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and the RMS for a function over all time is = [()]. The RMS over all time of a periodic function is equal to the RMS of one period of the function. The RMS value of a continuous function or signal can be approximated by taking the RMS of a sample consisting of equally spaced observations.
The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude. [1]
Half width at half maximum (HWHM) is half of the FWHM if the function is symmetric. The term full duration at half maximum (FDHM) is preferred when the independent variable is time . FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of ...
The solid body shows the places where the electron's probability density is above a certain value (here 0.02 nm −3): this is calculated from the probability amplitude. The hue on the colored surface shows the complex phase of the wave function. In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour ...
In statistics, the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag. Let { X t } {\displaystyle \left\{X_{t}\right\}} be a random process, and t {\displaystyle t} be any point in time ( t {\displaystyle t} may be an ...
The convolution of a function with a Gaussian is also known as a Weierstrass transform. A Gaussian function is the wave function of the ground state of the quantum harmonic oscillator. The molecular orbitals used in computational chemistry can be linear combinations of Gaussian functions called Gaussian orbitals (see also basis set (chemistry)).
As the number of discrete events increases, the function begins to resemble a normal distribution. Comparison of probability density functions, () for the sum of fair 6-sided dice to show their convergence to a normal distribution with increasing , in accordance to the central limit theorem. In the bottom-right graph, smoothed profiles ...
If C xy is less than one but greater than zero it is an indication that either: noise is entering the measurements, that the assumed function relating x(t) and y(t) is not linear, or that y(t) is producing output due to input x(t) as well as other inputs. If the coherence is equal to zero, it is an indication that x(t) and y(t) are completely ...