This work is licensed under a Creative Commons-ShareAlike 4.0 International License
Original source: The Orange Grove
http://florida.theorangegrove.org/og/items/c7d013ec-2b4d-6971-65f9-b1a6af2d9092/
1/
,Contents
Chapter 1 Introduction ..................................................................................................1
1.1 Themes ................................................................................................................................1
1.2 Signals Represent Information ........................................................................................2
1.2.1 Analog Signals..........................................................................................................3
1.2.2 Digital Signals...........................................................................................................4
1.3 Structure of Communication Systems .............................................................................5
1.4 The Fundamental Signal ...................................................................................................7
1.4.1 The Sinusoid ............................................................................................................7
Exercise 1.4.1 ............................................................................................................8
Exercise 1.4.2 ............................................................................................................8
1.4.2 Communicating Information with Signals ............................................................8
1.5 Introduction Problems.......................................................................................................9
1.6 Solutions to Exercises in Chapter 1 ................................................................................10
Chapter 2 Signals and Systems ...................................................................................11
2.1 Complex Numbers ...........................................................................................................11
2.1.1 Definitions ..............................................................................................................11
Exercise 2.1.1 ..........................................................................................................13
Exercise 2.1.2 ..........................................................................................................13
2.1.2 Euler's Formula ......................................................................................................13
2.1.3 Calculating with Complex Numbers....................................................................14
Exercise 2.1.3 .....................................................................................................15
Example 2.1 ............................................................................................................16
2.2 Elemental Signals..............................................................................................................16
2.2.1 Sinusoids ................................................................................................................16
2.2.2 Complex Exponentials ..........................................................................................17
2.2.3 Real Exponentials ..................................................................................................18
2.2.4 Unit Step .................................................................................................................18
2.2.5 Pulse........................................................................................................................20
2.2.6 Square Wave ..........................................................................................................20
2.2.7 Signal Decomposition ...........................................................................................21
Example 2.2 ............................................................................................................21
Exercise 2.3.1 ..........................................................................................................21
, 2.4.1 Sources ...................................................................................................................27
2.4.2 Amplifiers ...............................................................................................................27
2.4.3 Delay .......................................................................................................................28
2.4.4 Time Reversal.........................................................................................................28
Exercise 2.6.1 ..........................................................................................................28
2.4.5 Derivative Systems and Integrators ...................................................................29
2.4.6 Linear Systems.......................................................................................................29
2.4.7 Time-Invariant Systems ........................................................................................30
2.5 Signals and Systems Problems .......................................................................................32
Problem 2.1: Complex Number Arithmetic ................................................................32
Problem 2.2: Discovering Roots ...................................................................................32
Problem 2.3: Cool Exponentials ...................................................................................32
Problem 2.4: Complex-valued Signals .........................................................................33
Problem 2.5: ...................................................................................................................34
Problem 2.6: ...................................................................................................................35
Problem 2.7: Linear, Time-Invariant Systems .............................................................36
Problem 2.8: Linear Systems ........................................................................................37
Problem 2.9: Communication Channel .......................................................................37
Problem 2.10: Analog Computers ................................................................................38
2.6 Solutions to Exercises in Chapter 2 ................................................................................38
Chapter 3 Analog Signal Processing ...........................................................................40
3.1 Voltage, Current, and Generic Circuit Elements ...........................................................40
Exercise 3.1.1 ..................................................................................................................41
3.2 Ideal Circuit Elements .....................................................................................................41
3.2.1 Resistor ...................................................................................................................42
3.2.2 Capacitor ................................................................................................................42
3.2.3 Inductor ..................................................................................................................43
3.2.4 Sources ...................................................................................................................44
3.3 Ideal and Real-World Circuit Elements ..........................................................................44
3.4 Electric Circuits and Interconnection Laws....................................................................45
3.4.1 Kirchhof's Current Law .........................................................................................46
Exercise 3.4.1 ..........................................................................................................47
3.4.2 Kirchhof's Voltage Law (KVL) ................................................................................47
Exercise 3.4.2 ..........................................................................................................48
3.5 Power Dissipation in Resistor Circuits ...........................................................................48
Exercise 3.5.1 ..................................................................................................................50
Exercise 3.5.2 ..................................................................................................................50
3.6 Series and Parallel Circuits ..............................................................................................50
Exercise 3.6.1 ..................................................................................................................52
Exercise 3.6.2 ..................................................................................................................54
Example 3.1 ....................................................................................................................55
Exercise 3.6.3 ..................................................................................................................56
3.7 Equivalent Circuits: Resistors and Sources....................................................................57
Exercise 3.7.1 ..................................................................................................................59
Example 3.2 ....................................................................................................................59
Exercise 3.7.2 ..................................................................................................................61
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller phanterpinky312. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.89. You're not tied to anything after your purchase.