合成波のFFT¶

下の例に従って，sin(i/13)とsin(i/2)の合成波を作成し，FFTをかけた後，周波数での強度を表示せよ．合成波(2sin(i2)+sin(i/2))との違いをのべよ．

In [10]:

%matplotlib inline
from scipy.fft import fft
import matplotlib.pyplot as plt
import numpy as np

def func(i):
    return np.sin(i/(13))+np.sin(i/(2))

i= np.linspace(0, 256, 256) #0から2πまでの範囲を100分割したnumpy配列 
plt.plot(i, np.sin(i/(13)), color = 'r', linewidth=0.8)
plt.plot(i, np.sin(i/(2)), color = 'b', linewidth=0.8)
plt.grid() 
plt.show()

In [11]:

plt.plot(i, func(i))

Out[11]:

[<matplotlib.lines.Line2D at 0x7fa612052070>]

In [12]:

yy = func(i)
out = fft(yy)

def spectrum_power(x):
    re, im = x.real, x.imag
    return np.sqrt(re**2+im**2)

plt.plot(i,spectrum_power(out))
plt.xlim(0,128)
plt.ylim(0, 250)
plt.show()

plt.plot(i,spectrum_power(out))
plt.xlim(0,128)
plt.yscale('log')
plt.show()

In [4]:

%matplotlib inline
from scipy.fft import fft
import matplotlib.pyplot as plt
import numpy as np

def func(i):
    return np.sin(i*2)*2+np.sin(i/(2))

i= np.linspace(0, 256, 256) #0から2πまでの範囲を100分割したnumpy配列 
plt.plot(i, np.sin(i/(13)), color = 'r', linewidth=0.8)
plt.plot(i, np.sin(i/(2)), color = 'b', linewidth=0.8)
plt.grid() 
plt.show()

In [5]:

plt.plot(i, func(i))

Out[5]:

[<matplotlib.lines.Line2D at 0x7fa6121a8790>]

In [8]:

yy = func(i)
out = fft(yy)

def spectrum_power(x):
    re, im = x.real, x.imag
    return np.sqrt(re**2+im**2)

plt.plot(i,spectrum_power(out))
plt.xlim(0,128)
plt.ylim(0, 250)
plt.show()

plt.plot(i,spectrum_power(out))
plt.xlim(0,128)
plt.yscale('log')
plt.show()

$\sin\left(\frac{i}{13}\right) + \sin\left(\frac{i}{2}\right)$ $\sin\left(2i\right)+\sin\left(\frac{i}{2}\right)$

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