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已同步 2025-08-07 15:10:13 +08:00
Cleared up notation for form of builtin waveforms.
这个提交包含在:
@@ -101,9 +101,9 @@ gaussian
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A Gaussian waveform.
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.. math:: I = e^{-\zeta(t-\chi)^2}
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.. math:: W(t) = e^{-\zeta(t-\chi)^2}
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where :math:`I` is the current, :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency.
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where :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency.
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.. figure:: images/gaussian.png
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@@ -115,9 +115,9 @@ gaussiandot
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First derivative of a Gaussian waveform.
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.. math:: I = -2 \zeta (t-\chi) e^{-\zeta(t-\chi)^2}
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.. math:: W(t) = -2 \zeta (t-\chi) e^{-\zeta(t-\chi)^2}
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where :math:`I` is the current, :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency.
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where :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency.
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.. figure:: images/gaussiandot.png
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@@ -129,9 +129,9 @@ gaussiandotnorm
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Normalised first derivative of a Gaussian waveform.
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.. math:: I = -2 \sqrt{\frac{e}{2\zeta}} \zeta (t-\chi) e^{-\zeta(t-\chi)^2}
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.. math:: W(t) = -2 \sqrt{\frac{e}{2\zeta}} \zeta (t-\chi) e^{-\zeta(t-\chi)^2}
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where :math:`I` is the current, :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency.
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where :math:`\zeta = 2\pi^2f^2`, :math:`\chi=\frac{1}{f}` and :math:`f` is the frequency.
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.. figure:: images/gaussiandotnorm.png
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@@ -143,9 +143,9 @@ gaussiandotdot
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Second derivative of a Gaussian waveform.
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.. math:: I = 2\zeta \left(2\zeta(t-\chi)^2 - 1 \right) e^{-\zeta(t-\chi)^2}
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.. math:: W(t) = 2\zeta \left(2\zeta(t-\chi)^2 - 1 \right) e^{-\zeta(t-\chi)^2}
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where :math:`I` is the current, :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency.
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where :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency.
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.. figure:: images/gaussiandotdot.png
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@@ -157,9 +157,9 @@ gaussiandotdotnorm
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Normalised second derivative of a Gaussian waveform.
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.. math:: I = \left( 2\zeta (t-\chi)^2 - 1 \right) e^{-\zeta(t-\chi)^2}
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.. math:: W(t) = \left( 2\zeta (t-\chi)^2 - 1 \right) e^{-\zeta(t-\chi)^2}
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where :math:`I` is the current, :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency.
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where :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency.
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.. figure:: images/gaussiandotdotnorm.png
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@@ -171,9 +171,9 @@ ricker
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A Ricker (or Mexican Hat) waveform which is the negative, normalised second derivative of a Gaussian waveform.
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.. math:: I = - \left( 2\zeta (t-\chi)^2 -1 \right) e^{-\zeta(t-\chi)^2}
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.. math:: W(t) = - \left( 2\zeta (t-\chi)^2 -1 \right) e^{-\zeta(t-\chi)^2}
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where :math:`I` is the current, :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency.
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where :math:`\zeta = \pi^2f^2`, :math:`\chi=\frac{\sqrt{2}}{f}` and :math:`f` is the frequency.
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.. figure:: images/ricker.png
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@@ -185,7 +185,7 @@ sine
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A single cycle of a sine waveform.
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.. math:: I = R\sin(2\pi ft)
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.. math:: W(t) = R\sin(2\pi ft)
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and
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@@ -197,7 +197,7 @@ and
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0 &\text{if $ft>1$}.
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\end{cases}
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:math:`I` is the current, :math:`t` is time and :math:`f` is the frequency.
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:math:`f` is the frequency
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.. figure:: images/sine.png
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@@ -209,7 +209,7 @@ contsine
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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).
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.. math:: I = R\sin(2\pi ft)
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.. math:: W(t) = R\sin(2\pi ft)
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and
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@@ -221,7 +221,7 @@ and
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1 &\text{if $R>1$}.
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\end{cases}
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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.
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where :math:`R_c` is set to :math:`0.25` and :math:`f` is the frequency.
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.. figure:: images/contsine.png
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