import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

f = np.ones(101)
g = np.ones(101)/10
#y = np.linspace(1001)
for i in xrange(len(f)):
    if i > 11:
        f[i] = 0
        g[i] = 0

plt.subplot(131)
plt.plot(f)
plt.subplot(132)
plt.plot(g)
plt.subplot(133)
plt.plot(f+g)

plt.subplot(131)
plt.plot(np.fft.fft(f))
plt.subplot(132)
plt.plot(np.fft.fft(g))
plt.subplot(133)
plt.plot(np.fft.fft(f+g))

f = np.ones(101)
g = np.ones(101)
#y = np.linspace(1001)
for i in xrange(len(f)):
    if i > 11:
        f[i] = 0
    if i > 21:
        g[i] = 0

plt.subplot(141)
plt.plot(f)
plt.subplot(142)
plt.plot(g)
plt.subplot(143)
plt.plot(np.fft.fftshift(np.fft.fft(f)))
plt.subplot(144)
plt.plot(np.fft.fftshift(np.fft.fft(g)))

st = np.zeros(101) # saw tooth function
for i in xrange(len(st)):
    st[i] = i%9

tr = np.zeros(101) # triangular function
for i in xrange(len(tr)):
    if i%20 < 10:
        tr[i] = i%10
    if i%20 > 9:
        tr[i] = 10-i%10

plt.subplot(121)
plt.plot(st)
plt.subplot(122)
plt.plot(tr)

plt.subplot(121)
plt.plot(np.fft.fftshift(np.fft.fft(st)))
plt.subplot(122)
plt.plot(np.fft.fftshift(np.fft.fft(tr)))

x = np.linspace(-5,5,501)
a = 0
b = 1
plt.subplot(121)
plt.plot(np.exp(-(x-a)**2/(2*b**2)))
plt.subplot(122)
plt.plot(np.fft.fftshift(np.fft.fft(np.exp(-(x-a)**2/(2*b**2)))))
plt.xlim([240,260])

from ipywidgets import StaticInteract, RangeWidget, RadioWidget

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

#var = 1

def plot(var):
    fig, ax = plt.subplots(figsize=(4, 3),subplot_kw={'axisbg':'#EEEEEE','axisbelow':True})
    ax.grid(color='w', linewidth=2, linestyle='solid')
    #ax.legend(loc='upper right')
    x = np.linspace(-2, 2, 201)
    y = (1./(var*(2*np.pi)**(1./2)))*np.exp(-x**2/(2*var**2))
    ax.plot(x, y, lw=5, alpha=0.4,label=var)
    return fig

StaticInteract(plot,var=RangeWidget(0.01, 0.1, 0.01))

from ipywidgets import StaticInteract, RangeWidget, RadioWidget

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

#var = 1

def plot(var):
    fig, ax = plt.subplots(figsize=(4, 3),subplot_kw={'axisbg':'#EEEEEE','axisbelow':True})
    ax.grid(color='w', linewidth=2, linestyle='solid')
    #ax.legend(loc='upper right')
    x = np.linspace(-2, 2, 201)
    y = np.fft.fftshift(np.fft.fft((1./(var*(2*np.pi)**(1./2)))*np.exp(-x**2/(2*var**2))))
    ax.plot(y, lw=5, alpha=0.4,label=var)
    #ax.set_xlim(150,200)
    return fig

StaticInteract(plot,var=RangeWidget(0.01, 0.1, 0.01))