Lecture I
collection
Signals : of data
system : relations btwn signals
operator on signals
can involve
systems chained combination
X(t)
continuous
independent
S discrete
>
value -
-
var
Analog signal : CT
Digital Signal : DS
CT Vs . PS Time
signals
CT : x (t) .
tER I real #)
DS : X [n] ,
nez (int)
CT
CT
CT
DS
DS
DS
, -
A/D
4 pre-process lanti-aliasing)
Ts =
Es :
52,000
↳ Spa fix into : x (nTs)
M
fs
M
*
=
1/ Ts
↑
*
* g
8
= · =
sampling rate (H2)
>
-
= samples/sea
T
↳ Index period (sec)
w/int :X [M]
sampling
-
D/A Ismooth interpolation btwn points)
·
Need is to
get back
Aliasing for videoSignals Wagon wheel effect
-
-
R
sample int too
large >
-
wrong result
Nyquist Sampling Theorem
-
*
1) fs = > 2 BW Complex BW of a real-valued
> -
signal the real freq
-
I is 2x max
Wm < 0 5
.
Ws
Bandwidth
2) Smooth interpolation func (low pass filter
if the
sampling sys fail w/ these conditions >
-
pre-processing
, Theoretical Real Computer
- X (t) , tER Xct)
-
,
teRT creal) -Xin] ,
nezt
-
x[n] , nez
·
z side ·
i side ·
Iside
(streaming)
·
+El 0 d)
-
,
·
+Elo 2) starts when start
,
vec · finite length
·
Amp CT
Amp CT
·
Amp DS
BASIC SIGNALS IN THEORY
TAKE-AWAYS
rector of samples ints
PS
&
·
Ts /fs
, Signal Energy & Power
CT Time
Y
R
75
ENERGY larea under (x(t)# POWER
it
>
E
Sto-1xct)1dt 40
= Stat
* =
sig
=
a ti
Es
=lim Sxcts de R
W
= 1s P = orIR
=
b DS Time H
R= a +
8 = arctant P (x(t))
=
*
En
a = rX Cost
d =
rxSin E=
%
E= PXT
Eo =Y Ins Poin
·
If Eg is finite .
Po =
·
if Po >O ,
Ex = *
1) Finite Energy finite : Ex zeroPo (Energy signal
P (RMS)
3
=
2) Finite Power : Ex = - finite Po (Power Signall
3) Infinite Power : E0 = 0 Po = & (i . e ·
fit) = et(
collection
Signals : of data
system : relations btwn signals
operator on signals
can involve
systems chained combination
X(t)
continuous
independent
S discrete
>
value -
-
var
Analog signal : CT
Digital Signal : DS
CT Vs . PS Time
signals
CT : x (t) .
tER I real #)
DS : X [n] ,
nez (int)
CT
CT
CT
DS
DS
DS
, -
A/D
4 pre-process lanti-aliasing)
Ts =
Es :
52,000
↳ Spa fix into : x (nTs)
M
fs
M
*
=
1/ Ts
↑
*
* g
8
= · =
sampling rate (H2)
>
-
= samples/sea
T
↳ Index period (sec)
w/int :X [M]
sampling
-
D/A Ismooth interpolation btwn points)
·
Need is to
get back
Aliasing for videoSignals Wagon wheel effect
-
-
R
sample int too
large >
-
wrong result
Nyquist Sampling Theorem
-
*
1) fs = > 2 BW Complex BW of a real-valued
> -
signal the real freq
-
I is 2x max
Wm < 0 5
.
Ws
Bandwidth
2) Smooth interpolation func (low pass filter
if the
sampling sys fail w/ these conditions >
-
pre-processing
, Theoretical Real Computer
- X (t) , tER Xct)
-
,
teRT creal) -Xin] ,
nezt
-
x[n] , nez
·
z side ·
i side ·
Iside
(streaming)
·
+El 0 d)
-
,
·
+Elo 2) starts when start
,
vec · finite length
·
Amp CT
Amp CT
·
Amp DS
BASIC SIGNALS IN THEORY
TAKE-AWAYS
rector of samples ints
PS
&
·
Ts /fs
, Signal Energy & Power
CT Time
Y
R
75
ENERGY larea under (x(t)# POWER
it
>
E
Sto-1xct)1dt 40
= Stat
* =
sig
=
a ti
Es
=lim Sxcts de R
W
= 1s P = orIR
=
b DS Time H
R= a +
8 = arctant P (x(t))
=
*
En
a = rX Cost
d =
rxSin E=
%
E= PXT
Eo =Y Ins Poin
·
If Eg is finite .
Po =
·
if Po >O ,
Ex = *
1) Finite Energy finite : Ex zeroPo (Energy signal
P (RMS)
3
=
2) Finite Power : Ex = - finite Po (Power Signall
3) Infinite Power : E0 = 0 Po = & (i . e ·
fit) = et(
