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1answer
24 views

FFT function of Gaussian pulse

I need gaussian pulse fft. I set the sigma of gaussian pulse 1e-10 and define the gaussian function in time and use the fft. as you know the amplitude of should be unit in frequency domain. but my ...
0
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0answers
11 views

Gaussian filter at different order?

What effect does the Gaussian have at different order.. I mean comparing a Gausian Kernel with at 2. order Gaussian kernel.. What benefits, or when would it be appropriate to take the derivative.. ?? ...
0
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1answer
20 views

Gaussian kernel - How is made?

How do i make a 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 how would each value be if should ...
0
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2answers
19 views

Why/How a Gaussian Channel is both band-limited and Power limited?

All physical channels are band-limited, such that, X(f) = 0 for |f| > W A Gaussian Channel is limited in both power and bandwidth. For this reason we encounter phrases, such as, "A band-limited ...
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1answer
28 views

Can we decompose a correlated random variable into correlated plus uncorrelated?

Assume a random sequence $ Y_k = X_k \cdot H_k + W_k $ where $X_k$ is a deterministic quantity, $H_k$ is a correlated random sequence, $W_k$ is Additive White Gaussian random sequence. Can we ...
0
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1answer
73 views

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 ...
0
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1answer
37 views

Is there a closed form expression for noise other than white noise?

For white noise, where the PSD is constant, we can model that as a simple Gaussian. Is there any way to model the probability density function of other types of noise (pink noise, red noise, blue ...
0
votes
1answer
27 views

What type of sensors have complex Gaussian noise?

What type of sensors have complex Gaussian noise? Do strain gauges also exhibit such noise?
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0answers
24 views

Effect of Gaussian Smoothing to mean image intensity

I am implementing Perona-Malik Diffusion in using the formulas: Creating image at time k+1 using equation This is my implementation: ...
0
votes
1answer
21 views

How to determine stopband of discrete Gaussian, stdev sigma, support N

I would like to analyse a gaussian smoothing kernel with a set standard deviation and support (let's say, in MATLAB, fspecial('gaussian', [5 1], 1.3) so sigma is 1.3 and support is 5) in the DTFT ...
0
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0answers
20 views

Relation between Gaussian and Savitsky-Golay kernels

I would like to make a mathematical comparison between two methods in my field. One smooths with a Gaussian filter, and one smooths using a second-order Savitsky-Golay filter. Let's say the window ...
2
votes
1answer
50 views

Gaussian noise generator algorithm trouble

I stumbled upon the following algorithm for Gaussian noise generation and I just can't figure out how this is supposed to work at all. The algorithm is as follows: First of all: j = argmin_i (q_1 ...
1
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2answers
64 views

imshow command for Gaussian function

I'm trying to plot 2D gaussian function using "imshow" in MATLAB. However I could not see any white points in image. I tried to change sampling values and limits of x and y values. In addition to ...
2
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2answers
90 views

carrier frequency difference

Papers use wireless device-dependent radio-metrics as fingerprints. A radio-metric is a component of radio signal, amplitude, frequency and bandwidth. Each device creates a unique set of radio-metrics ...
0
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1answer
31 views

use scale space representation to filter one image

Currently I hope to use scale space representation to filter one image. Features in one image can be filtered using an Gaussian smooth filter with one optimal sigma. It means different features in one ...
1
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0answers
184 views

Horizontal banding (flickering) due to electronic rolling shutters

It is a well-known artifact that in CMOS cameras with electronic rolling shutter, horizontal banding (flickering), i.e. brightness intensity variations, are observed when the image is recorded under ...
0
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0answers
35 views

What is the relation between Gaussian filter and Wiener filter?

These are probably quite obvious, but wanted to make sure I got them right. Let $f$ be the noisy version of $f_0$ to which noise $w$ has been added, i.e. $f = f_0 + w$ Weiner filter lets us obtain ...
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0answers
132 views

Generate band limited white noise to be used as excitation in ODE

I am trying to repeat an example I found in a paper. I have to solve this ODE: $25 \ddot{x} + 15 \dot{x} + 330000 x = p(t)$ where $p(t)$ is a white noise sequence band-limited into the 10-25 Hz ...
1
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1answer
85 views

Spacing between gaussian windows for STFT

I'm computing discrete short time Fourier transform. Data is split into overlapping chunks and gaussian window is used for each chunk. However, I'm not sure how much overlap there should be between ...
0
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1answer
26 views

Different results for seperable filtering v/s direct filtering on 2-D image in MATLAB

I compared the difference between seperable and direct filtering for MATLAB's cameraman image. The difference is huge. I would like to understand the reason for this. Code below. ...
2
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2answers
178 views

Discrete approximation to Gaussian filter

One method of producing a discrete approximation kernel to a Gaussian filter of variance $\sigma^2$ is to assume a cutoff of $5\sigma$. This seems to suggest the following procedure: Create a ...
1
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1answer
830 views

Simple fft to Gaussian pulse with MATLAB

trying simply to create femtosecond pulse in MATLAB exactly like in the attached image, the carrier frequency is around 374THz, and my sampling frequency is 10 times the carrier. The results of ...
0
votes
1answer
127 views

Fixed SNR with unitary noise variance

I've just one question : How can I write a model like y = x + w,( with w a white gaussian noise) with a fixed SNR and a noise variance equal to 1. What coefficient may I have before x ? Thanks !
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0answers
18 views

Gaussian kernel standard deviation and spacing

Suppose I know the normalized gaussian weights for a kernel of standard deviation 1.0 evaluated in the sample positions $O = \{-2, -1, 0, 1, 2\}$. Let's call these G. I know that the same values G ...
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0answers
40 views

sine signal-->gaussian noise-->fading channel for SNR analysis

I'm new to matlab and need some help. I have a project whereby i want to to analyse the SNR of a sine signal which passes through an Additive White Gaussian Noise (simulating weather conditions) and a ...
-1
votes
1answer
103 views

Comparison between average kernel and gaussian kernel?

In image processing, we have two kinds of major kernels that are average kernel and gaussian kernel. For image segmentation, which is difference between average kernel and gaussian kernel? I found ...
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0answers
48 views

What is purpose of correlation kernel? IIs it high pass filter or low pass filter?

I am research about correlation kernel and I have some questions that need your help. Let see the pp. 3302-3303 in the paper: Changyang Li, et al., Robust Model for Segmenting Images With/Without ...
2
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1answer
134 views

What is correlation kernel and compare with gaussian kernel

I read a paper that said about correlation kernel that defined: $$W(x-y)=(α/1+d(|y − x|))$$ where $α = (\int(1+d(y − x)dy)^{-1}$, $(d(|y − x|))$ is spatial Euclidean distance from the central pixel. ...
2
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2answers
181 views

Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary process in time (in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary ...
0
votes
1answer
105 views

simulating range-bearing sensor with Matlab with Gaussian noise

I would like to simulate a sensor that provides range and direction of a beacon. This is for EKF localization, so the noise must be Gaussian (i.e. $\mathcal{N}(0, \sigma^{2})$. Also, I would like to ...
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vote
1answer
53 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? ...
0
votes
1answer
72 views

Intuition behind the Gaussian Filter in Image Processing

I've been using a Gaussian Filter and know how to use it but I don't understand the physical significance behind using the filter. We use it but why? What is the significance? I'm just starting out in ...
1
vote
1answer
99 views

Expectation of product of Filtered White Gaussian Noise

Assume I have a random process $X(t)$ that is white gaussian noise with psd $S(f)$. Now, let's filter that noise through a LPF of bandwidth $B$. How would I evaluate the following expression: ...
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0answers
23 views

Localization of a Gaussian

Studying for an exam I'll have I ran into a question about computing the localization of a Gaussian Filter in 1D, but sadly I have no idea of what such localization is. Can you give me a hint? ...
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2answers
151 views

Nonuniform sampling band-limited gaussian white noise

I'd like to sample band-limited Gaussian white noise non-uniformly. One way to approximate this would be to filter Gaussian white noise with a lower cutoff frequency and non-uniformly pick samples ...
1
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2answers
289 views

Computer Vision - Gaussian Pyramid, Scale Space and Pattern Matching

I am planning to implement a pattern matching algorithm using something like correlation as a matching metric. I know that the template I am going to use will, if present, have different sizes in the ...
1
vote
1answer
74 views

Standard deviation of Gaussian corresponding to perfect low pass filter [1,1]

For a time discrete signal, the rect-filter (for 1D signal [1,1]) is a perfect low pass filter. I was wondering, what is the best gaussian approximation of this filter? For a current problem, I ...
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5answers
5k views

noise of zero mean and variance?

It might be a very silly question, however I'm facing problem with it. Now, the Gaussian noise is a signal with zero mean and variance. I understand what the mean and the variance mean however, I'm ...
0
votes
0answers
41 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 ...
0
votes
0answers
131 views

Constant amplitude, uniform phase - what's the distribution of the complex signal then?

The well-known relationships for zero-mean circularly-symmetric complex Gaussian $z = a + jb = |z| \exp(j\varphi)$ signals are the amplitudes $|z| = \sqrt{a^2 + b^2}$ are Rayleigh-distributed the ...
1
vote
1answer
596 views

How to generate AWGN with given power spectral density

I am a little unsure about the generation of a additive white Gaussian noise, so I would appreciate to hear from you if I`m doing it correctly. My goal is to generate the time-domain noise ...
1
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0answers
45 views

Thresholding for Movement Classification

I have an application which creates a Gaussian model of the background based on consecutive frame difference and auto-generates a threshold for separating no-changes to movements. The application ...
1
vote
0answers
41 views

Is a Stationary VAR Process with Zero Mean Gaussian Innovations a Gaussian Stationary Process?

Consider the stationary VAR process $${\bf X}_t = \sum_{\tau = 1}^{L} A_\tau {\bf X}_{t-\tau} +{\bf \epsilon}_t$$ If the innovations $\epsilon_t \sim MVN({\bf 0},\Sigma)$ then is ${\bf X}_t$ a ...
0
votes
1answer
81 views

frequency components of discrete Gaussian-windowed signal

When we are do a discrete Gabor transform on a 1D signal, we apply a Gaussian window on a segment of the signal. However, due to the tapering ends of the Gaussian window, the magnitude of the data ...
0
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2answers
79 views

Calculating information loss in a signal after smoothing?

I have a signal. I applied Gaussian smoothing to it and then for baseline reduction I appied Tophat filter to the smoothed version. This is the original signal: This is the final signal: I read ...
1
vote
1answer
108 views

Highpass filter applied to noise

Suppose the input signal is represented as $$y=x+w$$ where $x$ is the signal to be estimated and $w$ is AWGN. I design a high pass filter $H$. What does $$H^{T}Hw$$ represent? Will it be just AWGN but ...
1
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0answers
47 views

Fitting VAR Process with Generalised Gaussian Noise

Consider the $m$-dimensional VAR process $${\bf x}_t = \sum_{l=1}^{P} A_l{\bf x}_{t-l} + {\bf e}_t$$ where the componenets of ${\bf e}_t$ are spatially and temporally independent and follow a ...
2
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3answers
184 views

Which sigma to use for edge detection

I know that in many edge detection algorithm the first step is choosing a scale to work on. We actually operate on the chosen scale by applying a gaussian blur on the original image. I wanted to ...
6
votes
1answer
469 views

Is the discrete Gaussian kernel an eigenfunction of the DFT?

So the Gaussian function is an eigenfunction of the Fourier transform because it transforms into itself, right? But this isn't true for the sampled Gaussian in the DFT because the tails of the ...
2
votes
2answers
123 views

Situations where complexity is too big to exceed linearity and gaussianity

I'm studing about Kalman Filter and Particle Filter in multiple target tracking in computer vision (tracking pedestrians). Reading sientific papers I'm colliding with a lot of sentences like: The ...