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%matplotlib inline
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
import numpy.linalg as la


    

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plt.rcParams['figure.figsize'] = (24.0, 16.0)


    

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gen = (2*n for n in range(10))


    

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for i in gen:
    print i


    

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def y_itr(x_itr):
    # Force first y to be 0, ignoring x[0]
    next(x_itr)
    yield 0
    prev_x = 0
    prev_y = 0
    for x in x_itr:
        y = x - prev_x/2.0 - 2*prev_y
        yield y
        prev_x = x
        prev_y = y


    

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x = [0 for i in range(51)]
x[0] = 1
x[1] = -.5
x_itr = (z for z in x)


    

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for y in y_itr(x_itr):
    print y


    

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def f(omega):
    return pow(np.cos(np.pi/4.0*omega),2.0)
omegas = np.arange(-6, 6, 0.1)
Y1s = f(omegas)
Y2s = f(omegas-1)
Ys  = Y1s + Y2s
plt.plot(omegas, f(omegas))
plt.plot(omegas, f(omegas-1))
plt.plot(omegas, Ys)
plt.ylabel('X(Omega) axis')
plt.xlabel('Omega axis')


    

    
Out[30]:





<matplotlib.text.Text at 0x10636fe10>






    

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f0=0
f1=10
t1=2
alpha=(f1-f0)/t1
def clamp(t,c):
    return [min(i,c) for i in t]
def chirp(t):
    # return np.cos(2*np.pi*f0*t + alpha*np.pi*t*t)
    return np.cos(alpha*np.pi*t*clamp(t,100))
ts = np.arange(0, 10, 1.0/50)
chirps = chirp(ts)
print alpha
plt.plot(ts,chirps)


    

    




5






    
Out[114]:





[<matplotlib.lines.Line2D at 0x10acb0810>]






    

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rands=sp.randn(10000)


    

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plt.hist(rands,100);


    

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def J(theta):
    return 2*pow(theta,4) + 2
x = (J(1.01)-J(.99))/.02


    

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x


    

    
Out[123]:





8.000800000000007

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