voice classification

I'm working to prepare research article for my project. While preparing for it, I've gone through the topics like Gaussian mixture model and Fourier transform for voice classification problems. I've ...
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1answer
51 views

Signal Denoising Uniformly in Frequency Domain

I have a noisy sparse signal containing number of frequency components. Is there any method to uniformly denoise this signal. in other words, a method that estimated and eliminates the noise power ...
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2answers
58 views

How to approximate gaussian kernel for image blur

From wiki, a $3 \times3$ gaussian kernel is approximated as: $$\frac{1}{16}\begin{bmatrix}1&2&1\\2&4&2\\1&2&1 \end{bmatrix}.$$ Applying this kernel in an image equals to ...
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1answer
82 views

Is there a clever way to implement cascaded moving average filters?

I'd like to effeciently approximate a gaussian filter's step response using cascaded moving average filters. I know about recursive moving average, but is there some clever algorithm to cascade them ...
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2answers
72 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 $N_0/2$...
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1answer
48 views

ARMA Model - DSP

I'm taking a DSP course and we're being introduced to the whole probability/stats side of DSP and I'm just confused on things like the ARMA models. These things don't seem intuitive to me at all. ...
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5answers
3k views

Why is random noise assumed to be normally distributed? [duplicate]

From residual in the linear regression to noise in signal processing are assumed to be normally distributed? By considering them as normally distributed we are kind of telling the pattern in the noise ...
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2answers
1k 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 ...
1
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1answer
71 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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2answers
350 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 this answer and I am also reading ...
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1answer
33 views

SIFT About Difference-of-Gaussian function extrema?

How to get formula (2) by formula(1)?
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1answer
345 views

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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1answer
377 views

Generate Complex White Gaussian Noise in MATLAB

n_3=sqrt(0.1)*randn(1,K); n_4=sqrt(0.1)*randn(1,K); beta_NLoS=(n_3+1i*n_4); % CN(0,0.1) I want to create a $CN(0,0.1)$,does my code have any problem?
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1answer
58 views

Covariance matrix associated with random DC level in Gaussian noise

Given a signal $x[n] = A + w[n]$ where $A$ is a Gaussian random variable and $w[n]$ is Gaussian white noise, then the covariance matrix of the signal is given by $[C(\sigma^2_A)]_{ij}=E[x[i-1]x[j-...
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1answer
47 views

What Is a Weighted Local Histogram?

I'm reading through a couple of academic papers, and this terms often comes up "local weighted histogram". An example of quote is the following: First, cumulative histograms are built for every ...
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0answers
73 views

Noise PSD and sampling rate relation

Let's consider generating samples of a random process like white Gaussian noise (AWGN). Let's assume I am generating $N$ samples of AWGN with variance $\sigma ^2$ in MATLAB by using randn() funtion i....
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0answers
36 views

Modulation to achieve Shannon capacity in AWGN channels

If my understanding is correct, to achieve the Shannon capacity in AWGN channels, we need a modulation that codewords follow Normal distribution, or uniform on surface of a sphere (sphere hardening ...
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0answers
94 views

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 ...
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0answers
35 views

power spectral density window function gaussian

I'm using psd in python using mlab library ...
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1answer
84 views

What Are Different Approaches to Realize a Gaussian Blur (Smoothing) Step on an Image? [closed]

Could some review some methods to apply Gaussian Filter (Blur) on an image besides the direct one using Truncated FIR (classic convolution with Truncated Kernel) approximation?
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1answer
84 views

What's the relationship between the parameters of this noise generator and the gaussian curve it produces in the frequency domain?

This algorithm produces a sequence $y$ having a magnitude spectrum that resembles a normal distribution, peaking at frequency $\omega$: $$b[n]=(1-\sigma)b[n-1]+\frac{\sigma}{\omega} C$$ $$p[n]=p[n-1]+...
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0answers
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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 ...
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0answers
134 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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1answer
418 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 ...
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0answers
24 views

Estimating a Function from its Covariance Function

I am trying to solve this question: Suppose that $n(t)$, $−∞ < t < ∞$ is a stationary Gaussian random process with covariance function $E\{n(t)n(t-\tau)\} = \delta(\tau) + {5 \over 4}e^{-\left|\...
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1answer
42 views

Play with a Gaussian random set in the frequency domain to obtain desired effect in the time-domain

Please assume we have a set of 100 random numbers obeying Gaussian PDF in time-domain. Let's index them 1-100. Within a time-accurate simulation, I apply four operations on this dynamic set every ...
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1answer
126 views

Zero padding effect on a FFT of gaussian noise

I have a gaussian noise $\nu(t)$ with variance $\sigma^2$. After a FFT I get $X(\omega)$. If now I do the IFFT on the $X(\omega)$ can I say that the result is still a gaussian noise of variance $\...
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1answer
248 views

Gaussian window and standard deviation

I am trying to figure out how to use the matlab gausswin function which constructs a Gaussian window for $N$ samples with a given standard deviation $\sigma$. The function is defined by ...
2
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1answer
142 views

Matched Filter of Gaussian Signal

How can we evaluate the matched filter's impulse response of a Gaussian function $x(t) = \exp(-\frac{t^2}{2})$. As far as we know, for a signal of finite duration $T$, the impulse response of it's ...
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0answers
31 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\}...
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0answers
55 views

temporal smoothing and signal distortion

I compare two signals (blue and red). Each signal is an average of many observations (shades are standard error of mean). I need to show that the the blue signal is significantly above red one at the ...
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0answers
27 views

how to use Gaussian mixture model in voice morphing

I need to use GMM in voice morphing but I couldn't determine the aproprieate number of gaussian I'm using lpc for features extraction with order 18 Another thing I wanted to ask is what will be the ...
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2answers
416 views

Fitting a gaussian image using opencv

I'm reading through the opencv documentation and some questions in SO but it doesn't seem to provide this information. I've an image $I(x,y)$ and I want to find a gaussian function $f_{\mu,\Sigma}(x,...
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1answer
54 views

Does a collection of Gaussian random variables necessarily constitute a Gaussian Process?

If $\{X(t)\}$ is a Gaussian Process then the random variables $X(t_k)$ where $k = 1,2,3...n$, are jointly Gaussian. If each random variable $X(t)$ is a Gaussian variable, then will the random ...
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84 views

Removing Gaussian noise and processing the remaining signal

I need to describe the process in which a given signal that has been superimposed with significant amounts of Gaussian noise. However there is a reference signal that has an accurate estimate of the ...
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2answers
70 views

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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1answer
30 views

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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0answers
105 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} \...
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2answers
88 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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2answers
80 views

Derivation of $ R_{N(t)}(\tau) $ from its $f_{N(t)}(\eta)$

How can we prove the auto-correlation function of white gaussian noise $\{ R_{N(t)}(\tau) \}$ is $\frac{N_0}{2} \delta(\tau)$ from its p.d.f in equation below? $$ f_{N(t)}(\eta)=\frac{1}{\sqrt{2 \pi \...
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2answers
170 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 ...
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0answers
109 views

Binomial Approximation of Gaussian Distribution

It is said that we may use the binomial coefficients ( a layer from Pascal's triangle) to approximate the 1-D Gaussian kernel with certain $\sigma$, where $\frac{n}{4} = \sigma$ and $n$ is the index ...
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2answers
115 views

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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2answers
222 views

Why does second order Gaussian called Laplacian Gaussian?

We usually use Laplacian of Gaussian as the filter for edge detection or blob detection. But the filter itself is essentially a second order Gaussian. So why do we call it Laplacian of Gaussian? Is ...
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1answer
659 views

How to generate random samples of Gaussian distribution directly in the frequency domain?

One can easily draw (pseudo-)random samples from a normal (Gaussian) distribution by using, say, NumPy: ...
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1answer
121 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[...
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1answer
224 views

Shannon capacity with distribution different from Gaussian

If I understand correctly, in AWGN channel, for a given SNR, there is a code for $M$ input codeword $\mathbf{X}_{i, 1 \leq i \leq M}$ that $$\lim_{n \to \infty} R=\lim_{n \to \infty}\frac{\log(M)}{n} ...
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2answers
427 views

What is DC level in white gaussian noise?

Am studying unbiased estimators and keep seeing this term "DC Level". What is the expansion of DC and what is a DC Level? Even the Wikipedia page on WGN says nothing about it.