course

from pylab import *
import pywt as pw
from numpy import *

SCALE = 3
N = 2 ** SCALE

def f1(x):
    return np.sin(2 * x)

def f2(x):
    return np.sin(x ** 2)

def f3():
    return np.sin(2 * np.pi * (2 ** np.linspace(2, 10, 1024)) * np.arange(1024) / 48000) + np.random.normal(0, 1, 1024) * 0.15

def check_level(level):
    max_level = int(np.log2(N))
    if level is None:
        return max_level
    elif level < 0:
        raise ValueError("Level value of %d is too low. Minimum level is 0 ." % level)
    elif level > max_level:
        print(("Level value of {0} is too high. The maximum level value of {1} will be used.").format(level, max_level))
        return max_level
    return level

def dwt(data):
    size = len(data) // 2
    cA = np.zeros(size)
    cD = np.zeros(size)

    for i, j in zip(range(0, len(data), 2), range(size)):
        c = 2 * (data[i] + data[i + 1]) / np.sqrt(N)
        cA[j] = c

    for i, j in zip(range(0, len(data), 2), range(size)):
        c = 2 * (data[i] - data[i + 1]) / np.sqrt(N)
        cD[j] = c

    return cA, cD

def wavedec (data, level = None):
    coeffs_list = []

    level = check_level(level)
    if level == 0:
        return[np.array(data)]
    a = data

    for i in range(level):
        a, d = dwt(a)
        coeffs_list.append(d)

    coeffs_list.append(a)
    coeffs_list.reverse()

    return coeffs_list

def idwt(a, d):
    res = []
    for i in range(len(a)):
        x = (a[i] + d[i]) * np.sqrt(N) / 4
        y = (a[i] - d[i]) * np.sqrt(N) / 4
        res.extend([x, y])
    return np.array(res)

def waverec(coeffs):
    if len(coeffs) < 1:
        raise ValueError("Coefficient list too short (minimum 1 arrays required).")
    elif len(coeffs) == 1:

        return coeffs[0]

    a, ds = coeffs[0], coeffs[1:]

    for d in ds:
        a = idwt(a, d)
    return a

x = linspace(0, 8, num = 1024)
chirp_signal = np.sin(2 * np.pi * (2 ** np.linspace(2, 10, 1024)) * np.arange(1024) / 48000) + np.random.normal(0, 1, 1024) * 0.15
fig, ax = subplots(figsize=(6, 1))
ax.set_title("Исходный сигнал")
ax.plot(chirp_signal)
show()
x = linspace(0, 50, num = 1024)
y = np.sin(2 * np.pi * (2 ** np.linspace(2, 10, 1024)) * np.arange(1024) / 48000) + np.random.normal(0, 1, 1024) * 0.15
st='sym5'
(cA, cD) = pywt.dwt(y,st)
subplot(2, 1, 1)
plot(cA,'b',linewidth=2, label='cA,level-1')
title("Коэффициенты аппроксимации")
legend(loc='best')
grid()
subplot(2, 1, 2)
plot(cD,'r',linewidth=2, label='cD,level-1')
title("Коэффициенты детализации")
grid()
legend(loc='best')
show()

(cA, cD) = pywt.dwt(cA,st)
subplot(2, 1, 1)
plot(cA,'b',linewidth=2, label='cA,level-2')
title("Коэффициенты аппроксимации")
legend(loc='best')
grid()

subplot(2, 1, 2)
plot(cD,'r',linewidth=2, label='cD,level-2')
title("Коэффициенты детализации")
grid()
legend(loc='best')
show()

(cA, cD) = pywt.dwt(cA,st)
subplot(2, 1, 1)
plot(cA,'b',linewidth=2, label='cA,level-3')
title("Коэффициенты аппроксимации")
legend(loc='best')
grid()

subplot(2, 1, 2)
plot(cD,'r',linewidth=2, label='cD,level-3')
title("Коэффициенты детализации")
grid()
legend(loc='best')
show()

(cA, cD) = pywt.dwt(cA,st)
subplot(2, 1, 1)
plot(cA,'b',linewidth=2, label='cA,level-4')
title("Коэффициенты аппроксимации")
legend(loc='best')
grid()

subplot(2, 1, 2)
plot(cD,'r',linewidth=2, label='cD,level-4')
title("Коэффициенты детализации")
grid()
legend(loc='best')
show()

signal = [1, 2, 3, 4, 5, 6, 7, 8]
print('Signal: ', signal)
(cA, cD) = pywt.dwt(signal, 'db1')
print('Coefficients in wavelet transform:', '\ncA: ', cA, '\nCd: ', cD)
signal_restored = pywt.idwt(cA, cD, 'db1')
print('Signal restored: ',signal_restored)