python实现方波，三角波的合成与分析

###最近matlab在一些军工学校已经被禁了，（据说哈工大已经不能用matlab了）最近学院的一些学术作业也都要转移到python平台来实现了，最近会更新一些原本用matlab做着很简单，到了python不知所措的小作业。供学习参考。

方波，三角波的合成与分析

程序结构

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fft变换

定义所需函数

合成方波

合成三角波

方波频谱

三角波频谱

自定义函数

#定义Harmonic synthesis(谐波合成)函数 Har_synth

#第一个参数为奇数谐波的最高次，第二个参数为信号时间的list

def Har_synth(i,x):

#定义Rect wave(方波生成)函数 Rec_wav

#第一个参数为方波时间对应的list，第二个参数为方波的幅度的list。

def Rec_wave(x,A):

#定义Triangle wave(三角波)函数 Trg_wave

#第一个参数为方波信号时间的list，第二个参数为方波对应时间的幅度的list

def Trg_wave(x,y):

#定义Frequece Amplitude函数 Fre_ampl

#第一个参数为信号时间的list，第二个参数为信号对应时间的幅度的list
#返回两个参数，第一个参数为frequecy的list(所得频率序列需除以总时长)，第二个参数为amplitude的list

def Fre_ampl(x,y):

主要进程

a.

利用多次谐波的相加接近方波，最后通过规律，得出较为理想的生成方波函数。

b.

通过上一步得到的方波，对其进行积分运算得出三角波

c.

定义合适的方波和三角波，通过对其fft变换，并单边化处理，归一化处理，得出所需要的频谱图。

附整体代码

import matplotlib.pyplot as plt
import math
import numpy as np
import scipy.integrate as si#定义Harmonic synthesis(谐波合成)函数 Har_synth
#第一个参数为奇数谐波的最高次，第二个参数为信号时间的list
def Har_synth(i,x):length=len(x)tmp=np.zeros(length)y0=list(tmp)result=y0number=(i+1)/2while number>0:cof=i+2-number*2y=[math.sin(xx*cof)/cof for xx in x]tmp+=np.array(y)number =number - 1result=list(tmp)return result##定义Rect wave函数 Rec_wav
#第一个参数为方波时间对应的list，第二个参数为方波的幅度。
def Rec_wave(x,A):y=np.zeros(len(x))for i in range(1,101,2):y+=4*A/np.pi*np.sin(2*np.pi*i*x)/ireturn y#定义Triangle wave(三角波)函数 Trg_wave
#第一个参数为方波信号时间的list，第二个参数为方波对应时间的幅度的list
def Trg_wave(x,y):length=len(x)tmp=np.zeros(length)y0=tmpresult=list(y0)i=0tmp[i]=0#对方波信号进行积分while i<length-1:i=i+1x_frag=x[0:i]y_frag=y[0:i]y0[i]=si.simps(y_frag,x_frag)result=list(y0)return result#定义Frequece Amplitude函数 Fre_ampl
#第一个参数为信号时间的list，第二个参数为信号对应时间的幅度的list
#返回两个参数，第一个参数为frequecy的list(所得频率序列需除以总时长)，第二个参数为amplitude的list
def Fre_ampl(x,y):y_f=np.fft.fft(y)f=np.arange(len(x))abs_y=np.abs(y_f)normalization_y=abs_y/(len(x)) half_x=f[range(int(len(x)/2))]normalization_y=normalization_y[range(int(len(x)/2))]return half_x,normalization_y#方波的合成：
fig=plt.figure(num=1,figsize=(6,4))
plt.axis([0,10,-1.2,1.2])
ax = plt.gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))
#a.只考虑从 t=0s 到 t=10s 这段时间内的信号
x = np.arange(0, 10, 0.01)
#b.画出基波分量 y(t)=sin(t)
y1=[math.sin(xx) for xx in x]
#c.将三次谐波加到基波之上，并画出结果，并显示
y2=[math.sin(3*xx)/3 for xx in x]
tmp2=np.array(y1)+np.array(y2)
y2=list(tmp2)
#d.再将一次，三次，五次，七次，九次谐波加在一次。
y3=Har_synth(9,x)
#e.合并从基波到十九次谐波的各奇次谐波分量
#f.将上述波形分别画在一幅画中
y4=Har_synth(19,x)
plt.plot(x,y1,label='question b',color='darkviolet')
plt.plot(x,y2,label='question c',color='c')
plt.plot(x,y3,label='question d',color='b')
plt.plot(x,y4,label='question e',color='r')
plt.xlabel('time / s')
plt.ylabel('amplitude')
plt.legend(loc='upper right')#三角波的合成
fig1=plt.figure(num=2,figsize=(6,4))
x = np.arange(0, 10, 0.01)
y5=Har_synth(10001,x)
y5=Trg_wave(x,y5)
plt.axis([0,10,0,math.pi])
plt.plot(x,y5,color='c')
plt.xlabel('time / s')
plt.ylabel('amplitude')#定义方波，观察其频谱
yr=Rec_wave(x,3)
plt.figure(num=3,figsize=(6,4))
plt.axis([0,100,0,2])
ax = plt.gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))freq,ampl=Fre_ampl(x,yr)
plt.vlines(freq/10,0,ampl)
plt.xlabel('frequence/Hz')
plt.ylabel('amplitude/V')#定义三角波，观察其频谱
yt=Trg_wave(x,yr)
plt.figure(num=4,figsize=(6,4))
plt.axis([0,100,0,0.3])
ax = plt.gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(('data', 0))freq,ampl=Fre_ampl(x,yt)
plt.vlines(freq/10,0,ampl)
plt.xlabel('frequence/Hz')
plt.ylabel('amplitude/V')plt.show()