module1.pdf
-
Upload
sabrina-noor -
Category
Documents
-
view
212 -
download
0
Transcript of module1.pdf
-
Digital Signal Processing
Module 1: IntroductionDigital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
What is a signal?
Description of the evolution of a physical phenomenon
Examples:
temperature (weather)
pressure (sound)
magnetic deviation (recorded sound)
gray level on paper (photograph)
...
1 1
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
uu
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u u
u
u
u
u
u
u
u
u
u
u
u
u
u
C
0
5
10
15
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
Key ingredients:
discrete time
discrete amplitude
1 3
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
The circle point out (from left to right): Pythagoras, Parmenides, Plato,
Euclid. Green for philosophers, red for mathematicians
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
A B
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
A BC
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
A BC D E FG
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
A BC D E FG
n=1
1
2n= 1
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Idea here is: you got a point, nameless geometrical entity. Descartes comes and
puts a reference around it, point gets a name. Then more complex things get
names (such as lines) and can be described in terms of algebra
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
01
2
3
4
5
6
0 1 2 3 4 5 6 7 8 9 10x
y
(6, 4)
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
01
2
3
4
5
6
0 1 2 3 4 5 6 7 8 9 10x
y
y = x + c
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Calculus: ideas at the service of war
b
b
b
b
b b
b
b
b
b
~x(t) = ~v0t + (1/2)~g t2
Galileo, 1638
1 9
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Calculus: ideas at the service of war
b
b
b
b
b b
b
b
b
b
~x(t) = ~v0t + (1/2)~g t2
Galileo, 1638
1 9
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Continuous-time signal processing: the average
a b
x =1
b a
b
a
f (t)dt
1 10
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Continuous-time signal processing: the average
a b
x =1
b a
b
a
f (t)dt
1 10
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Discrete-time signal processing: the average
b b
b
b
b
b
b
b
b
b
b
b
b b
b
b
b
b
b
b
0 N 1
x =1
N
N1n=0
x [n]
1 11
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Discrete-time signal processing: the average
b b
b
b
b
b
b
b
b
b
b
b
b b
b
b
b
b
b
b
0 N 1
x =1
N
N1n=0
x [n]
1 11
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Are we missing pieces?
What if the signal is too fast?
f (t) =?
1 12
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
The Sampling Theorem (1920)
Under appropriate slowness conditions for x(t) we have:
x(t) =
n=
x [n]sin((t nTs)/Ts)
(t nTs)/Ts
1 16
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
1 17
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
1 17
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
1 17
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
1 17
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
1 17
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
1 17
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
1 17
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
1 17
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
1 17
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
The world is analog, the computer is digital
1 18
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
So, what is resolution, really?
1 19
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
Key ingredients:
discrete time
discrete amplitude
1 20
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
x(t)
1 21
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
x(t)
1 21
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
x [n]
1 21
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
x [n]
1 21
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Signals
b b
b
b b
b b b
b
b b b
b b
b
b b b
b
b b
b b b
b
b b b
b b
b
b b
x [n]
1 21
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital amplitude
Why it is important:
storage
processing
transmission
1 22
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Data storage
Analog storage:paper, wax cylinders, reel-to-reel, vinyl, compact cassette, VHS, Betamax, silver plates,
Kodachrome, Super8, 8-Track, microfilm, ...
Digital storage:
{0, 1}
1 23
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Data storage
Analog storage:paper, wax cylinders, reel-to-reel, vinyl, compact cassette, VHS, Betamax, silver plates,
Kodachrome, Super8, 8-Track, microfilm, ...
Digital storage:
{0, 1}
1 23
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Data storage
Analog storage:paper, wax cylinders, reel-to-reel, vinyl, compact cassette, VHS, Betamax, silver plates,
Kodachrome, Super8, 8-Track, microfilm, ...
Digital storage:
{0, 1}
1 23
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Data storage
Analog storage:paper, wax cylinders, reel-to-reel, vinyl, compact cassette, VHS, Betamax, silver plates,
Kodachrome, Super8, 8-Track, microfilm, ...
Digital storage:
{0, 1}
1 23
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Processing
1 25
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Data transmission
TX channel RX
1 26
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
What happens to analog signals
x(t) + x(t)
(t)
1/G
x(t) = x(t)/G + (t)
1 27
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
What happens to analog signals
5
0
5
x(t)
1 28
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
What happens to analog signals
5
0
5
x(t)/G
1 28
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
What happens to analog signals
5
0
5
x(t)/G + (t)
1 28
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
We can amplify to compensate attenuation
x(t) + x1(t)
(t)
1/G G
but: x1(t) = x(t) + G(t)
1 29
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x(t)
1 30
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x(t)/G
1 30
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x(t)/G + (t)
1 30
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x1(t) = G [x(t)/G + (t)] = x(t) + G(t)
1 30
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmitting a signal overseas
For a long, long channel we need repeaters
x(t) + x1(t) + . . . + xN(t)
(t) (t) (t)
1/G G 1/G G 1/G G
xN(t) = x(t) + NG(t)
1 33
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x(t)
1 34
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x(t)/G
1 34
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x(t)/G + (t)
1 34
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x1(t) = G [x(t)/G + (t)] = x(t) + G(t)
1 34
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x1(t)/G + (t)
1 34
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
x2(t) = G [x1(t)/G + (t)] = x(t) + 2G(t)
1 34
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of analog signals
5
0
5
xN(t) = x(t) + NG(t)
1 34
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
In digital signals we can threshold
x(t) + | | x1(t)
(t)
1/G G
x1(t) = sgn[x(t) + G(t)]
1 35
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of quantized signals
5
0
5
x(t)
1 36
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of quantized signals
5
0
5
x(t)/G + (t)
1 36
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of quantized signals
5
0
5
G [x(t)/G + (t)] = x(t) + G(t)
1 36
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Transmission of quantized signals
5
0
5
x1(t) = G sgn[x(t) + G(t)]
1 36
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital data throughputs
Transatlantic cable:
1866: 8 words per minute (5 bps)
1956: AT&T, coax, 48 voice channels (3Mbps)
2005: Alcatel Tera10, fiber, 8.4 Tbps (8.4 1012 bps)
2012: fiber, 60 Tbps
Voiceband modems
1950s: Bell 202, 1200 bps
1990s: V90, 56Kbps
2008: ADSL2+, 24Mbps
1 37
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Digital data throughputs
Transatlantic cable:
1866: 8 words per minute (5 bps)
1956: AT&T, coax, 48 voice channels (3Mbps)
2005: Alcatel Tera10, fiber, 8.4 Tbps (8.4 1012 bps)
2012: fiber, 60 Tbps
Voiceband modems
1950s: Bell 202, 1200 bps
1990s: V90, 56Kbps
2008: ADSL2+, 24Mbps
1 37
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
Final words
1 38
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013
-
END OF MODULE 1
Digital Sig
nal Proces
sing
Paolo Pran
doni and M
artin Vett
erli
2013