def FS_Zolotarev(N, R, x_min, x_max, x_num, plot_far=False, dB_limit=-40):
"""Function to evaluate Fourier series coefficients of Chebyshev far-field
pattern"""
if (N % 2 == 0):
print("Order needs to be an ODD number for null patterns")
else:
m_start = -N # make this (2*P+1) ... and take fourier for only half period
m_stop = N
m = zl.z_m_frm_R(N, R, a=0.1, b=0.9999999999999)
m = str(m)
N = str(N)
fun_str_re = 'zl.z_Zolotarev(' + N + ',' + 'np.sin(x)' + ',' + m + ')'
m_index, zm = FS(fun_str_re,
m_start=m_start,
m_stop=m_stop,
err_lim=1e-5)
if (plot_far):
x, AF = IFS(zm, 2 * np.pi, m_start, m_stop, x_min, x_max, x_num)
AF = 20 * np.log10(abs(AF))
AF = pl.cutoff(AF, dB_limit)
plt.plot(x * (180 / np.pi), AF)
plt.axis('tight')
plt.grid(True)
plt.title('Far-field Pattern')
plt.xlabel(r'$\phi$')
plt.ylabel('AF')
plt.show()
return m_index, zm
def FS_Zolotarev(N, R, x_min, x_max, x_num, plot_far=False, dB_limit= -40):
"""Function to evaluate Fourier series coefficients of Chebyshev far-field
pattern"""
if(N % 2 == 0):
print "Order needs to be an ODD number for null patterns"
else:
m_start = -N # make this (2*P+1) ... and take fourier for only half period
m_stop = N
m = zl.z_m_frm_R(N, R, a=0.1, b=0.9999999999999)
m = str(m)
N = str(N)
fun_str_re = 'zl.z_Zolotarev(' + N + ',' + 'np.sin(x)' + ',' + m +')'
m_index, zm = FS(fun_str_re, m_start=m_start, m_stop=m_stop, err_lim=1e-5)
if(plot_far):
x, AF = IFS(zm, 2 * np.pi, m_start, m_stop, x_min, x_max, x_num)
AF = 20 * np.log10(abs(AF))
AF = pl.cutoff(AF, dB_limit)
plt.plot(x * (180 / np.pi), AF); plt.axis('tight'); plt.grid(True)
plt.title('Far-field Pattern')
plt.xlabel(r'$\phi$')
plt.ylabel('AF')
plt.show()
return m_index, zm
def FS_Chebyshev(N, R, x_min, x_max, x_num, plot_far=False, dB_limit= -40):
"""Function to evaluate Fourier series coefficients of Chebyshev far-field
pattern"""
c = np.cosh(np.arccosh(R) / (N))
c = str(c)
if(N % 2 == 0):
m_start = int(-N / 2)
m_stop = int(N / 2)
N = str(N)
fun_str_re = 'special.eval_chebyt(' + N + ',' + c + '*np.cos(x/2))'
m_index, zm = FS(fun_str_re, m_start=m_start, m_stop=m_stop, err_lim=1e-5)
else:
m_start = -N # make this (2*P+1) ... and take fourier for only half period
m_stop = N
N = str(N)
fun_str_re = 'special.eval_chebyt(' + N + ',' + c + '*np.cos(x))'
m_index, zm = FS(fun_str_re, m_start=m_start, m_stop=m_stop, err_lim=1e-5)
if(plot_far):
x, AF = IFS(zm, 2 * np.pi, m_start, m_stop, x_min, x_max, x_num)
AF = 20 * np.log10(abs(AF))
AF = pl.cutoff(AF, dB_limit)
plt.plot(x * (180 / np.pi), AF); plt.axis('tight'); plt.grid(True)
plt.title('Far-field Pattern')
plt.xlabel(r'$\phi$')
plt.ylabel('AF')
plt.show()
return m_index, zm
def FS_Bayliss(N, R, mbar, alpha_x, x_min, x_max, x_num, plot_far=False, dB_limit= -40):
"""Function to evaluate Fourier series coefficients of Chebyshev far-field
pattern"""
R = str(R)
mbar = str(mbar)
alpha_x = str(alpha_x)
if(N % 2 == 0):
print "Order needs to be an ODD number for null patterns"
else:
m_start = -N
m_stop = N
N = str(N)
fun_str_re = 'eval_Bayliss(' + N + ',' + R + ',' + mbar + ',' + alpha_x + ',' + 'x' +')'
print fun_str_re
m_index, zm = FS(fun_str_re, m_start=m_start, m_stop=m_stop, err_lim=1e-5)
if(plot_far):
x, AF = IFS(zm, 2 * np.pi, m_start, m_stop, x_min, x_max, x_num)
AF = 20 * np.log10(abs(AF))
AF = pl.cutoff(AF, dB_limit)
plt.plot(x * (180 / np.pi), AF); plt.axis('tight'); plt.grid(True)
plt.title('Far-field Pattern')
plt.xlabel(r'$\phi$')
plt.ylabel('AF')
plt.show()
return m_index, zm
def FS_Taylor(N,
R,
mbar,
alpha_x,
x_min,
x_max,
x_num,
plot_far=False,
dB_limit=-40):
"""Function to evaluate Fourier series coefficients of Chebyshev far-field
pattern"""
R = str(R)
mbar = str(mbar)
alpha_x = str(alpha_x)
if (N % 2 == 0):
m_start = int(-N / 2)
m_stop = int(N / 2)
N = str(N)
fun_str_re = 'eval_Taylor(' + N + ',' + R + ',' + mbar + ',' + alpha_x + ',' + 'x' + ')'
print(fun_str_re)
m_index, zm = FS(fun_str_re,
m_start=m_start,
m_stop=m_stop,
err_lim=1e-5)
else:
m_start = -N
m_stop = N
N = str(N)
fun_str_re = 'eval_Taylor(' + N + ',' + R + ',' + mbar + ',' + alpha_x + ',' + 'x' + ')'
print(fun_str_re)
m_index, zm = FS(fun_str_re,
m_start=m_start,
m_stop=m_stop,
err_lim=1e-5)
if (plot_far):
x, AF = IFS(zm, 2 * np.pi, m_start, m_stop, x_min, x_max, x_num)
AF = 20 * np.log10(abs(AF))
AF = pl.cutoff(AF, dB_limit)
plt.plot(x * (180 / np.pi), AF)
plt.axis('tight')
plt.grid(True)
plt.title('Far-field Pattern')
plt.xlabel(r'$\phi$')
plt.ylabel('AF')
plt.show()
return m_index, zm
def FS_Chebyshev(N, R, x_min, x_max, x_num, plot_far=False, dB_limit=-40):
"""Function to evaluate Fourier series coefficients of Chebyshev far-field
pattern"""
c = np.cosh(np.arccosh(R) / (N))
c = str(c)
if (N % 2 == 0):
m_start = int(-N / 2)
m_stop = int(N / 2)
N = str(N)
fun_str_re = 'special.eval_chebyt(' + N + ',' + c + '*np.cos(x/2))'
m_index, zm = FS(fun_str_re,
m_start=m_start,
m_stop=m_stop,
err_lim=1e-5)
else:
m_start = -N # make this (2*P+1) ... and take fourier for only half period
m_stop = N
N = str(N)
fun_str_re = 'special.eval_chebyt(' + N + ',' + c + '*np.cos(x))'
m_index, zm = FS(fun_str_re,
m_start=m_start,
m_stop=m_stop,
err_lim=1e-5)
if (plot_far):
x, AF = IFS(zm, 2 * np.pi, m_start, m_stop, x_min, x_max, x_num)
AF = 20 * np.log10(abs(AF))
AF = pl.cutoff(AF, dB_limit)
plt.plot(x * (180 / np.pi), AF)
plt.axis('tight')
plt.grid(True)
plt.title('Far-field Pattern')
plt.xlabel(r'$\phi$')
plt.ylabel('AF')
plt.show()
return m_index, zm