I have been reading about the mathematics behind Perlin noise, a gradient noise function often used in computer graphics, from Ken Perlin’s presentation and Matt Zucker’s FAQ. I understand that each grid point, $X$, has a pseudo-random gradient associated with it, $g(X)$ – just a vector of unit length that appears random. When finding the […]

What is meant by a continuous-time white noise process? In a discussion following a question a few months ago, I stated that as an engineer, I am used to thinking of a continuous-time wide-sense-stationary white noise process $\{X(t) \colon -\infty < t < \infty\}$ as a zero-mean process having autocorrelation function $R_X(\tau) = E[X(t)X(t+\tau)] = […]

Intereting Posts

Primes dividing $11, 111, 1111, …$
“Number of Decompositions into $k$ Powers of $p$”-Counting Functions
Do groups, rings and fields have practical applications in CS? If so, what are some?
An integral$\frac{1}{2\pi}\int_0^{2\pi}\log|\exp(i\theta)-a|\text{d}\theta=0$ which I can calculate but can't understand it.
Is $\mathbb{Q}/\mathbb{Z}$ isomorphic to $\mathbb{Q}$?
a generalization of normal distribution to the complex case: complex integral over the real line
Is this proof for Theorem 16.4 Munkers Topology correct?
Integral $\int_0^1 \ln(x)^n \operatorname{Ei}(x) \, dx$
Square matrices satisfying certain relations must have dimension divisible by $3$
How to calculate true lengths from perspective projection?
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
How to show that the set of all Lipschitz functions on a compact set X is dense in C(X)?
Prove that $\int_{E}f =\lim \int_{E}f_{n}$
How find the value of the $x+y$
which is bigger $I_{1}=\int_{0}^{\frac{\pi}{2}}\cos{(\sin{x})}dx,I_{2}=\int_{0}^{\frac{\pi}{2}}\sin{(\sin{x})}dx$