53 lines
1.2 KiB
Python
53 lines
1.2 KiB
Python
import matplotlib.pyplot as plt
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import numpy as np
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from numpy import random
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import scipy.signal as sgl
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yi = random.normal(size=2**20)
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yr = np.roll(yi, -(2**10))
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figy, axy = plt.subplots()
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axy.plot(np.arange(2**10, 2**11), yi[2**10 : 2**11])
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axy.plot(np.arange(2**10, 2**11), yr[2**10 : 2**11])
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figf, axf = plt.subplots()
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axf.plot(*sgl.welch(yi))
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axf.plot(*sgl.welch(yr))
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eta = lambda r: yi + r * yr
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u = lambda r: -yi + r * yr
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def puv(eta, u):
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f, phi_eta = sgl.welch(eta)
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phi_u = sgl.welch(u)[1]
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phi_eta_u = np.abs(sgl.csd(eta, u)[1].real)
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return f, np.sqrt(
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(phi_eta + phi_u - 2 * phi_eta_u) / (phi_eta + phi_u + 2 * phi_eta_u)
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)
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figr, axr = plt.subplots()
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for r in np.arange(0, 1.1, 0.1):
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axr.plot(*puv(eta(r), u(r)), c="k")
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Rn = puv(
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eta(r) + 0.4 * random.normal(size=2**20),
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u(r) + 0.4 * random.normal(size=2**20),
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)
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axr.plot(
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*Rn,
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c="#ff6600",
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)
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axr.annotate(
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f"{r=:.1f}", (Rn[0][0], Rn[1][0]), bbox={"boxstyle": "square", "facecolor": "w"}
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)
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axr.grid()
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axr.autoscale(True, "x", tight=True)
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axr.set(ylim=(0, 1), ylabel="R", xlabel="f")
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axr.legend(("No noise", "40% noise"), loc="lower left")
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figr.savefig("out_r_test.pdf")
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plt.show()
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