Amplitudová modulace¶

import matplotlib.patches as mpp

#  Konstanty
fs=44100
Ts=1./fs
length=1
# modulační vlna
fm=500.
Tm=1./fm
# nosná vlna
m=0.8
fc=6000.
Tc=1./fc
Uc=3
# časová osa
t = arange(0,length,1./fs)

# modulační signál
um = 1*cos(2*pi*fm*t)

# převod do frekvenční oblasti
from scipy.fftpack import fft, ifft
Ck= fft(um)
absCk = 2./len(um) * numpy.abs(Ck)[:len(Ck)/2]
f = arange(0,fs/2,float(fs)/len(Ck))
# Modulační signá
fig=figure()
subplot(211)
plot(t,um)
title(u'Modulační signál')
grid('on')
xlabel(r't\,[s] $\rightarrow$', x=0.9)
ylabel('$\mathrm u_m$\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([-1.1*max(um), 1.1*max(um)])
xlim([0,3*Tm])

subplot(212)
title(ur'Modulační signál -- amplitudové spektrum')
plot(f,absCk,'.-')
xlabel(r'f\,[Hz] $\rightarrow$', x=0.9)
ylabel('$\mathrm U_m$\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([0,1.1*max(absCk)]);
xlim([0,10e3])
grid(1)
text(500,-0.2 , '$\mathbf{f_m}$', size=16)
#figtext(0,1 , '$\mathrm f_m$', size=16)
tight_layout()

# Nosná vlna před modulací

uc = Uc*cos(2*pi*fc*t)

Ck= fft(uc)
absCk = 2./len(uc) * abs(Ck)[:len(Ck)/2]
f = arange(0,fs/2,float(fs)/len(Ck))

figure()
subplot(211)
plot(t,uc)
title(u'Nosný signál')
grid('on')
xlabel(r't\,[s] $\rightarrow$', x=0.9)
ylabel('$\mathrm u_c$\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([-1.1*max(uc), 1.1*max(uc)])
xlim([0,3*Tm])

subplot(212)
title(u'Nosný signál -- amplitudové spektrum')
plot(f,absCk,'.-')
xlabel(r'f\,[Hz] $\rightarrow$', x=0.9)
ylabel('$\mathrm U_c$\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([0,1.1*max(absCk)]);
xlim([0,10e3])
text(6000,-0.6 , '$\mathbf{f_c}$', size=16)
grid(1)
tight_layout()

# Nosná vlna po modulací
m=0.8
uc = Uc*(1+m*um)*cos(2*pi*fc*t)

Ck= fft(uc)
absCk = 2./len(uc) * abs(Ck)[:len(Ck)/2]
f = arange(0,fs/2,float(fs)/len(Ck))

figure()
subplot(211)
plot(t,uc)
title(ur'Modulovaný signál m=80\%')
grid('on')
xlabel(r't\,[s] $\rightarrow$', x=0.9)
ylabel('$\mathrm u_c$\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([-1.1*max(uc), 1.1*max(uc)])
xlim([0,3*Tm])

subplot(212)
title(ur'Modulovaný signál m=80\%-- amplitudové spektrum')
plot(f,absCk,'.-')
xlabel(r'f\,[Hz] $\rightarrow$', x=0.9)
ylabel('$\mathrm U_c$\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([0,1.1*max(absCk)]);
xlim([0,10e3])
text(6000,-0.6 , '$\mathbf{f_c}$', size=16)
text(6500,-0.6 , '$\mathbf{f_c+f_m}$', size=16)
text(4800,-0.6 , '$\mathbf{f_c-f_m}$', size=16)
grid(1)
tight_layout()

# Nosná vlna po modulací
m=0.2
uc = Uc*(1+m*um)*cos(2*pi*fc*t)

Ck= fft(uc)
absCk = 2./len(uc) * abs(Ck)[:len(Ck)/2]
f = arange(0,fs/2,float(fs)/len(Ck))

figure()
subplot(211)
plot(t,uc)
title(ur'Modulovaný signál m=20\%')
grid('on')
xlabel(r't\,[s] $\rightarrow$', x=0.9)
ylabel('u\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([-1.1*max(uc), 1.1*max(uc)])
xlim([0,3*Tm])

subplot(212)
title(ur'Modulovaný signál m=20\%-- amplitudové spektrum')
plot(f,absCk,'.-')
xlabel(r'f\,[Hz] $\rightarrow$', x=0.9)
ylabel('U\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([0,1.1*max(absCk)]);
xlim([0,10e3])
text(6000,-0.6 , '$\mathbf{f_c}$', size=16)
text(6500,-0.6 , '$\mathbf{f_c+f_m}$', size=16)
text(4800,-0.6 , '$\mathbf{f_c-f_m}$', size=16)
grid(1)

tight_layout()

# Nosná vlna po modulací
m=0.8
uc = Uc*(1+m*um)*cos(2*pi*fc*t)


figure(figsize=(8,7))
ax=subplot(111)
plot(t,uc, alpha=0.3)
title(ur'Modulovaný signál m={:d}\%'.format(int(100*m)))
grid('on')
xlabel(r't\,[s] $\rightarrow$', x=0.9)
ylabel('u\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([-1.1*max(uc), 1.1*max(uc)])
xlim([0,3*Tm])

plot(t, 3+3*m*cos(2*pi*fm*t),'g--' )
#plot(t, -3-3*m*cos(2*pi*fm*t),'g--' )
axhline(y=3, xmin=0, xmax=1, linestyle='--', linewidth=1, color='g')
ax.add_patch( mpp.FancyArrowPatch((0.003,0), (0.003,3), arrowstyle='<->',lw=2, linestyle='solid', 
              mutation_scale=25, color='k', alpha=0.9, shrinkA=0, shrinkB=0 ),  )
ax.add_patch( mpp.FancyArrowPatch((0.002,3), (0.002,3*(m+1)), arrowstyle='<->',lw=2, linestyle='solid', 
              mutation_scale=25, color='k', alpha=0.9, shrinkA=0, shrinkB=0 ),  )

bbox_props = dict(boxstyle="round,pad=0.2", fc="0.9", ec="k", lw=0.5)
text(0.0025,4, "$\mathbf{\Delta U_c}$", ha="center", va="center",  size=20, bbox=bbox_props)
text(0.0033,1.5, "$\mathbf{U_c}$", ha="center", va="center",  size=20, bbox=bbox_props)

fm

# modulační signál
um = 1*cos(2*pi*500*t)+1.2*cos(2*pi*600*t)+0.8*cos(2*pi*700*t)+0.6*cos(2*pi*800*t)+0.4*cos(2*pi*900*t)
um = um/max(um)

# převod do frekvenční oblasti
from scipy.fftpack import fft, ifft
Ck= fft(um)
absCk = 2./len(um) * numpy.abs(Ck)[:len(Ck)/2]
f = arange(0,fs/2,float(fs)/len(Ck))
# Modulační signá
figure()
subplot(211)
plot(t,um)
title(u'Neharmonický modulační signál')
grid('on')
xlabel(r't\,[s] $\rightarrow$', x=0.9)
ylabel('u\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([-1.1*max(um), 1.1*max(um)])
xlim([0,6*Tm])

subplot(212)
title(ur'Neharmonický modulační signál -- amplitudové spektrum')
plot(f,absCk,'.-')
xlabel(r'f\,[Hz] $\rightarrow$', x=0.9)
ylabel('U\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([0,2]);
xlim([0,10e3])
grid(1)
tight_layout()

#text(400,-0.04, '$\mathbf{f_{min}}$', size=16)
annotate('$\mathbf{f_{min}}$', xy=(500,0),size=16, xytext=(100,-0.5), arrowprops=dict(arrowstyle="->",connectionstyle="arc3,rad=0", ),)
annotate('$\mathbf{f_{max}}$', xy=(900,0),size=16, xytext=(1000,-0.5), arrowprops=dict(arrowstyle="->",connectionstyle="arc3,rad=0", ),)

# Nosná vlna po modulací
m=0.9
uc = Uc*(1+m*um)*cos(2*pi*fc*t)

Ck= fft(uc)
absCk = 2./len(uc) * abs(Ck)[:len(Ck)/2]
f = arange(0,fs/2,float(fs)/len(Ck))

figure()
subplot(211)
plot(t,uc)
title(ur'Neharmonicky modulovaný signál m=90\%')
grid('on')
xlabel(r't\,[s] $\rightarrow$', x=0.9)
ylabel('u\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([-1.1*max(uc), 1.1*max(uc)])
xlim([0,6*Tm])

ax=subplot(212)
title(ur'Neharmonicky modulovaný signál m=90\% -- amplitudové spektrum')
plot(f,absCk,'.-')
xlabel(r'f\,[Hz] $\rightarrow$', x=0.9)
ylabel('U\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([0,1.1*max(absCk)]);
xlim([0,10e3])
grid(1,'major')
minorticks_on()
tight_layout()

text(6000,-0.7,r'$\mathbf{f_c}$',size=16, horizontalalignment='center')
annotate('$\mathbf{f_c-f_{max}}$', xy=(5100,0),size=16, xytext=(4200,-0.6), arrowprops=dict(arrowstyle="->",connectionstyle="arc3,rad=0", ),)
annotate('$\mathbf{f_c+f_{max}}$', xy=(6900,0),size=16, xytext=(6800,-0.6), arrowprops=dict(arrowstyle="->",connectionstyle="arc3,rad=0", ),)
annotate('$\mathbf{f_c-f_{min}}$', xy=(5500,0),size=16, xytext=(4700,-1.2), arrowprops=dict(arrowstyle="->",connectionstyle="arc3,rad=0", ),)
annotate('$\mathbf{f_c+f_{min}}$', xy=(6500,0),size=16, xytext=(6300,-1.2), arrowprops=dict(arrowstyle="->",connectionstyle="arc3,rad=0", ),)

ax.add_patch( mpp.FancyArrowPatch((5100,1), (6900,1), arrowstyle='<->', 
                        lw=2, linestyle='solid', mutation_scale=25,
                        color='green', alpha=0.9, shrinkA=0, shrinkB=0 ),  )
text(6200,1.3, '$\mathbf{B=2 f_{max}}$',size=20)
axvspan(5100, 6900, facecolor='g', alpha=0.2, ymax=0.3)