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1
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1answer
35 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
15 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
55 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
vote
1answer
173 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
49 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 !
0
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0answers
12 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 ...
0
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0answers
22 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 ...
0
votes
1answer
76 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 ...
0
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0answers
37 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
votes
1answer
95 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
votes
2answers
164 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
56 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 ...
1
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1answer
45 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
50 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
57 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: ...
0
votes
0answers
20 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? ...
1
vote
2answers
120 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 ...
0
votes
0answers
41 views

how to calculate feature points in SIFT?

i wanna know how to calculate key points? im doing it in matlab. when i select 3 DOG(differnce of gaussian) blured image and compared each pixels in the middle image with 26 neighbourhood(including 9 ...
1
vote
2answers
174 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
64 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 ...
0
votes
5answers
2k 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
49 views

MTF for laplacian of a gaussian

am trying to plot a modulation transfer function of a gaussian from -40 to 40 mm in conjunction with a laplacian of gaussian filter, width = 4 mm and sigma = 1. i have a trouble scaling the MTF for ...
0
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0answers
40 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
89 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
339 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
vote
0answers
44 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
38 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
76 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
votes
2answers
73 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
105 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
vote
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
votes
3answers
129 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
343 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
114 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 ...
6
votes
2answers
3k views

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 ...
2
votes
1answer
1k views

What is use of a gaussian filter over histogram?

I am working in the field of digital image processing and currently i am reading this paper and I have two questions about it.... After applying a gaussian filter to a histogram, will the pixel ...
0
votes
1answer
143 views

gaussian kernel and bionomial coefficients

The following image is from robert collins' ppt from http://www.cse.psu.edu/~rcollins/CSE486/ How to calculate sigma ? It shows [1 4 6 4 1] is corresponding to sigma=1. I learned that usually ...
6
votes
2answers
991 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 ...
5
votes
4answers
6k views

How to generate band-limited Gaussian white noise?

In some papers, I read that the additive noise is band-limited Gaussian white. How can I simulate this type of noise use Matlab?
3
votes
1answer
349 views

Determine Parameters of gaussian distribution to fit a certain Image-Filter

I'd like to know what the parameters for the two-dimensional gaussian distributions are, which create this (I think) quite common image-processing filter: $$ h_\sigma(x,y)= \left[ \matrix { ...
1
vote
1answer
71 views

Is there a need of Point interpolation before proceeding for gaussian smoothing of an incomplete distribution?

Suppose there is a distribution that has values sampled on the interval 1-25 with corresponding sample values that have to be smoothed. For example: ...
0
votes
1answer
181 views

Estimating number for iterations for gaussian smoothing

I have some data sets on which I applied Gaussian smoothing using [1 4 6 4 1] kernel. In my program I iterated this kernel 50 times on the data sets. But only a few ...
3
votes
2answers
766 views

Gaussian random generator

I have quite a straight-forward question. What I aim for is the generation of a certain set of random numbers with a normal distribution (mu = 0, ...
5
votes
2answers
146 views

What is the difference between a simple gaussian filter and gaussian filter multiplied by its sum of it elements?

1 2 1 1 2 1 2 4 2 (A) (1/16) * 2 4 2 (B) 1 2 1 1 2 1 Both matrices are the same ...
1
vote
2answers
340 views

When should the sum of all elements of a gaussian kernel be zero?

I found an approximation of a 5x5 2D convolution kernel like this : Here, the sum of the elements is zero and this one was used for Laplacian of Gaussian! Another one here : This one has all ...
1
vote
1answer
511 views

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 ...
2
votes
1answer
5k views

Fit data to Gaussian distribution

I want some data to fit the corresponding Gaussian distribution. The data is meant to be Gaussian already, but for some filtering reasons, they will not perfectly match the prescribed and expected ...
3
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0answers
80 views

Compensate for standard deviation loss

I am not sure if this question will be a little off-topic on this forum, that I will give it a try anyway, since it implies signal process arguments. By using ...
4
votes
1answer
303 views

Common use cases for 2D NONseparable convolution filters?

In the image processing world, I've noticed that a lot of the popular convolution filters are separable. Here's a quick list of common separable filters: Sobel Gaussian blur Box filter (all ones, ...
1
vote
1answer
304 views

How to obtain mathematically high frequency and low frequency component separately using Bilateral filter?

I have asked this question before in the sense that what does a high frequency and low frequency component signify in a image and i got satisfactory answers now i want to know that how i can get high ...