python实现傅里叶级数展开的实现

from pylab import *
x = mgrid[-10:10:0.02] # 这里类似于MATLAB用冒号产生步长为0.02的序列，但是语法和MATLAB不同
n = arange(1,1000)
def fourier_transform():
 a0 = (1-exp(-pi))/pi+1
 s=a0/2
 for i in range(1,100,1):
 s0 = ( (1-(-1)**i*exp(-pi))/(pi*(1+i**2))*cos(i*x)+1/pi*( (-i*(1-(-1)**i*exp(-pi)))/(1+i**2) + (1-(-1)**i)/i ) * sin(i*x) )
 s=s+s0
 plot(x,s,'orange',linewidth=0.6)
 title('fourier_transform')
 show() 

fourier_transform()

from pylab import *
def fourier1():
 s=pi/2

 for i in range(1,100,1):
 s0 = 2/pi*(1-(-1)**i)/i**2 * cos(i*x) 
 s=s+s0
 plot(x,s,'orange',linewidth=0.6)
 title('fourier1')
 show()
fourier1()