PDFs: modified script from Harm for PhasorSum distributions

This commit is contained in:
Eric Teunis de Boone 2023-11-14 15:22:45 +01:00
parent 4462d4ef2e
commit a32ae6b2ef

View file

@ -0,0 +1,154 @@
#!/usr/bin/env python3
__doc__ = """
Phase and Amplitude distributions for a phasor in the presence of noise.
Author: Harm Schoorlemmer
"""
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
import scipy.stats as stat
from scipy import special
from lib.util import MethodMappingProxy as MethodProxy
def expectation(x,pdfx):
dx = x[1]-x[0]
return np.sum(x*pdfx*dx)
def variance(x,pdfx):
mu = expectation(x,pdfx)
dx = x[1]-x[0]
return np.sum((x**2*pdfx*dx))-mu**2
def phase_distribution(theta,sigma,s):
theta = np.asarray(theta)
ct = np.cos(theta)
st = np.sin(theta)
k=s/sigma
pipi=2*np.pi
return (np.exp(-k**2/2)/pipi) + (
(pipi**-0.5)*k*np.exp(-(k*st)**2/2)) * (
(1.+special.erf(k*ct*2**-0.5))*ct/2)
def phase_distribution_gauss(theta,sigma,s):
theta = np.asarray(theta)
k=s/sigma
return (2*np.pi)**-0.5*k*np.exp(-(k*theta)**2/2)
def amplitude_distribution(a,sigma,s):
a = np.asarray(a)
k = s/sigma
return stat.rice.pdf(a,s/sigma,scale=sigma)
def amplitude_distribution_gauss(a,sigma,s):
a = np.asarray(a)
k=s/sigma
return (2*np.pi)**-0.5*np.exp(-((a-s)/sigma)**2/2)
signal_max= 4
amp_max = signal_max*2
thetas = np.linspace(-np.pi,np.pi,500)
amplitudes = np.linspace(0,amp_max,500)
signals = np.linspace(0,signal_max,5)
sigma = 1
## figure 1
if True:
fig, ax = plt.subplots(1,2,figsize=(2*8,1*8))
_fig1, _ax0 =plt.subplots(1,1, figsize=(1*8, 1*8))
_fig2, _ax1 =plt.subplots(1,1, figsize=(1*8, 1*8))
ax0 = MethodProxy(ax[0], _ax0)
ax1 = MethodProxy(ax[1], _ax1)
for s in signals:
pdfs_label='s/$\sigma$ ='+str(s)
phase_vals= phase_distribution(thetas,sigma,s)
amp_vals= amplitude_distribution(amplitudes,sigma,s)
phase_vals_g = phase_distribution_gauss(thetas,sigma,s)
ax0.plot(amplitudes,amp_vals, label=pdfs_label)
ax1.plot(thetas,phase_vals, label=pdfs_label)
ax0.legend()
_ax1.legend()# only in the separate figure
ax0.set_xlabel(r'$a$')
ax0.set_xlabel(r'$\theta$')
ax1.set_ylabel(r'$p(a)$')
ax1.set_ylabel(r'$p(\theta)$')
# ax[0].grid()
# ax[1].grid()
MethodProxy(fig, _fig1, _fig2).tight_layout()
fig.savefig('pdfs.pdf')
_fig1.savefig('pdfs-amplitudes.pdf')
_fig2.savefig('pdfs-phases.pdf')
plt.close(_fig1)
plt.close(_fig2)
## figure 2
amplitudes = np.linspace(0,amp_max*5,500)
signals = np.linspace(0.1,signal_max*5,101)
if False:
fig2, ax2 = plt.subplots(2,2,figsize=(2*8,2*8))
ax2 = fig2.get_axes()
V_theta = [variance(thetas,phase_distribution(thetas,sigma,s)) for s in signals ]
E_theta=[expectation(thetas,phase_distribution(thetas,sigma,s)) for s in signals ]
V_theta_g = [variance(thetas,phase_distribution_gauss(thetas,sigma,s)) for s in signals ]
E_theta_g=[expectation(thetas,phase_distribution_gauss(thetas,sigma,s)) for s in signals ]
V_a = [variance(amplitudes,amplitude_distribution(amplitudes,sigma,s)) for s in signals ]
E_a=[expectation(amplitudes,amplitude_distribution(amplitudes,sigma,s)) for s in signals ]
V_a_g = [variance(amplitudes,amplitude_distribution_gauss(amplitudes,sigma,s)) for s in signals ]
E_a_g=[expectation(amplitudes,amplitude_distribution_gauss(amplitudes,sigma,s)) for s in signals ]
ax2[0].plot(signals,E_a,label='$p(a)$')
ax2[0].plot(signals,E_a_g,ls='dashed',label='Gaussian approx.')
ax2[0].set_xscale('log')
ax2[0].set_yscale('log')
ax2[0].set_ylabel('$\mu_a$')
ax2[1].plot(signals,V_a,label='$p(a)$')
ax2[1].plot(signals,V_a_g,ls='dashed',label='Gaussian approx.')
ax2[1].set_xscale('log')
ax2[1].set_ylabel('$\sigma_a^2$')
ax2[2].plot(signals,E_theta,label=r'$p(\theta)$')
ax2[2].plot(signals,E_theta_g,ls='dashed',label='Gaussian approx.')
ax2[2].set_xscale('log')
ax2[2].set_ylim(-1.1,1.1)
ax2[2].set_ylabel(r'$\mu_\theta$')
ax2[3].plot(signals,V_theta,label=r'$p(\theta)$')
ax2[3].plot(signals,V_theta_g,ls='dashed',label='Gaussian approx.')
ax2[3].set_xscale('log')
ax2[3].set_yscale('log')
ax2[3].set_ylabel(r'$\sigma_\theta^2$')
for a in ax2:
a.grid(which='both')
a.set_xlabel(r'$s/\sigma$')
a.legend()
fig2.tight_layout()
fig2.savefig('expectation_variance.pdf')
## figure 3, beacon timing accuracy
if True:
fig3, ax3 = plt.subplots(1,1,figsize=(1*8,1*8))
ax3 = fig3.get_axes()
sigma_t = [variance(thetas,phase_distribution(thetas,sigma,s)) for s in signals ]
lfs=np.linspace(np.log10(50.),4,1)
for lf in lfs:
freq = (10**lf)*1e6
sigma_t = np.asarray(sigma_t)**0.5/(2*np.pi*freq)
ax3[0].plot(signals,sigma_t/1e-9,'o-')
ax3[0].set_ylim(0,2.5)
ax3[0].set_xlabel(r'$s/\sigma$')
ax3[0].set_ylabel(r'$\Delta t$(ns)')
fig3.tight_layout()
fig3.savefig('timing_accuracy.pdf')
plt.show()