In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form and with parametric extension for arbitrary real constants a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape.

The Gaussian is called a wavepacket because of its Fourier transform: it is a packet of waves with frequencies/wavenumbers clustered around a single value kc (the subscript “c” is for “car-rier”, as we explain below).

Superposition of 1D plane waves (blue) that sum to form a Gaussian wave packet (red) that propagates to the right while spreading. Blue dots follow each plane wave's phase velocity while the red line follows the central group velocity.

6 days ago · In one dimension, the Gaussian function is the probability density function of the normal distribution, f (x)=1/ (sigmasqrt (2pi))e^ (- (x-mu)^2/ (2sigma^2)), (1) sometimes also called the frequency curve.

In optics, a Gaussian beam is an idealized beam of electromagnetic radiation whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile.

Jul 24, 2014 · Know how to generate a gaussian pulse, compute its Fourier Transform using FFT and power spectral density (PSD) in Matlab & Python.

Wave vectors in the range k0 – ∆k to k0 + ∆k. In this range, equal amplitude of each state. Out side this range, amplitude = 0. Superposition of momentum eigenfunctions. Integrate over k about k0. Rapid oscillations in envelope of slow, decaying oscillations.

Apr 22, 2023 · The concept of a wave packet is universally introduced in introductory QM classics in order to "localize" a particle in free space (i.e. V(x) = 0 in the 1-Dimensional Schrodinger Eq.). Many textbooks use the example of the Gaussian wave …

Apr 12, 2017 · If you want a single Gaussian with bandwidth from f0 to f1 (with center at (f0+f1)/2) you'd set sigma to have a Gaussian with the required width (for +/- 3 standard deviations in the frequency domain, set sigma to (3/pi)*(1/(f1-f0))), then shift its center to (f0+f1)/2 by multiplying with cos(2*pi*t*(f0+f1)/2) in the time domain.

Aug 4, 2020 · I was wondering if it is possible to generate Gaussian shape wave with op amp. I am basically trying to modulate sine wave signal and Gaussian wave signal and send it to a short range pcb antenna.