# Questions tagged [gaussian]

The gaussian function, an exponential function with a negative square of the argument in the exponent, is interesting in signal processing because the Fourier Transform of a gaussian function is also a gaussian function.

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### Discrete Fourier Transform of the Gaussian

Cross-posted from here I encountered the following question in a Digital Image Processing examination: Find the 2D DFT of $\frac{1}{2 \pi \sigma^2} e^{-\frac{(x - x_0)^2 + (y - y_0)^2}{2 \sigma^2}}$ ...
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### Approximating variable-length coding by "aggregating" fixed-length coding

Consider the problem where I want to quantize a univariate standard Gaussian with two bits, and the objective is to minimize MSE reconstruction loss. According to these slides, the Lloyd algorithm and ...
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### Decomposing Gaussian Diffraction Pattern

I was recommended to post this question here from the physics stack exchange. I have the following diffraction pattern produced by a fabry-perot etalon. The red represents the center of that pattern. ...
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### Is it possible to reformulate a Kalman Filter as a Gaussian Markov Random Field?

The generic formulation of a KF uses a set of transitition equations, while the GMRF is typically specified through its mean and precision. However, a simple KF involves Gaussianity and Markov ...
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### Generating time-domain noise from PSD

I have a question regarding generating a time-domain noise from the power spectral density (PSD), this was addressed in this question (How to generate time-series from a given one-sided PSD?) but I ...
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### Can the standard deviation of the Gaussian window in a Gabor filter be made infinitesimally small?

My understanding is that the standard deviation of the Gaussian window in a Gabor filter dictates the temporal resolution. Wouldn't it always be better then to make the window smaller, thus achieving ...
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### Which probability density functions to use in a likelihood ratio test for the radar detection problem?

I am trying to understand the radar detection problem in the form of the generalized likelihood ratio test and am having a little trouble with understanding the noise distributions. Perhaps this will ...
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