深入浅出通信原理Python代码版

深入浅出通信原理（

傅里叶变换与反变换

Fourier Transform:

\[ X(f) = \int_{-\infty}^{+\infty}x(t)e^{-j2\pi ft}dt \\ X(\omega)= \int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt \]

Fourier inverse Transform:

\[ x(t)=\int_{-\infty}^{+\infty}X(f)e^{j2\pi ft}df \]

傅里叶变换性质

时域	频域
\(x(t)\)	\(X(\omega)\)
\(x(t)e^{j\omega_0t}\)	\(X(\omega-\omega_0)\)
\(x(t)e^{-j\omega_0t}\)	\(X(\omega+\omega_0)\)

信号x(t)在时域乘上\(e^{j\omega_0t}\), 相当于频谱X(w)右移\(\omega_0\);信号在时域乘上\(e^{-j\omega_0t}\), 相当于频谱左移\(\omega_0\);

信号x(t)调制载波\(cos\omega_0t\), 相当于频谱X(w)一分为二并分别左移右移\(w_0\)

# coswt频谱搬移作用x = np.arange(-np.pi/2,np.pi/2,0.01)y = np.cos(x)plt.plot(x,y,':')# y1 = np.cos(x-np.pi)/2plt.plot(x-3*np.pi,y/2,color='b')plt.plot(x+3*np.pi,y/2,color='b')plt.xticks([-3*np.pi,0,3*np.pi],['$-\omega_0$','0','$-omega_0$'])plt.yticks([1],['$X(\omega)$'])plt.show()

coswt频谱搬移作用

# 矩形脉冲调制余弦载波# 矩形脉冲# x = np.arange(-1.5,1.5,0.1)# y = [0 for x in x if x <= -0.5]# y.extend([1 for x in x  if x>-0.5 and x<=0.5])# y.extend([0 for x in x  if x>0.5])# plt.plot(x,y)plt.subplot(3,2,1)x = [-1.5,-0.5,0.5,1.5]y = [0,1,0,0]plt.plot(x,y,drawstyle='steps-post')# cos(2\pi*5t),5Hzplt.subplot(3,2,3)x = np.arange(-1.5,1.6,0.1)y = np.cos(2*np.pi*5*x)plt.plot(x,y)# time zone modulationplt.subplot(3,2,5)y = [0 for x in x if x <= -0.4]y.extend([ np.cos(2*np.pi*5*x) for x in x  if x>=-0.5 and x<=0.6])y.extend([0 for x in x  if x>=0.5])x = np.sort(np.append(x,[0.5,-0.5]))plt.plot(x,y)plt.plot()# 矩形脉冲 Spectrumplt.subplot(3,2,2)f = np.arange(-4,4,0.1)y = np.sinc(f)plt.plot(f,y)# cos wave spectrumplt.subplot(3,2,4)f = [-5,5]y = [0.5,0.5]plt.stem(f,y)# modulation Spectrumplt.subplot(3,2,6)f = np.arange(-10,10,0.1)X = 0.5*np.sinc(f-5)+0.5*np.sinc(f+5)plt.plot(f,X)plt.tight_layout()plt.show()

矩形脉冲调制余弦载波

无论信号经过多少处理，最终都会被转换成一连串脉冲（如矩形脉冲），再调制到载波发射出去

正脉冲与负脉冲的幅度谱和相位谱

# 正脉冲与负脉冲的幅度谱和相位谱f = np.arange(-4,4,0.1)plt.subplot(3,2,1)X = abs(np.sinc(f))plt.plot(f,X)plt.title('postive pulse magnitude')plt.subplot(3,2,3)f = np.arange(-4,5,1)P = [np.pi,0,np.pi,0,0,-np.pi,0,-np.pi,0]plt.plot(f,P,drawstyle='steps-post')plt.title('postive pulse phase')f = np.arange(-4,4,0.1)plt.subplot(3,2,2)X = abs(-np.sinc(f))plt.plot(f,X)plt.title('negative pulse magnitude')plt.subplot(3,2,4)f = np.arange(-4,5,1)P = [0,np.pi,0,np.pi,-np.pi,0,-np.pi,0,-np.pi]plt.plot(f,P,drawstyle='steps-post')plt.title('negative pulse phase')plt.subplot(3,2,5)x = np.arange(-1.5,2,0.5)y=[0,0,0,1,1,0,0]plt.plot(x,y,drawstyle='steps-pre')plt.subplot(3,2,6)y=[-1*t for t in y]plt.plot(x,y,drawstyle='steps-pre')plt.tight_layout()plt.show()

正脉冲与负脉冲的幅度谱和相位谱

# 连载84：采用对数坐标的矩形脉冲频谱plt.subplot(2,1,1)x = np.arange(-1.5,2,0.5)y=[0,0,0,1,1,0,0]plt.plot(x,y,drawstyle='steps-pre')plt.subplot(2,1,2)f=np.arange(-4,4.1,0.1)X=abs(np.sinc(f))plt.semilogy(f,X)# plt.set_yscale('log')plt.ylim([1.1*10**-6,1.1])# plt.yticks([1.1,1.1*10**-2,1.1*10**-4,1.1*10**-6],['0','-20','-40','-60'])# plt.ylabel('Aplitude(dB)')

采用对数坐标的矩形脉冲频谱

BPSK调制解调频谱

# BPSK调制频谱# input signalplt.subplot(3,1,1)t = np.arange(0,9,1)d = [0,1,1,0,1,1,0,0,0]plt.plot(t,d,drawstyle='steps-post')plt.ylim([-0.5,1.5])plt.annotate('0',xy=(0.5,1.2))plt.text(1.5,1.2,'1',fontdict={'size':'8'})# plt.annotate(['1','0'],xy=[(2.5,1.2),(3.5,1.2)]) #无法同时进行标注# 基带调制信号(映射+基带调制)plt.subplot(3,1,2)t = np.arange(0,9,1)d = [1,-1,-1,1,-1,-1,1,1,1]plt.plot(t,d,drawstyle='steps-post')plt.ylim([-1.5,1.8])plt.annotate('1',xy=(0.5,1.2))plt.annotate('-1',xy=(1.5,1.2))# 频带调制信号(5Hz Cosine Wave)plt.subplot(3,1,3)t = np.arange(0,8.1,0.01)y = [np.cos(2*np.pi*5*t) for t in t if t<1.1]y.extend([np.cos(2*np.pi*5*t+np.pi) for t in t if 1.1<=t<3.1])y.extend([np.cos(2*np.pi*5*t) for t in t if 3.1<=t<4.1])y.extend([np.cos(2*np.pi*5*t+np.pi) for t in t if 4.1<=t<6.1])y.extend([np.cos(2*np.pi*5*t) for t in t if 6.1<=t<8.1])plt.plot(t,y)plt.ylim([-1.8,1.8])plt.annotate('0',xy=(0.5,1.2))plt.annotate('$\pi$',xy=(1.5,1.2))plt.tight_layout()

输入,BPSK调制,频带调制

# 连载91 BPSK解调频域分析# 时域采用cosine wave调制，便采用cosine wave解调，频域处理直观来看将频谱搬回原点便可采用低通滤波解调，时域处理直观来看在一个码元周期积分便可# BPSK调制频谱imgnum = 6plt.figure(figsize=(5,10))# input signalplt.subplot(imgnum,1,1)t = np.arange(0,9,1)d = [0,1,1,0,1,1,0,0,0]plt.plot(t,d,drawstyle='steps-post')plt.ylim([-0.5,1.5])plt.annotate('0',xy=(0.5,1.2))plt.text(1.5,1.2,'1',fontdict={'size':'8'})# plt.annotate(['1','0'],xy=[(2.5,1.2),(3.5,1.2)]) #无法同时进行标注plt.title('input')# 基带调制信号(映射+基带调制)plt.subplot(imgnum,1,2)t = np.arange(0,9,1)d = [1,-1,-1,1,-1,-1,1,1,1]plt.plot(t,d,drawstyle='steps-post')plt.ylim([-1.5,1.8])plt.annotate('1',xy=(0.5,1.2))plt.annotate('-1',xy=(1.5,1.2))plt.title('BPSK Base Band Modulation')# 频带调制信号(5Hz Cosine Wave)plt.subplot(imgnum,1,3)t = np.arange(0,8.1,0.01)y = [np.cos(2*np.pi*5*t) for t in t if t<1.1]y.extend([np.cos(2*np.pi*5*t+np.pi) for t in t if 1.1<=t<3.1])y.extend([np.cos(2*np.pi*5*t) for t in t if 3.1<=t<4.1])y.extend([np.cos(2*np.pi*5*t+np.pi) for t in t if 4.1<=t<6.1])y.extend([np.cos(2*np.pi*5*t) for t in t if 6.1<=t<8.1])plt.plot(t,y)plt.ylim([-1.8,1.8])plt.annotate('0',xy=(0.5,1.2))plt.annotate('$\pi$',xy=(1.5,1.2))plt.title('BPSK Frequency Band Modulation')# 频带解调信号，乘上cos(2*np.pi*5*t)plt.subplot(imgnum,1,4)t = np.arange(0,8.1,0.01)y = y*np.cos(2*np.pi*5*t)plt.plot(t,y)plt.ylim([-1.8,1.8])plt.title('BPSK Frequency Band Demodulation')# 积分plt.subplot(imgnum,1,5)y = [1,-1,-1,1,-1,-1,1,1,1]plt.plot(y,drawstyle='steps-post')plt.axhline(color='black')plt.title('Intergration')# 会付出输入信号plt.subplot(imgnum,1,6)x = np.arange(1,9,1)y = [1,-1,-1,1,-1,-1,1,1]plt.stem(x,y,use_line_collection=True)plt.xlim(0,8.2)plt.ylim(-1.5,1.5)plt.axhline(color='b')plt.title('Recover Bits')plt.tight_layout()

BPSK调制解调全过程

连载93 BPSK解调

法1（时域）：接收信号乘上\(\cos\omega_0t\)再对码元周期内进行积分便可会付出传输信号x(t)

法2 (频域) ：接收信号乘上\(\cos\omega_0t\)再进行傅里叶变换（进入频域）得到频谱后进行低通滤波滤除高频分类后再进行傅里叶逆变换（回到时域）恢复出传输信号x(t)

DSP使得快速傅里叶变得应用广泛，使得频域处理简单

连载86 正负矩形脉冲调制正余弦载波

# 连载86 三维频谱：包含幅度和相位信息f = np.arange(1,9.01,0.01)x = 0.5*np.sinc(f-5)fig = plt.figure()# ax = fig.gca(projection='3d')ax = fig.add_subplot(1,2,1,projection='3d')ax.plot(f,x,0*x,label='positive side',color='r')f = np.arange(-9.01,-1,0.01)x = 0.5*np.sinc(f+5)ax.plot(f,x,0*x,label='negative side',color='r')# ax.legend()ax.set_title('正矩形脉冲调制余弦载波', fontproperties='stsong')# fig = plt.figure()ax2 = fig.add_subplot(1,2,2,projection='3d')f2 = np.arange(-9.01,-1,0.01)x2 = -0.5*np.sinc(f2+5)ax2.plot(f2,x2,0*x2,label='positive side',color='r')f2 = np.arange(1,9.01,0.01)x2 = -0.5*np.sinc(f2-5)ax2.plot(f2,x2,0*x2,label='negative side',color='r')# ax2.set_title('$\\tau$=1 negative Square wave to modulate the cosine wave spectrum')ax2.set_title('负矩形脉冲调制余弦载波', fontproperties='stsong')plt.tight_layout()

正负矩形脉冲调制余弦载波

# 连载88f = np.arange(1,9.01,0.01)x = 0.5*np.sinc(f-5)fig = plt.figure()# ax = fig.gca(projection='3d')ax = fig.add_subplot(1,2,1,projection='3d')ax.plot(f,x,0*x,label='positive side',color='r')f = np.arange(-9.01,-1,0.01)x = 0.5*np.sinc(f+5)ax.plot(f,x,0*x,label='negative side',color='r')# ax.legend()ax.set_title('正矩形脉冲调制余弦载波', fontproperties='stsong')ax2 = fig.add_subplot(1,2,2,projection='3d')f2 = np.arange(-9.01,-1,0.01)y = 0.5*np.sinc(f2+5)ax2.plot(0*f2,f2,y,label='positive side',color='r')f2 = np.arange(1.01,9,01.01)y = -0.5*np.sinc(f2-5)ax2.plot(0*f2,f2,y,label='negative side',color='r')# ax.legend()ax2.set_title('正矩形脉冲调制正弦载波', fontproperties='stsong')ax2.set_xlabel('x')ax2.set_ylabel('f')ax2.set_zlabel('y')ax2.view_init(30,20)plt.tight_layout()plt.show()

正矩形脉冲调制正余弦载波

QPSK调制解调

# 连载94： QPSK 时域 调制解调imgnum = 6a = 1/np.sqrt(2)plt.figure(figsize=(5,10))# input signalplt.subplot(imgnum,1,1)# t = np.arange(0,8.5,0.5)# d = [0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]t = np.arange(0,4.5,0.5)d = [0,1,1,0,1,1,0,0,0]plt.plot(t,d,drawstyle='steps-post')plt.ylim([-0.5,1.5])# plt.annotate('0',xy=(0.5,1.2))# plt.text(1.5,1.2,'1',fontdict={'size':'8'})plt.title('QPSK input')# I signalplt.subplot(imgnum,1,2)x = np.arange(0,5,1)d = [-a,a,-a,a,a]plt.plot(x,d,drawstyle='steps-post')plt.ylim([-1.5,1.5])plt.annotate('$-\\sqrt{2}$',xy=(0.5,1))plt.annotate('$\\sqrt{2}$',xy=(1.5,1))plt.title('Q signal')# Q signalplt.subplot(imgnum,1,3)x = np.arange(0,5,1)d = [a,-a,-a,a,a]plt.plot(x,d,drawstyle='steps-post')plt.ylim([-1.5,1.5])plt.annotate('$\\sqrt{2}$',xy=(0.5,1))plt.annotate('$-\\sqrt{2}$',xy=(1.5,1))plt.title('Q signal')# 频带调制信号plt.subplot(imgnum,1,4)t = np.arange(0,4.1,0.01)y = [np.cos(2*np.pi*5*t+3/4*np.pi) for t in t if t<1.1]y.extend([np.cos(2*np.pi*5*t+7/4*np.pi) for t in t if 1.1<=t<2.1])y.extend([np.cos(2*np.pi*5*t+5/4*np.pi) for t in t if 2.1<=t<3.1])y.extend([np.cos(2*np.pi*5*t+1/4*np.pi) for t in t if 3.1<=t<4.1])# t = np.arange(0,8.2,0.1)# y = y*2# y.extend([np.cos(2*np.pi*5*t) for t in t if 6.1<=t<8.1])plt.plot(t,y)plt.ylim([-1.8,1.8])# plt.annotate('0',xy=(0.5,1.2))# plt.annotate('$\pi$',xy=(1.5,1.2))plt.title('QPSK Frequency Band Modulation')# I Signalplt.subplot(imgnum,1,5)yI = y*np.cos(2*np.pi*5*t)plt.plot(t,yI)# Q Signalplt.subplot(imgnum,1,6)yQ = y*-np.sin(2*np.pi*5*t)plt.plot(t,yQ)plt.tight_layout()

QPSK调制解调