Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Fundamentals of Electrical Engineering I » Introduction Problems

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • OrangeGrove display tagshide tags

    This collection is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange Grove

    Click the "OrangeGrove" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Rice DSS - Braille display tagshide tags

    This collection is included inLens: Rice University Disability Support Services's Lens
    By: Rice University Disability Support Services

    Comments:

    "Electrical Engineering Digital Processing Systems in Braille."

    Click the "Rice DSS - Braille" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Rice Digital Scholarship display tagshide tags

    This collection is included in aLens by: Digital Scholarship at Rice University

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Bookshare

    This collection is included inLens: Bookshare's Lens
    By: Bookshare - A Benetech Initiative

    Comments:

    "Accessible versions of this collection are available at Bookshare. DAISY and BRF provided."

    Click the "Bookshare" link to see all content affiliated with them.

  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "The course focuses on the creation, manipulation, transmission, and reception of information by electronic means. It covers elementary signal theory, time- and frequency-domain analysis, the […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Lens for Engineering

    This module and collection are included inLens: Lens for Engineering
    By: Sidney Burrus

    Click the "Lens for Engineering" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
Download
x

Download collection as:

  • PDF
  • EPUB (what's this?)

    What is an EPUB file?

    EPUB is an electronic book format that can be read on a variety of mobile devices.

    Downloading to a reading device

    For detailed instructions on how to download this content's EPUB to your specific device, click the "(what's this?)" link.

  • More downloads ...

Download module as:

  • PDF
  • EPUB (what's this?)

    What is an EPUB file?

    EPUB is an electronic book format that can be read on a variety of mobile devices.

    Downloading to a reading device

    For detailed instructions on how to download this content's EPUB to your specific device, click the "(what's this?)" link.

  • More downloads ...
Reuse / Edit
x

Collection:

Module:

Add to a lens
x

Add collection to:

Add module to:

Add to Favorites
x

Add collection to:

Add module to:

 

Introduction Problems

Module by: Don Johnson. E-mail the author

Summary: Problems for introduction to signals and systems.

Problem Set

Problem 1

RMS Values

The rms (root-mean-square) value of a periodic signal is defined to be s=1T0Ts2tdt s 1 T t 0 T s t 2 where T T is defined to be the signal's period: the smallest positive number such that st=st+T s t s t T .

  1. What is the period of st=Asin2π f 0 t+φ st A 2 f 0 t φ ?
  2. What is the rms value of this signal? How is it related to the peak value?
  3. What is the period and rms value of the depicted square wave, generically denoted by sqt sq t ?
  4. By inspecting any device you plug into a wall socket, you'll see that it is labeled "110 volts AC". What is the expression for the voltage provided by a wall socket? What is its rms value?
Figure 1
Figure 1 (sig13.png)

Problem 2

Modems

The word "modem" is short for "modulator-demodulator." Modems are used not only for connecting computers to telephone lines, but also for connecting digital (discrete-valued) sources to generic channels. In this problem, we explore a simple kind of modem, in which binary information is represented by the presence or absence of a sinusoid (presence representing a "1" and absence a "0"). Consequently, the modem's transmitted signal that represents a single bit has the form xt=Asin2π f 0 t , 0tT x t A 2 f 0 t , 0 t T Within each bit interval TT, the amplitude is either AA or zero.

  1. What is the smallest transmission interval that makes sense with the frequency f 0 f 0 ?
  2. Assuming that ten cycles of the sinusoid comprise a single bit's transmission interval, what is the datarate of this transmission scheme?
  3. Now suppose instead of using "on-off" signaling, we allow one of several different values for the amplitude during any transmission interval. If NN amplitude values are used, what is the resulting datarate?
  4. The classic communications block diagram applies to the modem. Discuss how the transmitter must interface with the message source since the source is producing letters of the alphabet, not bits.

Problem 3

Advanced Modems

To transmit symbols, such as letters of the alphabet, RU computer modems use two frequencies (1600 and 1800 Hz) and several amplitude levels. A transmission is sent for a period of time TT (known as the transmission or baud interval) and equals the sum of two amplitude-weighted carriers. xt= A 1 sin2π f 1 t+ A 2 sin2π f 2 t , 0tT x t A 1 2 f 1 t A 2 2 f 2 t , 0 t T We send successive symbols by choosing an appropriate frequency and amplitude combination, and sending them one after another.

  1. What is the smallest transmission interval that makes sense to use with the frequencies given above? In other words, what should TT be so that an integer number of cycles of the carrier occurs?
  2. Sketch (using Matlab) the signal that modem produces over several transmission intervals. Make sure you axes are labeled.
  3. Using your signal transmission interval, how many amplitude levels are needed to transmit ASCII characters at a datarate of 3,200 bits/s? Assume use of the extended (8-bit) ASCII code.
Note:
We use a discrete set of values for A 1 A 1 and A 2 A 2 . If we have N 1 N 1 values for amplitude A 1 A 1 , and N 2 N 2 values for A 2 A 2 , we have N 1 N 2 N 1 N 2 possible symbols that can be sent during each TT second interval. To convert this number into bits (the fundamental unit of information engineers use to qualify things), compute log 2 ( N 1 N 2 ) 2 N 1 N 2 .

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Reuse / Edit:

Reuse or edit collection (?)

Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.

| Reuse or edit module (?)

Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.