deriv_dmp_osc_conv_cauchy

TRXASprefitpack.mathfun.deriv_dmp_osc_conv_cauchy(t: float | ndarray, fwhm: float, k: float, T: float, phase: float) → float | ndarray[source]

Compute derivative of convolution of damped oscillation and normalized cauchy distribution

Parameters:

  • t – time

  • fwhm – full width at half maximum of cauchy distribution

  • k – damping constant (inverse of life time)

  • T – period of vibration

  • phase – phase factor

Returns:

Gradient of Convolution of normalized cauchy distribution and damped oscillation \((\exp(-kt)cos(2\pi t/T+phase))\).

Note

  • 1st column: df/dt

  • 2nd column: df/d(fwhm)

  • 3rd column: df/dk

  • 4th column: df/dT

  • 5th column: df/d(phase)