forked from fukuroder/daubechies_wavelet_coefficients
/
test.py
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test.py
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# -*- coding: utf-8 -*-
import sympy
import sympy.mpmath as sm
import scipy.signal
import matplotlib.pyplot as plt
# precition
sm.mp.prec = 256
def daubechis(N):
# make polynomial
q_y = [sm.binomial(N-1+k,k) for k in reversed(range(N))]
# get polynomial roots y[k]
y = sm.mp.polyroots(q_y, maxsteps=200, extraprec=64)
z = []
for yk in y:
# subustitute y = -1/4z + 1/2 - 1/4/z to factor f(y) = y - y[k]
f = [sm.mpf('-1/4'), sm.mpf('1/2') - yk, sm.mpf('-1/4')]
# get polynomial roots z[k]
z += sm.mp.polyroots(f)
# make polynomial using the roots within unit circle
h0z = sm.sqrt('2')
for zk in z:
if sm.fabs(zk) < 1:
h0z *= sympy.sympify('(z-zk)/(1-zk)').subs('zk',zk)
# adapt vanising moments
hz = (sympy.sympify('(1+z)/2')**N*h0z).expand()
# get scaling coefficients
return [sympy.re(hz.coeff('z',k)) for k in reversed(range(N*2))]
def main():
for N in range(2,100):
# get dbN coeffients
dbN = daubechis(N)
# write coeffients
f = open('db' + str(N).zfill(2) +'_coefficients.txt', 'w')
f.write('# db' + str(N) + ' scaling coefficients\n')
for i, h in enumerate(dbN):
f.write('h['+ str(i) + ']='+ sm.nstr(h,40) + '\n')
f.close()
# get an approximation of scaling function
x, phi, psi = scipy.signal.cascade(dbN)
# plot scaling function
plt.plot(x, phi, 'k')
plt.grid()
plt.title('db' + str(N) + ' scaling function')
plt.savefig('db' + str(N).zfill(2) + '_scaling' + '.png')
plt.clf()
# plot wavelet
plt.plot(x, psi, 'k')
plt.grid()
plt.title( 'db' + str(N) + " wavelet" )
plt.savefig('db' + str(N).zfill(2) + '_wavelet' + '.png')
plt.clf()
if __name__ == '__main__':
main()