python实现简单的傅里叶变换
python实现简单的傅里叶变换傅里叶变换参考：傅里叶变换之掐死教程-前言-谷动谷力 (sunsili.com)傅里叶变换之掐死教程-傅里叶级数(Fourier Series)-谷动谷力 (sunsili.com)傅里叶变换之掐死教程-指数形式的傅里叶变换-谷动谷力 (sunsili.com)傅里叶变换之掐死教程-嘛叫频域 概念讲解-谷动谷力 (sunsili.com)傅里叶变换之掐死教程-宇宙耍帅第一公式：欧拉公式-谷动谷力 (sunsili.com)傅里叶变换之掐死教程-相位普-谷动谷力 (sunsili.com)
python实现实例实例1.
实例2.
实例3.
具体代码以第一个函数为例#!/usr/bin/env python
# -*- coding:utf-8 -*-
from pylab import *
import matplotlib.pyplot as plt
from sympy import * #用于求导积分等科学计算
from scipy.integrate import tplquad,dblquad,quad
#原函数f(x)={ exp(x),-pi≤x＜0
# 1， 0≤x＜pi}
ax1 = plt.subplot(2, 2, 1)
ax2 = plt.subplot(2, 2, 2)
ax3=plt.subplot(2, 2, 3)
ax4=plt.subplot(2, 2, 4)
#原函数
x_value=[]
y_value=[]
for i in np.arange(-pi, pi, 0.01):
if(i<0):
x_value.append(i)
y_value.append(i+pi)
else:
x_value.append(i)
y_value.append(pi-i)
plt.sca(ax1)
plt.plot(x_value,y_value,'orange',linewidth=0.6)
plt.title('original function')
a_value = []
b_value = []
from pylab import *
x = mgrid[-10:10:0.02]
def fourier_transform():
plt.sca(ax2)
m1, err1 = quad(lambda m: np.exp(m), -np.pi, 0)
m2,err2=quad(lambda m: 1, 0, np.pi)
a0 = 1 / pi * m1 + 1 / pi * m2
s=a0/2
for i in range(1,100,1):
mm1,errm1=quad(lambda m: np.exp(m)* np.cos(i * m), -np.pi, 0)
mm2,errm2=quad(lambda m: np.cos(i * m), 0, np.pi)
a=1 / pi * mm1 + 1 / pi * mm2
a_value.append(a)
nn1, errn1 = quad(lambda m: np.exp(m) * np.sin(i * m), -np.pi, 0)
nn2, errn2 = quad(lambda m: np.sin(i * m), 0, np.pi)
b = 1 / pi * nn1 + 1 / pi * nn2
b_value.append(b)
s0 = ( 1 / pi *a*cos(i*x) + 1 / pi *b* sin(i*x) )
s=s+s0
plot(x,s,'orange',linewidth=0.6)
title('fourier_transform')
fourier_transform()
plt.sca(ax3)
plot(np.arange(len(x_value)),x_value,'orange',linewidth=0.6)
title('X')
plt.sca(ax4)
plot(np.arange(len(y_value)),y_value,'orange',linewidth=0.6)
title('Y')
plt.show()
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