# In[2]:

get_ipython().magic(u'pylab')


# Out[2]:

#     Using matplotlib backend: TkAgg
#     Populating the interactive namespace from numpy and matplotlib
# 

# In[3]:

import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
get_ipython().magic(u'matplotlib inline')


# In[4]:

# Graphing helper function
def setup_graph(title='', x_label='', y_label='', fig_size=None):
    fig = plt.figure()
    if fig_size != None:
        fig.set_size_inches(fig_size[0], fig_size[1])
    ax = fig.add_subplot(111)
    ax.set_title(title)
    ax.set_xlabel(x_label)
    ax.set_ylabel(y_label)


# Import audio file.

# In[8]:

from scipy.io import wavfile
rate1,data1= wavfile.read('beethoven.wav')
print 'rate1 =', rate1
print 'data1 =', data1
length = np.size(data1)
print 'length = ', length
# zero pad to power of 2
data2 = np.concatenate( (data1, 128*np.ones(2**18 - length))) - [128]
t1 = np.linspace(0, float(length)/float(rate1), 2**18)
_ = plt.plot(t1, data2)
# now write zero padded data file
wavfile.write('beethoven-pad.wav', rate1, (data2+[128]).astype(uint8))
# print 'data2:', (data2[0:8]+[128]).astype(uint8)
setup_graph(title='$x[n]$', x_label='$n$', y_label='$ real x[n]$', fig_size=(6,3))
_ = plt.plot(t1[30000:32000],data2[30000:32000].real)


# Out[8]:

#     rate1 = 22050
#     data1 = [127 128 128 ..., 128 128 128]
#     length =  216032
# 

# image file:

# image file:

# Now calculate FFT

# In[6]:

Y = np.fft.fft(data2)
n1 = np.linspace(0,2**18, 2**18)
setup_graph(title='$Y$', x_label='$k$', y_label='real Y[k]', fig_size=(6,3))
_ = plt.plot(n1,Y.real)
# print Y[0:4].real
setup_graph(title='$Y$', x_label='$k$', y_label='$|Y[k]|$', fig_size=(6,3))
_ = plt.plot(n1[0:50000],np.abs(Y[0:50000]))


# Out[6]:

# image file:

# image file:

# Now apply ``ideal'' low pass filter to Y[k] to obtain Z[k], and plot z[n].

# In[10]:

## your code here to calculate Z[k]
##
##
z = np.fft.ifft(Z)
setup_graph(title='$z[n]$', x_label='$n$', y_label='real z[n]', fig_size=(6,3))
_ = plt.plot(n1,z.real)
setup_graph(title='$z[n]$', x_label='$n$', y_label='$real z[n]$', fig_size=(6,3))
_ = plt.plot(n1[30000:32000],z[30000:32000].real)
setup_graph(title='$z[n]$', x_label='$n$', y_label='$imag z[n]$', fig_size=(6,3))
_ = plt.plot(n1[30000:32000],z[30000:32000].imag)
wavfile.write('beethoven-lpf.wav', rate1, (z.real +[128]).astype(uint8))


# Out[10]:


    ---------------------------------------------------------------------------
    NameError                                 Traceback (most recent call last)

    <ipython-input-10-847be59c18f7> in <module>()
          2 ##
          3 ##
    ----> 4 z = np.fft.ifft(Z)
          5 setup_graph(title='$z[n]$', x_label='$n$', y_label='real z[n]', fig_size=(6,3))
          6 _ = plt.plot(n1,z.real)


    NameError: name 'Z' is not defined


# In[ ]: