Cleared up notation for form of builtin waveforms.

这个提交包含在:
Craig Warren
2016-02-10 12:17:47 +00:00
父节点 676dee3651
当前提交 e373631264

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@@ -101,9 +101,9 @@ gaussian
A Gaussian waveform. 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 .. figure:: images/gaussian.png
@@ -115,9 +115,9 @@ gaussiandot
First derivative of a Gaussian waveform. 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 .. figure:: images/gaussiandot.png
@@ -129,9 +129,9 @@ gaussiandotnorm
Normalised first derivative of a Gaussian waveform. 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 .. figure:: images/gaussiandotnorm.png
@@ -143,9 +143,9 @@ gaussiandotdot
Second derivative of a Gaussian waveform. 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 .. figure:: images/gaussiandotdot.png
@@ -157,9 +157,9 @@ gaussiandotdotnorm
Normalised second derivative of a Gaussian waveform. 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 .. 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. 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 .. figure:: images/ricker.png
@@ -185,7 +185,7 @@ sine
A single cycle of a sine waveform. A single cycle of a sine waveform.
.. math:: I = R\sin(2\pi ft) .. math:: W(t) = R\sin(2\pi ft)
and and
@@ -197,7 +197,7 @@ and
0 &\text{if $ft>1$}. 0 &\text{if $ft>1$}.
\end{cases} \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 .. 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). 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 and
@@ -221,7 +221,7 @@ and
1 &\text{if $R>1$}. 1 &\text{if $R>1$}.
\end{cases} \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 .. figure:: images/contsine.png