diff --git a/docs/source/plotting.rst b/docs/source/plotting.rst index ab0603e9..861c5961 100644 --- a/docs/source/plotting.rst +++ b/docs/source/plotting.rst @@ -101,9 +101,9 @@ gaussian A Gaussian waveform. -.. math:: I = e^{-\zeta(t-\chi)^2} +.. math:: W(t) = e^{-\zeta(t-\chi)^2} -where :math:`I` is the current, :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency. +where :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency. .. figure:: images/gaussian.png @@ -115,9 +115,9 @@ gaussiandot First derivative of a Gaussian waveform. -.. math:: I = -2 \zeta (t-\chi) e^{-\zeta(t-\chi)^2} +.. math:: W(t) = -2 \zeta (t-\chi) e^{-\zeta(t-\chi)^2} -where :math:`I` is the current, :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency. +where :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency. .. figure:: images/gaussiandot.png @@ -129,9 +129,9 @@ gaussiandotnorm Normalised first derivative of a Gaussian waveform. -.. math:: I = -2 \sqrt{\frac{e}{2\zeta}} \zeta (t-\chi) e^{-\zeta(t-\chi)^2} +.. math:: W(t) = -2 \sqrt{\frac{e}{2\zeta}} \zeta (t-\chi) e^{-\zeta(t-\chi)^2} -where :math:`I` is the current, :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency. +where :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency. .. figure:: images/gaussiandotnorm.png @@ -143,9 +143,9 @@ gaussiandotdot Second derivative of a Gaussian waveform. -.. math:: I = 2\zeta \left(2\zeta(t-\chi)^2 - 1 \right) e^{-\zeta(t-\chi)^2} +.. math:: W(t) = 2\zeta \left(2\zeta(t-\chi)^2 - 1 \right) e^{-\zeta(t-\chi)^2} -where :math:`I` is the current, :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency. +where :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency. .. figure:: images/gaussiandotdot.png @@ -157,9 +157,9 @@ gaussiandotdotnorm Normalised second derivative of a Gaussian waveform. -.. math:: I = \left( 2\zeta (t-\chi)^2 - 1 \right) e^{-\zeta(t-\chi)^2} +.. math:: W(t) = \left( 2\zeta (t-\chi)^2 - 1 \right) e^{-\zeta(t-\chi)^2} -where :math:`I` is the current, :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency. +where :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency. .. figure:: images/gaussiandotdotnorm.png @@ -171,9 +171,9 @@ ricker A Ricker (or Mexican Hat) waveform which is the negative, normalised second derivative of a Gaussian waveform. -.. math:: I = - \left( 2\zeta (t-\chi)^2 -1 \right) e^{-\zeta(t-\chi)^2} +.. math:: W(t) = - \left( 2\zeta (t-\chi)^2 -1 \right) e^{-\zeta(t-\chi)^2} -where :math:`I` is the current, :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency. +where :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency. .. figure:: images/ricker.png @@ -185,7 +185,7 @@ sine A single cycle of a sine waveform. -.. math:: I = R\sin(2\pi ft) +.. math:: W(t) = R\sin(2\pi ft) and @@ -197,7 +197,7 @@ and 0 &\text{if $ft>1$}. \end{cases} -:math:`I` is the current, :math:`t` is time and :math:`f` is the frequency. +:math:`f` is the frequency .. figure:: images/sine.png @@ -209,7 +209,7 @@ contsine A continuous sine waveform. In order to avoid introducing noise into the calculation the amplitude of the waveform is modulated for the first cycle of the sine wave (ramp excitation). -.. math:: I = R\sin(2\pi ft) +.. math:: W(t) = R\sin(2\pi ft) and @@ -221,7 +221,7 @@ and 1 &\text{if $R>1$}. \end{cases} -where :math:`I` is the current, :math:`R_c` is set to :math:`0.25`, :math:`t` is time and :math:`f` is the frequency. +where :math:`R_c` is set to :math:`0.25` and :math:`f` is the frequency. .. figure:: images/contsine.png