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% #   <font color='#4B9DA9'> level 1 </font>
% ##  <font color='#547792'> level 2 </font>
% ### <font color='#E37434'> level 3 </font>
% {dropdown} <font color='#84B179'> Text </font>


# <font color='#4B9DA9'> Vlastnosti signálov  </font>

V elektronickom obvode pokladáme za signál časovo premenlivé napätie alebo prúd, ktorý prenáša informáciu. 

##  <font color='#547792'> Binárne signály  </font> 

V ideálnych binárnych signáloch má napätie v každom okamžiku len jednu z dvoch hodnôt, označovaných ako H (High) alebo L (Low). Signál je tvorený postupnosťou impulzov o dĺžke $t$ s periódou $T$. Informácia v binárnom signáli môže byť prenášaná variabilným počtom impulzov, zmenou ich šírky alebo periódy. Skupina niekoľkých impulzov môže vytvárať *burst*. 

```{code-cell} ipython3  
:tags: ["remove-cell"]
from src.utils import *

data = r'''

include(lib_base.ckt)
include(lib_user.ckt)
include(lib_color.ckt)

right_;
move to (0,0);                              # "0" below;
#linethick_(1.25);
color_red;
line from (0,0) to (1,0) then to (1,1) then to (1.5, 1) then to (1.5, 0) then to (2.5, 0) then to (2.5, 1);
{"$L$" at last line.start rjust;}
line to (3,1) to (3,0) then to (4, 0); 

right_;
line from (5,0) to (5.5, 0)  then to (5.5,1) then to (6,1) then to (6,0) then to (7,0);
line from (4,0) to (5,0) dashed;
#then to (5.5, 1) then to (5.5, 0) then to (6.5,0);


#linethick_();
color_orange;
line from (1,-0.5) to (1, 1.75) dashed; 
line from (1.5, -0.5) to (1.5, 1.75) dashed; 
line from (2.5,-0.5) to (2.5, 1.75) dashed; 

color_black;
line <-> from (1, -0.55) to (2.5, -0.55); "$T$" at last line.center above; 

line -> from (0.5, 1.45) to (1,1.45)
line from (1,1.45) to (1.5, 1.45); "$t$" at last line.center above; 
line <- from (1.5, 1.45) to (2, 1.45)

color_blue;
line from (0,1) to (1,1) dotted; "$H$" at last line.start rjust;

'''

_ = cm_compile('img_0072c', data,  dpi=600)   
```

```{figure} ./src/img_0072c.png
:width: 450px
:name: img_0072c

Binárny signál.
```

##  <font color='#547792'> Harmonické signály  </font> 

Harmonický signál je reprezentovaný zmenou napätia alebo prúdu podľa vzťahu

$$
y(t) = A \cdot sin(\omega \, t + \phi)
$$

Informáciu je možné prenášať v harmonickom signáli zmenou niektorého z jeho parametrov - amplitúdy, frekvencie alebo fázy.


```{code-cell} ipython3  
:tags: ["remove-cell"]
from src.utils import *

data = r'''

include(lib_base.ckt)
include(lib_user.ckt)
include(lib_color.ckt)

line -> from (-0.25,0) to (2*pi+0.5,0); "$t$" ljust ;
move to (0,0); 
color_blue;
sinusoid(1.0, 1, -pi/2, 0, 2*pi);
move to (0,0);
color_red;
sinusoid(1.0, 1, -1.5*pi/2, 0, 2*pi, dashed);

color_orange;
line from (0, 1) to (2*pi,1) dotted;
line from (0, -1) to (2*pi,-1) dotted;

color_black;
line -> from (0, -1.25) to (0,1.25); 
"$y(t)$" at last line.end+(0, 0.25);# rjust;
"$A$" at last line.center+(0,1) rjust;
"$-A$" at last line.center+(0,-1) rjust;

line from (pi/2/1.95, 0.1) to (pi/2/1.95, -0.1); "$\phi$" at last line.end below;
line from (pi, 0.1) to (pi, -0.1); "$T/2$" at last line.end+(-0.1,0) below ;
line from (2*pi, 0.1) to (2*pi, -0.1); "$T$" at last line.start above;
'''

_ = cm_compile('img_0072a', data,  dpi=600)   
```

```{figure} ./src/img_0072a.png
:width: 450px
:name: img_0072a
Harmonický signál.
```

Stredná hodnota

$$
A_{mean} = \frac{1}{T} \int_0^T y(t) dt
$$

Efektívna hodnota

$$
A_{RMS} = \sqrt{ \frac{1}{T} \int_0^T y(t)^2 dt }
$$



##  <font color='#547792'> Modulované signály  </font> 

### <font color='#E37434'> Amplitúdová modulácia </font>

```{code-cell} ipython3  
:tags: ["remove-cell"]

from numpy import *
import pylab as plt
plt.rcParams['figure.dpi'] = 150

T = linspace(0, 5*pi*2, 1000)     # 2*pi*t

m  = 0.5
A0 = 1
ct = A0*(1 + m*cos(T))     # modulacny signal
am = ct * cos(10*T)        # amplitudova modulacia

plt.plot(T, am)
plt.plot(T, ct, 'k--')
plt.plot(T,-ct, 'k--')
plt.title(r'Modulačný činiteľ ' + str(m))
plt.grid()
plt.xlabel('t')
plt.ylabel('AM')

plt.savefig('am_signal.png', dpi=300)
plt.close()

```


```{figure} am_signal.png
:width: 500px
:name: sig_01

Amplitúdovo modulovaný signál.
```