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# Questions tagged [gaussian]

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498 views

### Gaussian wavelet generation of a given frequency

How can I generate a Gaussian wavelet (time domain) with a given central frequency. I mean, if I take the Fourier Transform then its spectrum should be around that given central frequency. For ...
144 views

### Is $A\cos(\omega t+\theta)$ a Gaussian random process?

$Z(t) = A\cos(\omega t+\theta)$ where $A$~$N(0,\sigma ^2)$ and $\theta$~$(0,2\pi)$ are independent. I'm trying to figure out if $Z(t)$ is a Gaussian random process and whether it is strict sense ...
978 views

### Gaussian filter in terms of pixel radius

So I'm writing an app that blurs and downscales large quantities of images, but all the image processing libraries I've come across define gaussian blurs in terms of sigma and kernel size rather than ...
3k views

### what is a Gaussian signal?

I am learning Wiener filtering for 2D images by myself. From one book, it reads It should be noted that the study of the more general problem of signal denoising dates back to at least Norbert Wiener ...
662 views

### Implementing a 1-D Kalman Filter Regression, Missing the smoothing action (getting the opposite)

I am implementing the 1D Kalman Filter in Python on a fundamentally noisy set of measurement data, and I should be observing a large amount of smoothing...but, instead, my Kalman Filter is doing the ...
523 views

### How do I calculate the autocorrelation of a train pulse having only the pdf?

I have a pulse train of a fixed period, but a random amplitude following a Gaussian distribution $(\mu=0,\sigma=1)$. I know how to work with a random period or delay, but how do I proceed to calculate ...
803 views

### How to make a 2D gaussian Blur terms?

I want to make a 2D gaussian Blur coeffients. Now I am making 1D gaussian Blur term as following. ...
71 views

### Curve fitting to distorted Gaussian

I have to measure the distance between two pulse trains, each of which looks like a slightly long tailed Gaussian distribution. Is there a relatively easy curve fitting method for this? I can do it ...
233 views

### Mutual information of $\infty$-PAM

I'm trying to compute using matlab the mutual information for an $\infty$-PAM input (the limit of a very dense PAM constellation) for a range of snr and I got stuck. I'm working with a real-valued ...
58 views

### How to derive the $\log$ of fraction of two Gaussian distribution

I am designing a function $A(x)$ that map $x\to \{0,1\}$. The function $A$ can be expressed as $$A(x)=\begin{cases} 1 \text{ if p_1(x) \ge p_2(x)}\\ 0 \text{ otherwises} \end{cases}$$ where $p_1$...
94 views

### What is the equivalent smoothing function to running the same Gaussian 8 times?

Suppose there is an image which is to be smoothed by convolving it with a Gaussian kernel with standard deviation $\sigma$. If the image is then smoothed with this kernel 8 consecutive times, is the ...
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 ...
648 views

### Uniform quantizer for gaussian input signal

I have a gaussian signal $x$ with zero mean and unit variance. I am quantizing it by using a uniform quantizer of step size $q$ calculated by q = \frac{x_\mathrm{max} - x_\mathrm{min}}{2^{M_\mathrm{...
205 views

### Plotting uniform and Gaussian random variables

I want to create uniform and Gaussian (normal) random variables in MATLAB via rand and randn syntax. And I would like to plot ...
217 views

### What is the most efficient way to perform Gaussian blurs for varying sizes of Gaussian kernels in an image?

I have detected corner points of images using Harris corner detector in GLSL and now, I intend on using Fast Retina Keypoint(FREAK) as keypoint descriptor to later match the keypoints between images. ...
83 views

### How does gaussian convution stacking work?

If I first convolve an image with a Gaussian filter with σ = 1, and then convolve the output of that image with a Gaussian with σ = 2 Does this give the same effect as convolving the original image ...
140 views

### Multiscale Shape and Detail Enhancement from Multi-light Image Collections

I have been working on a practical implementation in Matlab of the algorithm Raanan Fattal suggested in the following paper. I couldn't understand the meaning of eq. 11 on page 5: g is a gaussian, ...
133 views

### How can I implement image widowing in my image in Java?

My initial image is a medical image and my main objective is finding directionality. The original size of my image was 8X8 and I have rescaled the image to 32X32 to increase my accuracy. My input ...
373 views

### 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 ...
4k views

### Gaussian Filter Close to Image Border

When applying Gaussian filters close to the borders of an image, algorithms usually zero-pad or replicate/mirror/wrap the borders. This is not good enough for my case, so I wonder if there is ...
320 views

### equations to calculate coefficients of recursive IIR Gaussian blur filter

I am reading the implementation of IIR Gaussian blur filter from this link. In the source code, the coefficients are generated by the following code ...
466 views

### Complex Gaussian Channel + AWGN noise

If I define a channel to have complex Gaussian coefficients, do I still need to add noise to the signal passing through this channel using the command "awgn" or would that be redundant?
2k views

### filter coefficients to know high pass and low pass filter

Looked on few questions already there in dsp.stackexchange and couldn't get the direct answer. Basically I have a kernel of a gaussian separable filter. ...
940 views

### Complex normal Gaussian noise

I would like to create complex normal Gaussian noise with dimensions $(M,N)$. The noise should be zero mean and the variance should be equal to one. How can I do so?
6k views

### Question about Difference of Gaussian (DoG) algorithm

I am recently learning about Computer Vision and I am having a trouble understanding Difference of Gaussian (DoG) algorithm. I get how the algorithm works in high level idea, but I am trying to ...
1k views

### Downsampling and Gaussian filtering in the context of scale space pyramids

In the context of scale space image pyramids using Gaussian filters I noticed that it's common to downsample the image after blurring with $\sigma = 2*\sigma_{init}$ . My question is: What is the ...
197 views

### Gaussian in matlab

I have written a function that implements a gaussian filter. I use fft2 to transform my image and my filter to 2d fourier transform. Then I multiply them and then use ifft2. The resulting image is ...
460 views

### SURF feature extractor and descriptor

I am trying to understand how SURF extracts features using a Hessian matrix. What I am a bit confused about, is why a second derivative Gaussian filter is used, rather than a standard Gaussian filter?...
594 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 ...
6k views

### How to Calculate Gaussian Kernel for a Small Support Size?

How to calculate the values of 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 what would each ...
1k 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 ...
103 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 ...
1k 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 ...
423 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 ...
74 views

### What type of sensors have complex Gaussian noise?

What type of sensors have complex Gaussian noise? Do strain gauges also exhibit such noise?
133 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: ...
47 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 ...
56 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 ...
790 views

7k 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 the ...