def prime_error_terms_in_dst():
n = 128
samples_per_unit =10
cheby_list, cheby_ave_list, range_list= cheby_fun_real(n, samples_per_unit)
plt.figure(1)
plot_one_list(cheby_list, n, range_list, 'cheby')
plot_one_list(range_list, n, range_list, 'x')
#plt.show()
plt.figure(2)
# differ from cheby vs x itself
# error = cheby - x
error_terms = np.asarray(cheby_list) - np.asarray(range_list)
plot_one_list(error_terms, n, range_list, 'error')
#plt.show()
# create a function
# f2(x) = f(x) when x >=0
# f2() = -f(-x) when x < 0
# dst of f(x) will be -1/2j(fft(f2))
error_term_ud = np.flipud(error_terms)
error_term_ud_neg = np.multiply(-1, error_term_ud )
error_term_extended = np.concatenate([error_term_ud_neg, error_terms])
range_list_extended = range(0, len(error_term_extended))
plt.figure(3)
plot_one_list(error_term_extended, n,range_list_extended, 'error')
plt.show()
# fft of error terms, we use real fft, instead of fft
error_terms_fft = np.fft.fft(error_term_extended)
error_terms_fft_real = error_terms_fft.real
error_terms_fft_imag = error_terms_fft.imag
error_terms_fft_abs = np.absolute(error_terms_fft)
error_terms_fft_abs = -1*error_terms_fft_abs
error_terms_fft_abs_len = len(error_terms_fft_abs)
print 'error_terms_fft_abs_len =', error_terms_fft_abs_len
range_list2 = range(0, error_terms_fft_abs_len )
range_list2_arr = np.asarray(range_list2)
step = 1/float(samples_per_unit)
range_list2_arr = np.multiply(step, range_list2_arr )
plt.figure(3)
# When we plot, we skip the DC term, because it can be quite larger.
# plot_one_list(error_terms_fft_abs, n, range_list2_arr, 'error fft')
plot_one_list(error_terms_fft_abs[1:], n, range_list2_arr[1:], 'error fft')
plt.show()
print error_terms
def prime_error_terms_in_fft():
n = 128
samples_per_unit = 100
cheby_list, cheby_ave_list, range_list= cheby_fun_real(n, samples_per_unit)
plt.figure(1)
plot_one_list(cheby_list, n, range_list, 'cheby')
plot_one_list(range_list, n, range_list, 'x')
#plt.show()
plt.figure(2)
# differ from cheby vs x itself
# error = cheby - x
error_terms = np.asarray(cheby_list) - np.asarray(range_list)
plot_one_list(error_terms, n, range_list, 'error')
#plt.show()
# fft of error terms, we use real fft, instead of fft
error_terms_fft = np.fft.rfft(error_terms)
error_terms_fft_abs = np.absolute(error_terms_fft)
error_terms_fft_abs = -1*error_terms_fft_abs
error_terms_fft_abs_len = len(error_terms_fft_abs)
print 'error_terms_fft_abs_len =', error_terms_fft_abs_len
print 'len(range_list)', len(range_list)
range_list2 = range(0, error_terms_fft_abs_len )
range_list2_arr = np.asarray(range_list2)
step = 1/float(samples_per_unit)
range_list2_arr = np.multiply(step, range_list2_arr )
plt.figure(3)
# plot_one_list(error_terms_fft_abs, n, range_list2_arr, 'error fft')
plot_one_list(error_terms_fft_abs[1:], n, range_list2_arr[1:], 'error fft')
plt.show()
print error_terms