#!/usr/bin/env python
# coding: utf-8

# Frekvenční modulace
# ======================
# 
# Modulační a nosný signál
# ---------------------------

# In[1]:


import matplotlib.patches as mpp

#  Konstanty
fs=96000
Ts=1./fs
length=1
# modulační vlna
fm=100.
Tm=1./fm
# nosná vlna
B=15
fc=3000.
Tc=1./fc
Uc=3
# časová osa
t = arange(0,length,1./fs)

# modulační signál
um = 1*sin(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(figsize=(10,6))
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([0,1.5*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*Uc]);
xlim([0,6e3])
grid(1)
text(100,-0.34 , '$\mathbf{f_m}$', size=16)
#figtext(0,1 , '$\mathrm f_m$', size=16)
tight_layout()


# In[2]:


# 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(figsize=(10,6))
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([0,1.5*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*Uc]);
xlim([0,6e3])
text(3000,-0.6 , '$\mathbf{f_c}$', size=16)
grid(1)
tight_layout()


# In[3]:


# Nosná vlna po modulací
B=15
uc = Uc*cos(2*pi*fc*t+B*um)

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

figure(figsize=(10,8))

subplot(311)
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([0,1.5*Tm])

subplot(312)
plot(t,uc)
title(ur'Modulovaný signál $\beta={}, \Delta f={}\,\mathrm{{kHz}}$'.format(B,B*fm/100.))
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([0,1*Tm])

subplot(313)
title(ur'Modulovaný signál $\beta={}, \Delta f={}\,\mathrm{{kHz}}$  -- amplitudové spektrum'.format(B,B*fm/1000.))
plot(f,absCk,'.-')
xlabel(r'f\,[Hz] $\rightarrow$', x=0.9)
ylabel('$\mathrm U_c$\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([0,1.5*max(absCk)]);
xlim([0,6e3])
text(3000,-0.3 , '$\mathbf{f_c}$', size=16)
grid(1)

annotate('$\mathbf{f_c+f_m}$', xy=(3100,0),size=16, xytext=(3100,-0.6), arrowprops=dict(arrowstyle="->",connectionstyle="arc3,rad=0", ),)
annotate('$\mathbf{f_c+2f_m}$', xy=(3200,0),size=16, xytext=(3500,-0.4), arrowprops=dict(arrowstyle="->",connectionstyle="arc3,rad=0", ),)
tight_layout()


# In[4]:


# Nosná vlna po modulací
B=8
uc = Uc*cos(2*pi*fc*t+B*um)

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

figure(figsize=(10,8))

subplot(311)
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([0,1.5*Tm])

subplot(312)
plot(t,uc)
title(ur'Modulovaný signál $\beta={}, \Delta f={}\,\mathrm{{kHz}}$'.format(B,B*fm/100.))
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([0,1*Tm])

subplot(313)
title(ur'Modulovaný signál $\beta={}, \Delta f={}\,\mathrm{{kHz}}$  -- amplitudové spektrum'.format(B,B*fm/1000.))
plot(f,absCk,'.-')
xlabel(r'f\,[Hz] $\rightarrow$', x=0.9)
ylabel('$\mathrm U_c$\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([0,1.5*max(absCk)]);
xlim([0,6e3])

text(3000,-0.4 , '$\mathbf{f_c}$', size=16)
grid(1)

tight_layout()


# In[5]:


figure(figsize=(10,4))
ax=subplot(111)
title(ur'Modulovaný signál $\beta={}, \Delta f={}\,\mathrm{{kHz}}$  -- amplitudové spektrum'.format(B,B*fm/1000.))
plot(f,absCk,'.-')
xlabel(r'f\,[Hz] $\rightarrow$', x=0.9)
ylabel('$\mathrm U_c$\,[V] $\uparrow$', y=0.9, rotation=0)
ylim([0,1.5*max(absCk)]);
xlim([0,6e3])

text(3000,-0.25 , '$\mathbf{f_c}$', size=16)
grid(1)

ax.add_patch( mpp.FancyArrowPatch((2100,1.2), (3900,1.2), arrowstyle='<->', 
                        lw=2, linestyle='solid', mutation_scale=25,
                        color='green', alpha=0.9, shrinkA=0, shrinkB=0 ),  )
axvspan(2100, 3900, facecolor='g', alpha=0.2, ymax=0.78)
text(2500,1.22, r'$2(\Delta f+f_{max})$',size=16)

bbox_props = dict(boxstyle="round,pad=0.3", fc=".9", ec="b", lw=2)
t=annotate(u'Carsonův odhad', xy=(2400,1.3),size=16, xytext=(400,1.2),bbox=bbox_props,
          arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=-0.2", fc="w") 
         )