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# Questions tagged [gaussian]

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### 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 ...
415 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 ...
5k 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 ...
238 views

### Why Does 2D FFT of Gaussian Looks More Sharper than Gaussian Itself?

I am trying to understand why 2D FFT is done on a Gaussian process in a particular code. From my understanding from these posts: https://www.researchgate.net/post/...
937 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?
852 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 ...
68 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. ...
279 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 ...
63 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 ...
4k views

### How to convert a low-pass Gaussian filter to a high pass filter

I have the following code for a applying a Gaussian filter to an image. From what I understand this is a low pass filter. Now I have to convert this into a high-pass filter, and from what we were told ...
394 views

### Why is my laser beam intensity profile not Gaussian?

I am kind of new to laser physics and signal processing, I hope I am in the right place to ask this question. I am also sorry for my not-great English. I have been asked to study the transverse ...