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

# # A Gallery of SciPy's Window Functions

# ## This is mostly for quick visual reference and comparison between windows

# In[1]:


import matplotlib.pyplot as plt
import scipy.signal as sig
get_ipython().run_line_magic('matplotlib', 'inline')


# In[2]:


n_points = 1025


# ##1. Bartlett-Hann Window
# ## $ w(n) = a_{0} - a_{1} \left|\frac{n}{N - 1} - \frac{1}{2}\right| - \cos(\frac{2\pi n}{N - 1})$
# ## $a_{0} = 0.62, a_{1} = 0.48, a_{2} = 0.38$

# In[3]:


window = sig.barthann(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Bartlett-Hann')


# ##2. Bartlett Window
# ##$ w(n) = \frac{2}{M - 1}(\frac{M - 1}{2} - \left|n - \frac{M - 1}{2}\right|) $

# In[4]:


window = sig.bartlett(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Bartlett')


# ##3. Blackman Window
# ## $ w(n) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M) $

# In[5]:


window = sig.blackman(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Blackman')


# ##4. Blackman-Harris Window
# ##$ w(n) = a_{0} - a_{1}\cos(\frac{2\pi n}{N - 1}) + a_{2}\cos(\frac{4\pi n}{N - 1}) - a_{3}\cos(\frac{6\pi n}{N - 1}) $
# ##$ a_{0} = 0.38575, a_{1} = 0.48829, a_{2} = 0.14128, a_{3} = 0.01168 $

# In[6]:


window = sig.blackmanharris(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Blackman-Harris')


# ##5. Bohman Window
# ##$ w(n) = (1 - |x|)\cos(\pi|x|) + \frac{1}{\pi}\sin(\pi|x|) $
# ##$ x \in [-1, 1] $

# In[7]:


window = sig.bohman(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Bohman')


# ##6. Boxcar window
# (from the docs: included for correctness, equivalent to no window at all.)

# In[8]:


window = sig.boxcar(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Boxcar')


# ##7. Dolph-Chebyshev Window
# ##$ W(k) = \frac
# {\cos\{M \cos^{-1}[\beta \cos(\frac{\pi k}{M})]\}}
# {\cosh[M \cosh^{-1}(\beta)]} $
# ##$ \beta = \cosh \left [\frac{1}{M}
# \cosh^{-1}(10^\frac{A}{20}) \right ] $

# In[9]:


window = sig.chebwin(n_points, at=100)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Dolph-Chebyshev (attenutation 100 dB)')


# ##8. Cosine Window
# ##$ w(n) = \sin(\frac{\pi n}{N - 1}) $

# In[10]:


window = sig.cosine(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Cosine')


# ##9. Flat Top Window
# ##$ w(n) = \sum\limits_{k=0}^4 (-1)^{k} a_{k}\cos(\frac{2\pi kn}{N-1}) $
# ##$ a_{0} = 0.2156,  a_{1} = 0.4160,  a_{2} = 0.2781,  a_{3} = 0.0836,  a_{4} = 0.0069 $

# In[11]:


window = sig.flattop(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Flat Top')


# ##10. Gaussian Window
# ##$ w(n) = e^{ -\frac{1}{2}\left(\frac{n}{\sigma}\right)^2 } $

# In[12]:


window = sig.gaussian(n_points, std=130)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Gaussian ($\sigma$=130)')


# ##11. Generalized Gaussian
# ##$ w(n) = e^{ -\frac{1}{2}\left|\frac{n}{\sigma}\right|^{2p} } $

# In[13]:


window = sig.general_gaussian(n_points, sig=150, p=1.5)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Generalized Gaussian ($\sigma$=150, $p=1.5$)')


# ##12. Hamming Window
# ##$ w(n) = 0.54 - 0.46 \cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1 $

# In[14]:


window = sig.hamming(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Hamming')


# ##13. Hanning(Hann) Window
# ##$w(n) = 0.5 - 0.5 \cos\left(\frac{2\pi{n}}{M-1}\right)
# \qquad 0 \leq n \leq M-1$

# In[15]:


window = sig.hann(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Hann')


# ##14. Kaiser Window
# ##$ w(n) = I_0\left( \beta \sqrt{1-\frac{4n^2}{(M-1)^2}} \right)/I_0(\beta) $
# ##$ \quad -\frac{M-1}{2} \leq n \leq \frac{M-1}{2}, $
# ###where $ I_{0} $ is the modified 4th order Bessel Function

# In[16]:


window = sig.kaiser(n_points, beta=14)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Kaiser (beta=14)')


# ##15. Nuttall Window
# ##$ w(n) = \sum\limits_{k=0}^3 (-1)^{k} a_{k}\cos(\frac{2\pi kn}{N-1}) $
# ##$a_{0} = 0.3635819, a_{1} = 0.4891775, a_{2} = 0.1365995, a_{3} = 0.0106411$
# 

# In[17]:


window = sig.nuttall(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Nuttall')


# ##16. Parzen Window
# ### 4 - fold convolution of a rectangular window

# In[18]:


window = sig.parzen(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Parzen')


# ##17. Slepian (DPSS) Window

# In[19]:


window = sig.slepian(n_points, width=0.02)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('DPSS (width=0.002)')


# ##18. Triangular Window

# In[20]:


window = sig.triang(n_points)
plt.figure(figsize=(12, 8))
plt.plot(window)
plt.xlim([0, n_points])
plt.title('Triangular')


# #Overlay of all windows

# In[21]:


arg_map = {
'barthann': [sig.barthann, dict(M=n_points)],
'bartlett': [sig.bartlett, dict(M=n_points)],
'blackman': [sig.blackman, dict(M=n_points)],
'blackmanharris': [sig.blackmanharris, dict(M=n_points)],
'bohman': [sig.bohman, dict(M=n_points)],
'boxcar': [sig.boxcar, dict(M=n_points)],
'chebwin': [sig.chebwin, dict(M=n_points, at=100)],
'cosine': [sig.cosine, dict(M=n_points)],
'flattop': [sig.flattop, dict(M=n_points)],
'gaussian': [sig.gaussian, dict(M=n_points, std=130)],
'general_gaussian': [sig.general_gaussian, dict(M=n_points, sig=150, p=1.5)],
'hamming': [sig.hamming, dict(M=n_points)],
'hann': [sig.hann, dict(M=n_points)],
'kaiser': [sig.kaiser, dict(M=n_points, beta=14)],
'nuttall': [sig.nuttall, dict(M=n_points)],
'parzen': [sig.parzen, dict(M=n_points)],
'selpian': [sig.slepian, dict(M=n_points, width=0.02)],
'triang': [sig.triang, dict(M=n_points)]
}

plt.figure(figsize=(15, 15))
plt.xlim([0, n_points])
for name, calldata in arg_map.iteritems():
    function, args = calldata
    window = function(**args)
    plt.plot(window, label=name)
plt.legend()


# In[ ]: