brainpy.math.surrogate.squarewave_fourier_series#
- brainpy.math.surrogate.squarewave_fourier_series(x, n=2, t_period=8.0)[source]#
Judge spiking state with a squarewave fourier series.
If origin=False, computes the forward function:
\[\begin{split}g(x) = \begin{cases} 1, & x \geq 0 \\ 0, & x < 0 \\ \end{cases}\end{split}\]If origin=True, computes the original function:
\[g(x) = 0.5 + \frac{1}{\pi}*\sum_{i=1}^n {\sin\left({(2i-1)*2\pi}*x/T\right) \over 2i-1 }\]Backward function:
\[g'(x) = \sum_{i=1}^n\frac{4\cos\left((2 * i - 1.) * 2\pi * x / T\right)}{T}\]>>> import brainpy as bp >>> import brainpy.math as bm >>> import matplotlib.pyplot as plt >>> bp.visualize.get_figure(1, 1, 4, 6) >>> xs = bm.linspace(-3, 3, 1000) >>> for n in [2, 4, 8]: >>> f = bm.surrogate.SquarewaveFourierSeries(n=n) >>> grads1 = bm.vector_grad(f)(xs) >>> plt.plot(bm.as_numpy(xs), bm.as_numpy(grads1), label=f'n={n}') >>> plt.legend() >>> plt.show()
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