Class notes UW EE242 (EE242) Signals and Systems

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(