def problem_1():
f = sy.symbols('f')
symbol = wv.battle_lemarie_symbol()
# plot symbol
symbol_lambda = sy.lambdify(f, symbol, 'numpy') # lambdify for plotting
freq = np.linspace(-0.5, 0.5)
plt.figure()
plt.title('B-L Symbol')
plt.xlabel('frequency')
plt.plot(freq, [np.abs(symbol_lambda(v)) for v in freq])
plt.show()
def problem_2():
f = sy.symbols('f')
symbol = wv.battle_lemarie_symbol()
symbol_lambda = sy.lambdify(f, symbol)
exp = lambda f: np.sqrt(2)*symbol_lambda(f)
n_coef = 23
dc, hp, hn = f_coef(exp=exp, period=1, n=n_coef)
print 'dc:'
print np.real(dc)
print 'hp:'
for v in hp:
print np.real(v)
print 'hn:'
for v in hn:
print np.real(v)