This brief paragraph was put in before a section tag
to ensure that it was styled correctly.
This equation has been thrown in as a child of content for styling purposes.
cos2πft=ⅇⅈ2πft+ⅇ-ⅈ2πft2
2
f
t
2
f
t
2
f
t
2
(1)
General Example with Equation
The complex exponential defines the notion of frequency: It is
the
only signal that contains only one
frequency component. The sinusoid consists of two frequency
components: one at the frequency
+
f
0
+
f
0
and the other at
-
f
0
f
0
.
This is Euler's relation relating things like e's and cosines
cos2πft=ⅇⅈ2πft+ⅇ-ⅈ2πft2
2
f
t
2
f
t
2
f
t
2
(2)
Euler's relation
sin2πft=ⅇⅈ2πft-ⅇ-ⅈ2πft2ⅈ
2
f
t
2
f
t
2
f
t
2
(3)
Another Euler's relation
ⅇⅈ2πft=cos2πft+ⅈsin2πft
2
f
t
2
f
t
2
f
t
(4)
The complex exponential signal can thus be written in terms of
its real and imaginary parts using Euler's relation. Thus,
sinusoidal signals can be expressed as either the real or the
imaginary part of a complex exponential signal (the choice
depends on whether cosine or sine phase is needed) or as the
sum of two complex exponentials. These two decompositions are
mathematically equivalent to each other.
Section: ICSA
The Rice Sailing Team is part of a sailing coalition called ICSA which
stands for Inter-Collegiate Sailing Association. The ICSA is the
governing body for collegete sailing programs in the US. Volunteers of
ICSA develop the racing rules. They also organize the national
regattas. To be a member of ICSA, a college must pay money to a
sub-district.
SEISA
Rice is a member of the SEISA district of ICSA. SEISA stands for
South-Eastern Inter-Collegiate Sailing Association. SEISA is the
organization that the South-East colleges compete in. The schools gather
to compete for all normal regattas. One or two schools from SEISA will
qualify for the National competitions hosted by ICSA.
RUST: Rice University Sailing Team
RUST is Rice's competitive sailing team. Rice is a member of
SEISA. This
district is made up of several schools, including UT, A&M,
A&M
Galveston, UNO, Tulane, Kansas, and UWF. The Rice Sailing Club is
open to all
members of the student community, including graduate
students. Beginner and expert sailors alike are encouraged to
practice with the team. RUST is a small and easy-going club. There
are
no attendance requirements, and everyone who wants to sail can
sail. Members pay yearly dues to help cover expenses, but every
member not only gets to sail, but gets a sailing club T-shirt too!
For the benefit of Mr. Kite, there
will be a show tonight on trampoline. The Hendersons will
all be there, late Pablo Fanques Fair - what a scene. Over
men and horses, hoops and garters, lastly through a hogshead
of real fire! In this way Mr. K. will challenge the world!
The celebrated Mr. K. performs his feat on Saturday at
Bishopsgate. The Hendersons will dance and sing as Mr. Kite
flys through the ring - don't be late. Messrs. K and
H. assure the public their production will be second to
none. And course Henry The Horse dances the waltz!
This equation has been thrown in as a child of section for styling purposes
cos2πft=ⅇⅈ2πft+ⅇ-ⅈ2πft2
2
f
t
2
f
t
2
f
t
2
(5)
Section Three Point Two
Section 3.2
Section Three Point Three
Section 3.3
four levels down
five levels down
six levels down
seven levels down
eight levels down
nine levels down
how low can you go?
as low as you want
CNXML is limitless in it's powers
You get the picture!
List
Hello and welcome to my list of things to do. The following list
is
within a paragraph, whereas the subsequent
ordered list is
preceded by a paragraph.
- This is an item. The length of this item has been
extended for quality assurance of its style upon wrapping, assuming it
extends for more than the width of the screen, which is
why it may appear that I am dragging this sentence out for a
long time..
-
This is another item with a list nested inside of it.
This is not a new paragraph.
This is also not a new paragraph.
This is a new paragraph.
Example Enumerated List - This is an enumerated list item not located within
paragraph tags.
-
This is another item with a list nested inside of it.
- This is a subitem. But the subitem is not enumerated.
- This is another subitem.
- Yet another item
CNXN and Link
If you want to learn more about things in general, you can look
at other pages in CNX world. To learn more about CNXML, go to
the
CNXML 0.3
spec. Then you can write things like
<cnxn> and
<link> in CNXML.
You will also be able to make
CNXN's
between things you wrote and things other people have written.
For example, to learn more about Rice sailing, you can look right here at the
sailing section in this module. Or you
could link to something even less relevant, say
digital communication
receivers. To go to a topic which is a bit more relavant to
writing
<cnxn> tags, you could visit the
module about
using emacs. If you
have more questions about Connexions basics,
you could look at the
FAQ .
So if you want to learn more about the world in which you live,
Connexions is the
place to be. Extra cnxns:
subfigure 4.2 and
(Reference) and
Figure 2.
Example
Example 1
As an example of signal complexity, we can express the pulse
p
Δ
t
p
Δ
t
as a sum of delayed unit steps.
p
Δ
t=ut-ut-Δ
p
Δ
t
u
t
u
t
Δ
(8)
Thus, the pulse is a more complex signal than the step. Be that
as it may, the pulse is very useful to us.
Example 2: CNXML can be a pain This sentence, although it is very
unimportant and
irrelevant, contains emphasis within the
<example> tag. For an example of
<cite> within
<example>, see
Things That
Are a Pain to Style in CNXML by Max Starkenburg. For an
example of
<emphasis> within
<cite> within
<example>, please see
Things
That Are a Pain in the Butt to Style in
CNXML, also by Max Starkenburg. This sentence contains
emphasized codeline
within an example. This sentence contains a
cnxn within an example. This
sentence contains a
link. This
sentence contains a
term. This sentence contains a
codeline term.
This paragraph has just been thrown in to
ensure that it is styled correctly. It has nothing to say, but is long
anwyay, just to make sure that it continues to the next line.
Example 3
<html>
<head>
<title>Codeblock within the example tag</title>
</head>
<body bgcolor="#ffffff" link="#990000">
Example 4 Example List in Example- This is an enumerated list item.
- This is another item with a list inside of it.
- This is a bulleted list item
- This is another bulleted list item
Example 6
Table of Fourier Representations
| Transform |
Time Domain |
Frequency Domain |
Convolution |
| Continuous-Time Fourier Series |
L
2
0T
L
2
0
T
|
l
2
ℤ
l
2
|
Continuous-Time Circular |
| Continuous-Time Fourier Transform |
L
2
ℝ
L
2
|
L
2
ℝ
L
2
|
Continuous-Time Linear |
| Discrete-Time Fourier Transform |
l
2
ℤ
l
2
|
L
2
02π
L
2
0
2
|
Discrete-Time Linear |
| Discrete Fourier Transform |
l
2
0N-1
l
2
0
N
1
|
l
2
0N-1
l
2
0
N
1
|
Discrete-Time Circular |
Example 7
Definition 2:
note
A short letter.
Example Bob, Your son called. -Mary
theorem 2: Pythagorean Theorem
On a right triangle, the sum of the
squares of the sides equals the square of the hypotenus.
Proof:
proof name
Your favorite proof goes here.
Example
Take a right triangle whose sides are of length 3, 4, and 5.
In this case the sum of the square of the two shorter sides is
9+16=25. The square of the hypotenus is 25. So the theorem holds.
warning: Sulfuric and Hydrochloric Acid are very
dangerous. Please hande with caution.
note: Sulfuric and Hydrochloric Acid are very
dangerous. Please hande with caution.
Exercise
Problem 1
Express a square wave having period
T
T
and amplitude
A
A
as a superposition of delayed and amplitude-scaled pulses.
[
Click for Solution 1 ]
Solution 1
This is a paragraph that begins a
solution. The equation is nested in the paragraph.
t=∑n=-∞∞-1nA
p
T
/
2
t-nT2
t
n
1
n
A
p
T
/
2
t
n
T
2
(9)
[
Hide Solution 1 ]
Problem 2
This equation has been thrown in as a child of problem for styling purposes
cos2πft=ⅇⅈ2πft+ⅇ-ⅈ2πft2
2
f
t
2
f
t
2
f
t
2
(10)
[
Click for Solution 2 ]
Solution 2
The solution is to use Mozilla, and not IE, nor Netscape. The latter two browsers have serious CSS bugs. For an equation inside a solution, see the above exercise.
[
Hide Solution 2 ]
Codeline and Codeblock
Try running this in MATLAB.
for n=1:1000
y(n) = sum(a.*y(n-1:-1:n-p)) + sum(b.*x(n:-1:n-q));
end
The for command repeats its contents while
incrementing a counter.
<!-- some codeline and codeblock are
emphasized more than others -->
codeblock
can be
linked and
cnxn'ed
as well
Definition, Term, Meaning, and Example
Definition 3:
note
1. A short letter.
Example Bob, Your son called. -Mary
2. A different meaning for the term.
Example A second example.
I can also define a new term in the middle of a
sentence. A term is a new word that is being defined for the
first time.
The following definition will be the
child of a <para> tag to ensure that it
is styled well.
Definition 4:
#!/usr/local/bin/perl/
The first line of every Perl program
Example This program will produce a 2-column
listing of a file.
#!/usr/local/bin/perl/
while( $1 = >STDIN> ) {
chop( $1 );
if( $1 =~ s/^Desig:\s+// ) {
$desig = $1;
next;
}
if( $1 =~ s/^Area:\s+// ) {
$area = $1;
printf( "%-12s %\n", $desig, $area );
}
}
This sentence contains a term which is half regular
half codeline.
Feast your eyes on this:
#!/usr/local/bin/perl/ is a term
smack dab in the middle of a sentence! Amazing! This example,
#!/usr/local/bin/perl/
, is a codeline term with emphasis on
/local/. The next example is a
codeline term with a link
and cnxn.
Definition 5:
equation
This equation has been thrown in as a child of meaning for styling purposes
cos2πft=ⅇⅈ2πft+ⅇ-ⅈ2πft2
2
f
t
2
f
t
2
f
t
2
(11)
Note
Chemistry lab was always a lot of fun. We played
with a lot of chemicals such as Sulfuric and Hydrochloric acid.
warning: Sulfuric and Hydrochloric Acid are very
dangerous. Please handle with caution.
Chemistry lab was always a lot of fun. We played
with a lot of chemicals such as Sulfuri and Hydrochloric acid.
Note:
This note does not have a type attribute.
Please handle with caution.
Chemistry lab was always a lot of fun. We played
with a lot of chemicals such as Sulfuric and Hydrocholic acid.
Adding another footnote here.
Chemistry lab was always a lot of fun. We played
with a lot of chemicals such as Sulfuric and Hydrocholic acid.
FOOTNOTE: Sulfuric and Hydrochloric Acid are very
dangerous. Please handle with caution. Also handle this note with caution, because it contains the attribute type="FOOTNOTE", not type="footnote", and will thus be styled differently.
Rule
theorem 3: Pythagorean Theorem
On a right triangle, the sum of the
squares of the sides equals the square of the hypotenus.
Proof:
This proof was thrown into to have a child of equation for styling purposes
cos2πft=ⅇⅈ2πft+ⅇ-ⅈ2πft2
2
f
t
2
f
t
2
f
t
2
(12)
Example
Take a right triangle whose sides are of length 3, 4, and 5.
In this case the sum of the square of the two shorter sides is
9+16=25. The square of the hypotenus is 25. So the theorem holds.
property 1
If
st
s
t
is real,
c
−
k
=
c
k
*
c
−
k
c
k
*
This result follows from the integral that calculates the
c
k
c
k
from the signal. Furthermore, this result means that
Re
c
k
=Re
c
−
k
Re
c
k
Re
c
−
k
: The real part of the Fourier coefficients for real-valued signals is even. Similarly,
Im
c
k
=-Im
c
−
k
Im
c
k
Im
c
−
k
: The imaginary parts of the Fourier coefficients have odd symmetry. Consequently,
if you are given the Fourier coefficients for positive indices and zero and are
told the signal is real-valued, you can find the negative-indexed coefficients,
hence the entire spectrum. This kind of symmetry,
c
−
k
=
c
k
*
c
−
k
c
k
*
, is known as
conjugate symmetry. We can phrase the property concisely by
saying:
property 2
Real-valued periodic signals have a conjugate-symmetric spectrum.
The Fourier series obeys:
theorem 4: Parseval's Theorem
Power calculated in the time domain
equals the power calculated in the frequency domain.
Cite
Useful information about the color blue can be found in
The Big Book of the Color Blue.
Emphatic information about emphasizing can be found in The
Gigantic Book of Emphasis.
Tables
Here's is a very simple example of a table, similiar to ones
seen previously in this module.
Budget - Comparison by year
| Item |
Year |
| 1998 |
1999 |
2000 |
| Income |
12,293 |
12,398 |
14,298 |
| Expenditure |
293 |
398 |
298 |
| Surplus |
12000 |
12000 |
14000 |
Quotes and Foreign Terms
Two new elements added in CNXML 0.5 are
quote and
foreign. A
quote of type "block" might look like this:
I define the real as that which holds its characters on such a tenure that it makes not the slightest difference what any man or men may have thought them to be, or ever will have thought them to be, here using thought to include, imagining, opining, and willing (as long as forcible means are not used); but the real thing's characters will remain absolutely untouched. --C.S. Peirce, Collected Papers 6.495.
Anyone involved in interface design and usability should consider Einstein's axiom (shown here in a
quote of type 'inline'):
Everything should be made as simple as possible, but not one bit simpler.
In order to appear urbane and literate, we should liberally sprinkle our discourse with foreign terms and phrases, such as Fahrvergnügen and sang-froid.
irrelevant: It is possible to include a block quote inside a note, with
foreign elements interspersed:
"Freundschaftsbezeigungen" seems to be "Friendship demonstrations," which is only a foolish and clumsy way of saying "demonstrations of friendship." "Unabhängigkeitserklärungen" seems to be "Independencedeclarations," which is no improvement upon "Declarations of Independence," so far as I can see. "Generalstaatsverordnetenversammlungen" seems to be "General-statesrepresentativesmeetings," as nearly as I can get at it -- a mere rhythmical, gushy euphuism for "meetings of the legislature," I judge. --Mark Twain, "The Awful German Language"
Conclusion
For more information on all of the CNXML used in this
module, please refer to the
CNXML Spec.
Glossary
glossary:
A listing of terms together with their meanings.