ECEN3513 Signal Analysis Lecture

1
ECEN3513 Signal AnalysisLecture 35 13
November 2006

• Final Exam Final Exam, 0800-0950, Friday, 15
  December
• No reading or HW assignments this week

2
RLC transfer functions

• Know how to find H(f)
• May not always be in voltage divider form
• Use techniques learned in ECEN 2613 3714
• KCL or KVL
• Write i/o time domain equation
• Take Fourier (or Laplace) Transform
• Xc 1/(j?C) 1/sC
• XL j?L sL
• Find H(f) Vout(f)/Vin(f)
  DefaultIf have H(s), replace s with j?

3
Ideal "Brick-Wall" Low Pass Filteringof Serial
Bit Stream
4.5
z
k
0
z2
k
4.5
0
20
40
60
80
100
120
140
127
0
k
4
Ideal "Brick-Wall" FilteringActual I/O
relationship
4.5
z
k
0
z2
k
4.5
127
0
k
5
Ideal "Brick-Wall" Filteringif somehow done in
real time (not possible)
Note output constantly goes hi or lo prior to
input!
4.5
z
k
0
z2
k
4.5
0
20
40
60
80
100
120
140
127
0
k
6
Example Task

• Given an analog voice signal
• Generate a representative bit stream
• Logic 1's 0's
• Will transmit over a digital network
• Reconstruct replica of signal at receiver

7
A/D Convertor. 1 bit/sample.
Input to the transmitter. Output at the receiver.
2.5 v
-2.5 v
Considerable Round-Off error exists.
8
A/D Convertor. 2 bits/sample.
Input to the transmitter. Output at the receiver.
3.75 v
1.25 v
-1.25 v
-3.75 v
Receive 11? Output 3.75vReceive 10? Output
1.25v Receive 00? Output -1.25v Receive 01?
Output -3.75v Reduced Round-Off error exists.
9
1/8th Second of Voice
10
1/8th Second of Voice
11
Sampling in the Time Domain
Ideal Sampler
x(t)
xs(t) x(nts) x(n)
8 fs ? X(f - nfs) Xs(f) n -8
8 fs ? X(f - nfs) ? xs(t) n
-8 Fourier Transform Pair
12
Sampling in the Frequency Domain
Not Testable
13
The plot below is not continuous.MathCad is
drawing lines between the sampled points.
Not Testable
14
Sampling in the Frequency Domain
Ideal Sampler
X(f)
Xs(f) X(nfs)
8 fs ? x(t - nfs) ? Xs(-f) n
-8 Fourier Transform Pair
Not Testable
Duplicates of the time domain signal should show
up every fs seconds. Previous example has a fs
25 samples/Hz
15
Sampling in Frequency DomainCauses time domain
signal to be replicated every "fs" seconds.
Not Testable
16
1 MHz Sinusoid
1 vp 1 MHz
17
1 MHz Sinusoid
1 vp 1 MHz
Power Spectrum
freq (Hertz)
1,000,000
18
1 MHz EM Wave
Oscillating Electric voltage, connected to an
antenna, via a cable.
1 MHzSinusoidSource
19
1 MHz EM Wave
300,000,000 meters/second
EM wave will radiate in all directions. Propagates
at near speed of light in a vacuum. Shown
Electric Field propagating to right. Not shown
Electric field in other directions. Not shown
Magnetic Field
1 MHzSinusoidSource
20
1 MHz EM Wave
300 meters
300,000,000 meters/second
1 MHzSinusoidSource
21
1 MHz EM Wave
300 meters
Situation at t 0
375m
300 300 75 675m
1 MHzSinusoidSource
Field Strength Meter
22
1 MHz EM Wave
300 meters
Situation at t .000000250 seconds
375m
300 300 75 675m
1 MHzSinusoidSource
Field Strength Meter
23
(No Transcript)