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Year Name Authors References Language Short description 1983 BHCYL Craig F. Bohren and Donald R. Huffman [1]Fortran Mie solution (infinite series) to scattering, absorption and phase function of electromagnetic waves by a homogeneous cylinder.
Otherwise it is called unwrapped phase, which is a continuous function of argument t, assuming s a (t) is a continuous function of t. Unless otherwise indicated, the continuous form should be inferred. Instantaneous phase vs time. The function has two true discontinuities of 180° at times 21 and 59, indicative of amplitude zero-crossings.
The pseudocode below performs the GS algorithm to obtain a phase distribution for the plane "Source", such that its Fourier transform would have the amplitude distribution of the plane "Target". The Gerchberg-Saxton algorithm is one of the most prevalent methods used to create computer-generated holograms .
Consider a continuous-time Markov process with m + 1 states, where m ≥ 1, such that the states 1,...,m are transient states and state 0 is an absorbing state. Further, let the process have an initial probability of starting in any of the m + 1 phases given by the probability vector (α 0,α) where α 0 is a scalar and α is a 1 × m vector.
Many familiar distributions can be written as oscillatory integrals. The Fourier inversion theorem implies that the delta function, () is equal to ().If we apply the first method of defining this oscillatory integral from above, as well as the Fourier transform of the Gaussian, we obtain a well known sequence of functions which approximate the delta function:
The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
Conversely, a phase reversal or phase inversion implies a 180-degree phase shift. [ 2 ] When the phase difference φ ( t ) {\displaystyle \varphi (t)} is a quarter of turn (a right angle, +90° = π/2 or −90° = 270° = −π/2 = 3π/2 ), sinusoidal signals are sometimes said to be in quadrature , e.g., in-phase and quadrature components of a ...
In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to functions given by integration against a rapidly-varying complex exponential. This method originates from the 19th century, and is due to George Gabriel Stokes and Lord Kelvin . [ 1 ]