# What is Gaussian filter kernel?

## What is Gaussian filter kernel?

In electronics and signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response is physically unrealizable as it has infinite support).

**What is the maximum value of a Gaussian kernel?**

1

The maximum value of a Gaussian kernel is 1.

**What is the standard deviation of a Gaussian?**

The nature of the gaussian gives a probability of 0.683 of being within one standard deviation of the mean. The mean value is a=np where n is the number of events and p the probability of any integer value of x (this expression carries over from the binomial distribution ).

### Is the Gaussian kernel a self-similar function?

This phenomenon, i.e. that a new function emerges that is similar to the constituting functions, is called self- similarity. The Gaussian is a self-similar function.

**What is the standard deviation of the Gaussian kernel?**

In statistics, when we consider the Gaussian probability density function it is called the standard deviation, and the square of it, s2, the variance. In the rest of this book, when we consider the Gaussian as an aperture function of some observation, we will refer to s as the inner scale or shortly scale.

**How is the NXN Gaussian kernel produced in convolution?**

To produce an nxn Gaussian kernel the distribution is first sampled and stored in an nx1 vector v. Each sample is the integral over the distribution function in the range [-0.5, 0.5] centered around the sample point. The vector is them multiplied with itself to produce the full nxn kernel.

## Where can I find the Gaussian kernel on the Euro?

The Gaussian kernel is apparent on every German banknote of DM 10,- where it is depicted next to its famous inventor when he was 55 years old. The new Euro replaces these banknotes. The Gaussian kernel is defined in 1-D, 2D and N-D respectively as G1 DH x; s L = þ þþ þþ þþþþ þþþþþþþþ1 ! !!!!!!! 2p s e- þþþþþþþþx2þ þþ þþ