Questions tagged [gaussian]

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2
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0answers
62 views

The LMMSE (Linear Minimum Mean Squared Error) Estimate Under Gaussian Prior

I am learning estimation theory through Steven M.Kay's book Fundamentals Of Statistical Signal Processing--Estimation Theory. In the ...
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0answers
39 views

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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3answers
311 views

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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78 views

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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1answer
73 views

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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1answer
40 views

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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71 views

Blind Estimation of Signal Parameters for Zero mean Normal distribution

Let $\mathbb{s}$ be zero mean with a normal distribution. Let one of the observed set of signals be given by $K\mathbb{s}$ and another by $L\mathbb{s^*}$, where $K$ and $L$ both are constants, and $\...
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3answers
85 views

If $X$ and $Y$ are zero mean independent Gaussian random variables with different variances, what is the density of $\sqrt{X^2+Y^2}$

Let $X\sim\mathcal{N}(0,\sigma_X^2)$ and $Y\sim\mathcal{N}(0,\sigma_Y^2)$ be independent Gaussian random variables. What will be PDF of $Z=\sqrt{X^2+Y^2}$ and $W=\arctan{\left(\frac{Y}{X}\right)}$. ...
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1answer
102 views

Why are the real- & imaginary part of complex white gaussian noise independent processes?

Assume we transmit a bandpass signal over an AWGN channel adding the Gaussian noise contribution $n$ \begin{equation} Acos(\omega_ct) + n(t) \end{equation} Further, the bandpass signal is generated ...
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26 views

How do I make a Gaussian pulse that works on different wavelengths in MATLAB?

I want to make this MATLAB code to plot a Gaussian pulse in THz, then use FFT on it. This is the MATLAB code I used to get the FFT of time domain Gaussian signal at 800nm wavelength: ...
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2answers
142 views

Signal with Complex Gaussian noise

If I have: $$ y = x_r+jx_i + n_r +j n_i$$ with $n_r$ and $n_i$ Gaussian with mean 0 and variance $\sigma^2$, what is the pdf of the envelope |y| and phase(y)? Is it still Rayleigh-distributed and ...
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1answer
24 views

Position of centroids after convolution

One of the properties of convolution is that the centroids of the functions being convolved should add. See equation (18) of Wolfram Alpha's section on convolution Convolution Properties. For example,...
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2answers
178 views

Covariance Matrix Polar to Cartesian

Let $R$ and $\Theta$ be zero mean independent Gaussian random variables with variances $\sigma_R^2$ and $\sigma_\Theta^2$ respectively. Hence their covariance matrix would be diagonal give by $$C_{R,\...
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38 views

Understanding white Gaussian noise variance

Referring to the bellow figure, assume the WGN has a constant PSD equal to N0. When filtered at $B_1 = 100 Hz$, the variance of the time domain noise is $σ_1^2$, and when filtered at $B_2 = 5 Hz$, the ...
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0answers
15 views

Scalable gaussian window

I would like to determine fractional fourier transform of scalable gaussian window function Can I get help on implementing g(t,u) in MATLAB?
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1answer
68 views

Characteristic function of a random Gaussian variable

I have to find the characteristic function of a random Gaussian variable of $$ \sigma_z (w) = E e^{i w z } $$. This is the variable and I know , from the theory that the characteristic function of ...
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2answers
32 views

Bayesian Information criterion is independent of prior - What does 'prior' mean here?

I am trying to identify the possible number of states in my data. Each state corresponds to a different scenario. For example, I am measuring humidity and trying to identify the number of states in ...
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2answers
29 views

Understanding Communication Theory Jargon for Statistical Linear Models

Coming from a statistical background, I understand the following formula: \begin{equation} y = X\beta + \epsilon \end{equation} as a linear regression model, with data input-output pair: $(X,y)$, ...
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1answer
43 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 ...
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1answer
68 views

Gaussian signal generation

Edit: Could the following be the answer? Generate WGN-like-signal which is centered around a set dBm value. Treat that signal like it was a frequency domain representation of an unknown X time-domain ...
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1answer
77 views

Kronecker delta instead of dirac delta as correlation function of white noise

From my understanding, if you have a sample $x_{t_1},\dots,x_{t_n}$ of $X_{t_1},\dots,X_{t_n}$ which are iid $N(0,1)$, then $x_{t_1},\dots,x_{t_n}$ is a sample path of Gaussian white noise. However, ...
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53 views

Comparing the performance of a digital communication sim against a reference

I have a complex baseband simulation of binary FSK modulation and demodulation. The modulated signal $s[k]$ is computed as $$ s[k] = e^{-j2\pi f_ik/f_s} , i \in [0,1] $$ where the sampling rate is $...
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2answers
192 views

Formula to calculate/generate gaussian noise?

What is the formula to calculate gaussian noise, given we have variance and mean? I am trying to search google for formula but i am unable to find any much relevant result. If for example i have mean ...
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1answer
38 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 ...
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20 views

Channel Impulse Response is zero mean Gaussian random variable?

In the Paper "Key Generation From Wireless Channels" the channel estimation is given as: $\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||S_B||^2}$, $\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||...
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2answers
41 views

Channel noise - A misnomer?

I was discussing with a colleague with background in communication about white Gaussian (WG) channel noise. He said noise is not added by the channel and it's just a misnomer. Noise, which is thermal ...
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1answer
20 views

The notation to express a datum filtered by arbitray 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 ...
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1answer
153 views

Scaling a wavelet in continuous wavelet transform

The mexican hat wavelet, obtained from the second derivative of a Gaussian, has a functional form of $$ \frac{2}{\sqrt{3 \sqrt{\pi} \sigma \ }} \left(1-\frac{t^2}{\sigma^2} \right) e^{-t^2/(2\sigma^...
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13 views

Spread out flux in 2D gaussian

I want to generate a 2D Gaussian model with flux spread out for a given radius. From theory, I found out that the total integrated flux of a Gaussian model. Now I want to image it such that total flux ...
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0answers
22 views

Finding the error in the total integrated intensity of a fitted 2D Gaussian

I have been trying to fit signals to a 2D Gaussian function, and while I have bene able to use sciKit-image's curve_fit function to find the covariance matrix for ...
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11 views

How to get sigma of gaussian from accelerometer noise ug/sqrt(HZ)

I'm trying to model an accelerometer with gaussian noise in my application. The actual accelerometer has the following specs: ...
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0answers
44 views

Determine Gaussian distribution parameters from the signal-to-noise ratio

Is there a straightforward formula for determining the mean and standard deviation of the gaussian distribution followed by noise applied on an image, knowing the signal-to-noise ratio between the ...
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17 views

Is splitting single white gaussian noise samples-stream in multiple sample-streams still gaussian noises?

Suppose I have a random generator that generates gaussian distributed samples (mean = 0, variance = sigma) at a rate of 4*N samples per second. I want to generate 4 different streams from this ...
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0answers
50 views

AWGN for a specific dBc

I have a square-ware signal with 1V peak-to-peak (alternating between -500 and +500mV, so its absolute value is a constant 500mV) and I would like to add to this an AWGN expressed in dBc ("decibels ...
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23 views

How would I modify a squared-exponential covariance kernel to be periodic?

I want to create a Gaussian process that resembles one generated by an exponential kernel (smooth and with a lot of variance) with a single caveat: I need the final value to be the same as the initial ...
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1answer
87 views

Problem implementing KL expansion with square-exponential kernel: output just looks like Gaussian

I am trying to implement the Karhunen Loeve expansion for a 1-D Gaussian random field with a square-exponential kernel. Specifically, I know that a Gaussian process has a KL expansion $\hat{U}=\sum_{...
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2answers
76 views

Applying a Power on a Sum of Gaussians to Enhance Resolution

There is so-called Power Transform technique in signal processing where the unresolved signal is sharpened by raising each data to a constant positive power. The example shown below is a sum of two ...
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1answer
19 views

How good is the Leech lattice for AWGN coding or MSE quantization of Gaussian sources?

Anyone know where to find graphs showing how well it works vs other schemes? thanks
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1answer
163 views

2D Multi Scale Dot Enhancement Filter based on Gaussian Filter and Hessian Matrix

I'm trying to implement an algorithm that enhance dot and line like structures based on Hessian matrix, the algorithm uses Gaussian filter with different scales before calculating the hessian matrix ...
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0answers
101 views

Audio experiment with intermodulation by multiplying two analytic signals

1) First, I describe intended processing with a basic case: Let's say on left channel I have a sin wave with frequency F1, and constant amplitude A1. Then on right channel a sin wave with frequency ...
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1answer
65 views

Low-Pass FIR that keeps all values positive

Let's say, that I want to low-pass the norm (hence positive values) of an analytic signal (related to Hilbert transform). This allows me to perform experiments with the envelope of audio. For low-...
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0answers
30 views

Gaussian Energy Broadening implementation to meet detector response

Respected Coding experts, I am trying to perform Gaussian broadening on an energy spectrum. The final result should convert "specrum.png" to a similar form of "Exp.png". The method is explained in ...
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1answer
54 views

Time derivative of signal - effect on noise distribution

I have an angular velocity measurement that has a certain amount of ripple that yields an histogram shaped like a gaussian curve. I quantify that ripple using a standard deviation. I am interested in ...
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0answers
57 views

additive white Gaussian noise -ask fsk psk

i want to simulate a system that uses ask,fsk ,psk in Matlab with additive Gaussian noise for each mode . figure shows the system propti and Eb/N0=6db my question is how to calculate the standard ...
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1answer
257 views

Relation between constellation SNR and baseband SNR

Let's say I have an I/Q modulation, ie. QPSK. I can simulate an the effects of an AWGN channel by adding to my QPSK symbols the realizations of a complex normal. $\mathcal{CN}(0,\frac{1}{\mathrm{SNR}...
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102 views

Use of gauspuls command in matlab, unable to broad signal at frequency spectrum

I have a doubt in the gauspuls command in matlab, i entered a fbr(fractional bandwidth of 1.5,ie. bandwidth= 0.75Mhz ) but as i plot the signal in the frequency spectrum using fft. i dont see the ...
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2answers
375 views

STFT calculation with Gaussian Window

$$ f(t)=\exp(jat^2) \,\,\, and \,\,\, g(t)\,\,is\,\, a\,\, Gaussian\,\, Window:$$ $$ g(t)= \left (πσ^2\right)^{\frac{-1}{4}}\exp\left (\frac{-t^2}{2σ^2} \right ) , \,\,\,\,\,\,\left \|g(t) \right \|=...
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205 views

I want to plot a gaussian pulse in MATLAB in the frequency domain, with its centre at the highest value

I have tried one way but i am getting 2 peaks at the edges as shown in the picture. I have used 1 part of my code for the signal generation where i used the gauspuls command (reference: www.simsonic....
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86 views

Should I increase the mean or the variance of Gaussian noise?

I am new in DSP. I am currently working with a project and I want to try which algorithm works better given different image noises. To test it out, I have been using the Gaussian noise in images. ...
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236 views

How to implement one dimensional low pass Gaussian filter with zero-phase shift?

I am trying to apply a low pass Gaussian filter on a signal and find the exact location of maximum/minimum in the resulting smoothed signal. I have to do it for a few values of sigma (Gaussian ...

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