#!/usr/bin/env python
# coding: utf-8

# https://github.com/htygithub/SandS

# In[23]:


get_ipython().run_line_magic('matplotlib', 'inline')
import numpy as np
import matplotlib.pyplot as plt
x=np.array([0.,0,0,2,4,6,4,2,0,0,0])
plt.stem(x)


# In[24]:


y=x*0
y[0]=1/3*(x[0]+x[1]+x[2])
y[1]=1/3*(x[1]+x[2]+x[3])


# In[25]:


for ii in range(5):
    print(ii)


# In[26]:


for ii in range(len(x)-2):
    y[ii]=1/3*(x[ii]+x[ii+1]+x[ii+2])
    print(y[ii])


# In[27]:


plt.stem(x,'r')
plt.stem(y,'g')


# In[35]:


get_ipython().run_line_magic('matplotlib', 'inline')
import numpy as np
import matplotlib.pyplot as plt
n=np.arange(100)
w_hat=2.5
x_n=np.exp(1.0j*w_hat*n)
x_n_1=np.exp(1j*w_hat*(n-1))
x_n_2=np.exp(1j*w_hat*(n-2))
y=(x_n+x_n_1+x_n_2)/3

plt.figure(figsize=(15,5), dpi=300)
plt.plot(np.real(x_n),'r*-')
plt.plot(np.real(x_n_1),'go-')
plt.plot(np.real(x_n_2),'b*-')

params = {'backend': 'ps',
          'xtick.labelsize': 24,
          'ytick.labelsize': 24,}
plt.rcParams.update(params)


# In[36]:


plt.figure(figsize=(15,5), dpi=300)
plt.plot(np.real(x_n_2),'r*-')
plt.plot(np.real(y),'b*-')
print("Amplitude: %f" % np.abs(y)[0])

params = {'backend': 'ps',
          'xtick.labelsize': 24,
          'ytick.labelsize': 24,}
plt.rcParams.update(params)


# In[38]:


ii=0

for w_hat in np.arange(-np.pi*4,np.pi*4,0.1):
    x_n=np.exp(1j*w_hat*n)
    x_n_1=np.exp(1j*w_hat*(n-1))
    x_n_2=np.exp(1j*w_hat*(n-2))
    y=(x_n*1/3+x_n_1*1/3+x_n_2*1/3)
    #y=(x_n-x_n_1)
    if ii==0:
        w_hat_all=np.array(w_hat)
        y_abs=np.array(np.abs(y)[0])
    else:
        w_hat_all=np.append(w_hat_all,w_hat)
        y_abs=np.append(y_abs,np.abs(y)[0])
 
    ii+=1
  
plt.plot(w_hat_all,y_abs)


# In[ ]: