Angel Canales, Solo sé que tiene nombre de mujer

Angel Canales, Solo sé que tiene nombre de mujer

Solo sé que tiene nombre de mujer, solo sé que tiene nombre de mujer,
solo sé que vive que respira y anda que es una esperanza para mi amanecer,
solo sé que vive que respira y anda que es una esperanza para mi amanecer.

Solo sé que tiene canela en su piel, ay solo se que tiene canela en su piel,
sus labios rosados y en sus ojos miel, sus labios rosados y en sus ojos miel,
que sobre su pecho tengo fino estampa su pelo azabache le suele caer,
que sobre su pecho tengo fino estampa su pelo azabache le suele caer
No sé donde se encuentra pero la buscaré,
ay no sé donde se encuentra pero la buscaré,
y si se me esconde yo la encontraré, y si se me esconde yo la encontraré,

Desde que yo creo en su existencia que tengo la esperanza de volverla a ver,
desde que yo creo en su existencia que tengo la esperanza de volverla a ver.

Aaaaaaaaabreme la pueeeerta , abreme la puerta buena
buena suerte mira que yo la quiero volver a ver.

Coro:
Abreme la puerta buena suerte que yo la quiero volver a ver
Yo quiero, yo quiero, yo quiero concocer a esa mujer por que yo quiero ser su negro

Abreme la puerta buena suerte que yo la quiero volver a ver
Yo quiero yo quiero yo quiero conocerla por que la quiero sacar a comer

Abreme la puerta buena suerte que yo la quiero volver a ver
abreme la puerta buena suerte mira que yo la quiero volver a ver.

eeeeeeeehh
aleeleeleelelele alaleleeeeaa

aaaaabreme la puerta buena suerte mira que yo la quiero, la quiero, la quiero, la quiero,
la quiero, la quiero volver a ver

ábreme la puerta buena suerte que yo la quiero verla
yo quiero ir la a bailar con ella, yo quiero también sacarla a comer

ábreme la puerta buena suerta que yo la quiero volver a ver
y cuando yo me encuentre con ella te juro que la voy hacer mi mujer

ábreme la puerta buena suerta que yo la quiero volver a ver
ábreme la puerta, ábreme la puerta,
ábreme la puerta buena suerte mira que aqui afuera
se encuentra tu querer.

Angel canales Hace tiempo

Angel canales, Hace tiempo

Hace tiempo que no duermo... tú ve
Porque estoy pensando en ti
Y es lo mucho que te quiero, mamá
Y tú no me quiere a mí.

Muchas mamis que me invitan... tú ve
Pero yo me muero por ti
No me hagas sufrir tanto, no, no
Ay, no me hagas padecer así.

(Ay, ay, ay, no me haga padecer así)
Ay, eche mozo más vinillo
Mire que me quiero emborrachar
(Ay, ay, ay) Ay, pero que ay, ay, ay
(No me haga padecer así)
Oye, por qué mi vida se ha ido tras de aquella
Ay, que no supo mi amor nunca apreciar
(Ay, ay, ay) Ay, pero que ay, ay, ay
(No me haga padecer así)
Ay, mamita, dame tu cosita, oye mami
Ay, que dame, dame, que dámela
(Ay, ay, ay) Ay, como una vida entera
(No me haga padecer así)
Oye, porque una vida entera, morena
La rumba buena contigo yo quiero bailar.

Ay, pero que quítate la ropa
Y ven y monta mi caballito, mira que es bien mansito.

La hora de Ricaldo…

Nooooo... ay, no o o o
(Ay, ay, ay) Ay, pero que ay, ay, ay
(No me haga padecer así)
Ay, nooooo… ay, no o o o
(Ay, ay, ay) Ay, pero que ay, ay, ay
(No me haga padecer así)
Oye, mamita, que a mí me da el sol en el alumbrado
Cuando te encuentro yo aquí a mi lado
(Ay, ay, ay) Ay, pero que ay, ay, ay
(No me haga padecer así)
Ay, pero así no me haga padecer
Ay, no me hagas así padecer
(Ay, ay, ay) Ay, que ay, ay, ay
(No me haga padecer así)
Ay, mamita, ay dame tu cosita, mami
(No me haga padecer así)
Ay, pero que no me haga padecer así, pero que no
(No me haga padecer así)
ay mamita mira que te llevo en mi corazón
(No me haga padecer así)
Lleva! Oh…oh.

Ya, pa’ que no haya más discusión
(No me haga padecer así)
Ay, no me haga mami, no o o
(No me haga padecer así)
Oye, que to’a la noche yo le rezo al santo
Al santo loco y de rodillas
(No me haga padecer así)
Pero que de rodillas yo le pido cosas buena
Y que vuelvas a mí
(No me haga padecer así)
Ay, pero que no haga, no
(No me haga padecer así)
Ay, no me haga padecer así, mami, no…

Planteamiento del problema de la paz en Colombia

Planteamiento del problema de la paz en Colombia

Habilitar USB en Android para transferencia de datos How to Enable USB Storage on Android Devices

http://www.infonucleo.com/2012/02/17/como-leer-la-tarjeta-de-memoria-microsd-en-el-samsung-galaxy-mini-desde-la-pc-usando-usb/

Como leer la tarjeta de memoria MicroSD en el Samsung Galaxy Mini desde la PC (usando USB)

Hoy quise acceder desde la PC a la tarjeta de memoria externa Micro SD de mi Samsung Galaxy Mini para transferir música y resulta que no es tan sencillo como debería ser, no basta con solo conectar el cable al móvil y a la PC, de hecho tuve que seguir algunos pasos que detallo a continuación:
En primer lugar desconectar el cable USB del móvil y la PC
Ir a “Configuración” o “Ajustes” luego entrar a “Aplicaciones” y luego a “Desarrollo” aquí debemos DESMARCAR donde dice “Depuración USB”

Conectar el cable USB al móvil y la PC, en algunos casos se vuelve a marcar “Depuración USB”, hay que volver a DESMARCAR esta opción
Aparecerá el ícono de Android  y un botón que dice “Activar el almacenamiento USB”, hacemos click en este botón y ya podremos ver desde la PC el contenido de nuestra tarjeta Micro SD, pasar música, vídeos, libros o lo que queramos.

Ojo, si no aparece el ícono de Android (como me sucedió a mi) deslicen la bandeja de notificaciones de la parte superior de la pantalla y allí verán que dice: “USB conectado. Seleccionar para copiar…bla bla” clickean allí y obtendrán la pantalla con el ícono de Android que menciono en el punto anterior, allí siguen el procedimiento tal cual he mencionado.
Espero con esto solucionar el problema de como acceder a la memoria Micro SD en el Samsung Galaxy Mini (y otros smartphones Samsung) desde la PC.
Cualquier comentario, duda o sugerencia es siempre bienvenido!.

5 Tools to Introduce Programming to Kids

http://blogs.kqed.org/mindshift/2011/05/5-tools-to-introduce-programming-to-kids/

5 Tools to Introduce Programming to Kids

May 16, 2011 | 9:39 AM | By Audrey Watters

• Print
• 38 Comments
• inShare21
• Email Post

Arduino

It’s hard to argue with the importance of teaching students how to use computers — how to turn on, log on, search the Web, and use applications. These skills are absolutely necessary for students’ academic success as well as for their future job prospects.
Being able to use the Internet and operate computers is one thing, but it may be just as valuable to teach students how to code. Giving students an introduction to programming helps peel back the layers of what happens inside computers and how computers communicate with one another online. Programming knowledge, even at a very basic level, makes technology seem less magical and more manageable. Programming also teaches other important skills, including math and logic.
Many students don’t have access to computer science courses until college, and that’s a missed opportunity to introduce younger students to programming. There are many tools out there that provide a great introduction to computer science for K-12 students, but here are a few of our favorites.
SCRATCH
Developed by the MIT Media Lab, Scratch is a visual programming language for children age 6 and up. Since its release in 2007, over 800,000 users have joined the Scratch website and have shared over 1.7 million projects — from games to animations. That sharing aspect is an important part of the Scratch community, so the projects that are uploaded to the site are licensed under the Creative Commons attribute and share alike license so that others can download and remix them. Scratch is available free of charge and runs on Mac, Windows, and Linux computers.
ALICE
Alice is a free and open source 3D programming environment designed to teach students object-oriented and event-driven programming. With Alice, students drag and drop graphic tiles in order to animate an object and create a program. A variant of Alice, Storytelling Alice was developed by Caitlin Kelleher as part of her doctoral work in Computer Science at Carnegie Mellon University. By emphasizing animations and social interactions, this approach was found to greatly increase the level of student interest in programming.
HACKETY HACK
Hackety Hack is an open source application that teaches the basics of programming in the popular Ruby language. Hackety Hack offers an interactive tutorial that runs on Windows, Mac, and Linux operating systems. While both Scratch and Alice use a graphical programming language with “blocks,” Hackety Hack teaches the basics of Ruby syntax. The tutorial and the text editor are well-integrated, so there isn’t any flipping back-and-forth to move between the How-To guide and the actual coding. Hackety Hack gives students a solid foundation in the language so they can quickly and easily start building their own apps in Ruby.
ARDUINO
Arduino is an open-source electronics prototyping platform with both hardware and software components. Arduino’s hardware is programmed with a language similar to C++, and although it may not be the easiest of entry points for learning programming, there’s something about building things that actually move that can be pretty compelling. Projects that use Arduino to introduce children to programming include a modification of Scratch to support simple programming on the Arduino hardware. As Google recently announced that it would allow Android mobile devices to communicate with Arduino hardware, look for more opportunities to work with this platform in the future, perhaps even via the Android App Inventor, a tool that provides a visual interface for building Android apps.
LEGO MINDSTORMS
One of the most popular toys in history, Lego may be best known for its brick-building. But Lego Mindstorms also enables robotics-building. Lego Mindstorms’ kits — which can be purchased in educational and consumer versions — include sensors and motors, and the programming is command-box rather than code programming. The kits come with languages supplied by Lego, but can be modified to work with third party languages. Like several of the tools on this list, Lego Mindstorms has its roots at the MIT Media Lab.
These are just a few of the options for introducing someone to programming. What other languages or tools have you used — in the classroom or at home?

FILED UNDER: Teaching With Tech, Alice, Arduino, Hackety Hack, Lego, programming, Ruby, Scratch

bash script tutorial

http://linuxconfig.org/Bash_scripting_Tutorial

bash script tutorial

Last Updated on Wednesday, 02 November 2011 06:35

Article Index
1. Hello World Bash Shell Script
2. Simple Backup bash shell script
3. Variables
3.1. Global vs. Local variables
4. Passing arguments to the bash script
5. Executing shell commands with bash
6. Reading User Input
7. Bash Trap Command
8. Arrays
8.1. Declare simple bash array
8.2. Read file into bash array
9. Bash if / else / fi statements
9.1. Simple Bash if/else statement
9.2. Nested if/else
10. Bash Comparisons
10.1. Arithmetic Comparisons
10.2. String Comparisons
11. Bash File Testing
12. Loops
12.1. Bash for loop
12.2. Bash while loop
12.3. Bash until loop
12.4. Control bash loop with
13. Bash Functions
14. Bash Select
15. Case statement conditional
16. Bash quotes and quotations
16.1. Escaping Meta characters
16.2. Single quotes
16.3. Double Quotes
16.4. Bash quoting with ANSI-C style
17. Arithmetic Operations
17.1. Bash Addition Calculator Example
17.2. Bash Arithmetics
17.3. Round floating point number
17.4. Bash floating point calculations
18. Redirections
18.1. STDOUT from bash script to STDERR
18.2. STDERR from bash script to STDOUT
18.3. stdout to screen
18.4. stdout to file
18.5. stderr to file
18.6. stdout to stderr
18.7. stderr to stdout
18.8. stderr and stdout to file

>PDF DOWNLOAD< >PDF DOWNLOAD<

This bash script tutorial assumes no previous knowledge of bash scripting.As you will soon discover in this quick comprehensive bash scripting guide, learning the bash shell scripting is very easy task. However, if you do not find an answer to your questions by reading this bash tutorial or you need extra help, feel free to ask us on our new Linux Forum. We will be more than happy to help you with your bash questions there. Lets begin this bash scripting tutorial with a simple "Hello World" script. Let's start with Learning the bash Shell: Unix Shell Programming Bash Scripting Beginners Guide FREE PDF DOWNLOAD Bash Scripting Advanced Guide FREE PDF DOWNLOAD

1. Hello World Bash Shell Script

First you need to find out where is your bash interpreter located. Enter the following into your command line:

$ which bash

Open up you favorite text editor and a create file called hello_world.sh. Insert the following lines to a file:
NOTE:Every bash shell script in this tutorial starts with shebang:"#!" which is not read as a comment. First line is also a place where you put your interpreter which is in this case: /bin/bash.
Here is our first bash shell script example:

#!/bin/bash
# declare STRING variable
STRING="Hello World"
#print variable on a screen
echo $STRING

Navigate to a directory where your hello_world.sh is located and make the file executable:

$ chmod +x hello_world.sh 

Now you are ready to execute your first bash script:

./hello_world.sh 

2. Simple Backup bash shell script

#!/bin/bash
tar -czf myhome_directory.tar.gz /home/linuxconfig

3. Variables

In this example we declare simple bash variable and print it on the screen ( stdout ) with echo command.

#!/bin/bash
 STRING="HELLO WORLD!!!"
 echo $STRING 

Your backup script and variables:

#!/bin/bash
 OF=myhome_directory_$(date +%Y%m%d).tar.gz
 tar -czf $OF /home/linuxconfig 

3.1. Global vs. Local variables

#!/bin/bash
#Define bash global variable
#This variable is global and can be used anywhere in this bash script
VAR="global variable"
function bash {
#Define bash local variable
#This variable is local to bash function only
local VAR="local variable"
echo $VAR
}
echo $VAR
bash
# Note the bash global variable did not change
# "local" is bash reserved word
echo $VAR

4. Passing arguments to the bash script

#!/bin/bash
# use predefined variables to access passed arguments
#echo arguments to the shell
echo $1 $2 $3 ' -> echo $1 $2 $3'

# We can also store arguments from bash command line in special array
args=("$@")
#echo arguments to the shell
echo ${args[0]} ${args[1]} ${args[2]} ' -> args=("$@"); echo ${args[0]} ${args[1]} ${args[2]}'

#use $@ to print out all arguments at once
echo $@ ' -> echo $@'

# use $# variable to print out
# number of arguments passed to the bash script
echo Number of arguments passed: $# ' -> echo Number of arguments passed: $#' 

/arguments.sh Bash Scripting Tutorial 

5. Executing shell commands with bash

#!/bin/bash
# use backticks " ` ` " to execute shell command
echo `uname -o`
# executing bash command without backticks
echo uname -o 

6. Reading User Input

#!/bin/bash
 
echo -e "Hi, please type the word: \c "
read  word
echo "The word you entered is: $word"
echo -e "Can you please enter two words? "
read word1 word2
echo "Here is your input: \"$word1\" \"$word2\""
echo -e "How do you feel about bash scripting? "
# read command now stores a reply into the default build-in variable $REPLY
read
echo "You said $REPLY, I'm glad to hear that! "
echo -e "What are your favorite colours ? "
# -a makes read command to read into an array
read -a colours
echo "My favorite colours are also ${colours[0]}, ${colours[1]} and ${colours[2]}:-)" 

7. Bash Trap Command

#!/bin/bash # bash trap command trap bashtrap INT # bash clear screen command clear; # bash trap function is executed when CTRL-C is pressed: # bash prints message => Executing bash trap subrutine ! bashtrap() { echo "CTRL+C Detected !...executing bash trap !" } # for loop from 1/10 to 10/10 for a in `seq 1 10`; do echo "$a/10 to Exit." sleep 1; done echo "Exit Bash Trap Example!!!"

8. Arrays

8.1. Declare simple bash array

#!/bin/bash
#Declare array with 4 elements
ARRAY=( 'Debian Linux' 'Redhat Linux' Ubuntu Linux )
# get number of elements in the array
ELEMENTS=${#ARRAY[@]}

# echo each element in array 
# for loop
for (( i=0;i<$ELEMENTS;i++)); do
    echo ${ARRAY[${i}]}
done 

8.2. Read file into bash array

#!/bin/bash
# Declare array
declare -a ARRAY
# Link filedescriptor 10 with stdin
exec 10<&0
# stdin replaced with a file supplied as a first argument
exec < $1
let count=0

while read LINE; do

    ARRAY[$count]=$LINE
    ((count++))
done

echo Number of elements: ${#ARRAY[@]}
# echo array's content
echo ${ARRAY[@]}
# restore stdin from filedescriptor 10
# and close filedescriptor 10
exec 0<&10 10<&-

Bash script execution with an output:

linuxconfig.org $ cat bash.txt 
Bash
Scripting
Tutorial
Guide
linuxconfig.org $ ./bash-script.sh bash.txt 
Number of elements: 4
Bash Scripting Tutorial Guide
linuxconfig.org $ 

9. Bash if / else / fi statements

9.1. Simple Bash if/else statement

Please note the spacing inside the [ and ] brackets! Without the spaces, it won't work!

#!/bin/bash
directory="./BashScripting"

# bash check if directory exists
if [ -d $directory ]; then
 echo "Directory exists"
else 
 echo "Directory does not exists"
fi 

9.2. Nested if/else

#!/bin/bash
 
# Declare variable choice and assign value 4
choice=4
# Print to stdout
 echo "1. Bash"
 echo "2. Scripting"
 echo "3. Tutorial"
 echo -n "Please choose a word [1,2 or 3]? "
# Loop while the variable choice is equal 4
# bash while loop
while [ $choice -eq 4 ]; do
 
# read user input
read choice
# bash nested if/else
if [ $choice -eq 1 ] ; then
 
        echo "You have chosen word: Bash"

else                   

        if [ $choice -eq 2 ] ; then
                 echo "You have chosen word: Scripting"
        else
         
                if [ $choice -eq 3 ] ; then
                        echo "You have chosen word: Tutorial"
                else
                        echo "Please make a choice between 1-3 !"
                        echo "1. Bash"
                        echo "2. Scripting"
                        echo "3. Tutorial"
                        echo -n "Please choose a word [1,2 or 3]? "
                        choice=4
                fi   
        fi
fi
done 

10. Bash Comparisons

10.1. Arithmetic Comparisons

-lt	<
-gt	>
-le	<=
-ge	>=
-eq	==
-ne	!=

#!/bin/bash
# declare integers
NUM1=2
NUM2=2
if [ $NUM1 -eq $NUM2 ]; then
 echo "Both Values are equal"
else 
 echo "Values are NOT equal"
fi 

#!/bin/bash
# declare integers
NUM1=2
NUM2=1
if [ $NUM1 -eq $NUM2 ]; then
 echo "Both Values are equal"
else 
 echo "Values are NOT equal"
fi 

#!/bin/bash
# declare integers
NUM1=2
NUM2=1
if   [ $NUM1 -eq $NUM2 ]; then
 echo "Both Values are equal"
elif [ $NUM1 -gt $NUM2 ]; then
 echo "NUM1 is greater then NUM2"
else 
 echo "NUM2 is greater then NUM1"
fi 

10.2. String Comparisons

=	equal
!=	not equal
<	less then
>	greater then
-n s1	string s1 is not empty
-z s1	string s1 is empty

#!/bin/bash
#Declare string S1
S1="Bash"
#Declare string S2
S2="Scripting"
if [ $S1 = $S2 ]; then
 echo "Both Strings are equal"
else 
 echo "Strings are NOT equal"
fi 

#!/bin/bash
#Declare string S1
S1="Bash"
#Declare string S2
S2="Bash"
if [ $S1 = $S2 ]; then
 echo "Both Strings are equal"
else 
 echo "Strings are NOT equal"
fi 

11. Bash File Testing

-b filename	Block special file
-c filename	Special character file
-d directoryname	Check for directory existence
-e filename	Check for file existence
-f filename	Check for regular file existence not a directory
-G filename	Check if file exists and is owned by effective group ID.
-g filename	true if file exists and is set-group-id.
-k filename	Sticky bit
-L filename	Symbolic link
-O filename	True if file exists and is owned by the effective user id.
-r filename	Check if file is a readable
-S filename	Check if file is socket
-s filename	Check if file is nonzero size
-u filename	Check if file set-ser-id bit is set
-w filename	Check if file is writable
-x filename	Check if file is executable

#!/bin/bash
file="./file"
if [ -e $file ]; then
 echo "File exists"
else 
 echo "File does not exists"
fi 

Similarly for example we can use while loop to check if file does not exists. This script will sleep until file does exists. Note bash negator "!" which negates the -e option.

#!/bin/bash
 
while [ ! -e myfile ]; do
# Sleep until file does exists/is created
sleep 1
done 

12. Loops

12.1. Bash for loop

#!/bin/bash

# bash for loop
for f in $( ls /var/ ); do
 echo $f
done 

Running for loop from bash shell command line:

$ for f in $( ls /var/ ); do echo $f; done 

12.2. Bash while loop

#!/bin/bash
COUNT=6
# bash while loop
while [ $COUNT -gt 0 ]; do
 echo Value of count is: $COUNT
 let COUNT=COUNT-1
done 

12.3. Bash until loop

#!/bin/bash
COUNT=0
# bash until loop
until [ $COUNT -gt 5 ]; do
        echo Value of count is: $COUNT
        let COUNT=COUNT+1
done 

12.4. Control bash loop with

Here is a example of while loop controlled by standard input. Until the redirection chain from STDOUT to STDIN to the read command exists the while loop continues.

#!/bin/bash
# This bash script will locate and replace spaces
# in the filenames
DIR="."
# Controlling a loop with bash read command by redirecting STDOUT as
# a STDIN to while loop
# find will not truncate filenames containing spaces
find $DIR -type f | while read file; do
# using POSIX class [:space:] to find space in the filename
if [[ "$file" = *[[:space:]]* ]]; then
# substitute space with "_" character and consequently rename the file
mv "$file" `echo $file | tr ' ' '_'`
fi;
# end of while loop
done 

13. Bash Functions

!/bin/bash
# BASH FUNCTIONS CAN BE DECLARED IN ANY ORDER
function function_B {
        echo Function B.
}
function function_A {
        echo $1
}
function function_D {
        echo Function D.
}
function function_C {
        echo $1
}
# FUNCTION CALLS
# Pass parameter to function A
function_A "Function A."
function_B
# Pass parameter to function C
function_C "Function C."
function_D 

14. Bash Select

#!/bin/bash
 
PS3='Choose one word: ' 

# bash select
select word in "linux" "bash" "scripting" "tutorial" 
do
  echo "The word you have selected is: $word"
# Break, otherwise endless loop
  break  
done

exit 0 

15. Case statement conditional

#!/bin/bash
echo "What is your preferred programming / scripting language"
echo "1) bash"
echo "2) perl"
echo "3) phyton"
echo "4) c++"
echo "5) I do not know !"
read case;
#simple case bash structure
# note in this case $case is variable and does not have to
# be named case this is just an example
case $case in
    1) echo "You selected bash";;
    2) echo "You selected perl";;
    3) echo "You selected phyton";;
    4) echo "You selected c++";;
    5) exit
esac 

16. Bash quotes and quotations

Quotations and quotes are important part of bash and bash scripting. Here are some bash quotes and quotations basics.

16.1. Escaping Meta characters

Before we start with quotes and quotations we should know something about escaping meta characters. Escaping will suppress a special meaning of meta characters and therefore meta characters will be read by bash literally. To do this we need to use backslash "\" character. Example:

#!/bin/bash
 
#Declare bash string variable
BASH_VAR="Bash Script"

# echo variable BASH_VAR
echo $BASH_VAR

#when meta character such us "$" is escaped with "\" it will be read literally
echo \$BASH_VAR 

# backslash has also special meaning and it can be suppressed with yet another "\"
echo "\\" 

16.2. Single quotes

Single quotes in bash will suppress special meaning of every meta characters. Therefore meta characters will be read literally. It is not possible to use another single quote within two single quotes not even if the single quote is escaped by backslash.

#!/bin/bash
 
 #Declare bash string variable
 BASH_VAR="Bash Script"
 
 # echo variable BASH_VAR
 echo $BASH_VAR
 
 # meta characters special meaning in bash is suppressed when  using single quotes 
 echo '$BASH_VAR  "$BASH_VAR"' 

16.3. Double Quotes

Double quotes in bash will suppress special meaning of every meta characters except "$", "\" and "`". Any other meta characters will be read literally. It is also possible to use single quote within double quotes. If we need to use double quotes within double quotes bash can read them literally when escaping them with "\". Example:

#!/bin/bash
 
#Declare bash string variable
BASH_VAR="Bash Script"

# echo variable BASH_VAR
echo $BASH_VAR

# meta characters and its special meaning in bash is 
# suppressed when using double quotes except "$", "\" and "`"

echo "It's $BASH_VAR  and \"$BASH_VAR\" using backticks: `date`" 

16.4. Bash quoting with ANSI-C style

There is also another type of quoting and that is ANSI-C. In this type of quoting characters escaped with "\" will gain special meaning according to the ANSI-C standard.

\a	alert (bell)	\b	backspace
\e	an escape character	\f	form feed
\n	newline	\r	carriage return
\t	horizontal tab	\v	vertical tab
\\	backslash	\`	single quote
\nnn	octal value of characters ( see [http://www.asciitable.com/ ASCII table] )	\xnn	hexadecimal value of characters ( see [http://www.asciitable.com/ ASCII table] )

The syntax fo ansi-c bash quoting is: $'' . Here is an example:

#!/bin/bash
 
# as a example we have used \n as a new line, \x40 is hex value for @
# and \56 is octal value for .
echo $'web: www.linuxconfig.org\nemail: web\x40linuxconfig\56org' 

17. Arithmetic Operations

17.1. Bash Addition Calculator Example

#!/bin/bash
 
let RESULT1=$1+$2
echo $1+$2=$RESULT1 ' -> # let RESULT1=$1+$2'
declare -i RESULT2
RESULT2=$1+$2
echo $1+$2=$RESULT2 ' -> # declare -i RESULT2; RESULT2=$1+$2'
echo $1+$2=$(($1 + $2)) ' -> # $(($1 + $2))' 

17.2. Bash Arithmetics

#!/bin/bash
 
echo '### let ###'
# bash addition
let ADDITION=3+5
echo "3 + 5 =" $ADDITION

# bash subtraction
let SUBTRACTION=7-8
echo "7 - 8 =" $SUBTRACTION 

# bash multiplication
let MULTIPLICATION=5*8
echo "5 * 8 =" $MULTIPLICATION

# bash division
let DIVISION=4/2
echo "4 / 2 =" $DIVISION

# bash modulus
let MODULUS=9%4
echo "9 % 4 =" $MODULUS

# bash power of two
let POWEROFTWO=2**2
echo "2 ^ 2 =" $POWEROFTWO


echo '### Bash Arithmetic Expansion ###'
# There are two formats for arithmetic expansion: $[ expression ] 
# and $(( expression #)) its your choice which you use

echo 4 + 5 = $((4 + 5))
echo 7 - 7 = $[ 7 - 7 ]
echo 4 x 6 = $((3 * 2))
echo 6 / 3 = $((6 / 3))
echo 8 % 7 = $((8 % 7))
echo 2 ^ 8 = $[ 2 ** 8 ]


echo '### Declare ###'

echo -e "Please enter two numbers \c"
# read user input
read num1 num2
declare -i result
result=$num1+$num2
echo "Result is:$result "

# bash convert binary number 10001
result=2#10001
echo $result

# bash convert octal number 16
result=8#16
echo $result

# bash convert hex number 0xE6A
result=16#E6A
echo $result 

17.3. Round floating point number

#!/bin/bash
# get floating point number
floating_point_number=3.3446
echo $floating_point_number
# round floating point number with bash
for bash_rounded_number in $(printf %.0f $floating_point_number); do
echo "Rounded number with bash:" $bash_rounded_number
done 

17.4. Bash floating point calculations

#!/bin/bash
# Simple linux bash calculator 
echo "Enter input:" 
read userinput
echo "Result with 2 digits after decimal point:"
echo "scale=2; ${userinput}" | bc 
echo "Result with 10 digits after decimal point:"
echo "scale=10; ${userinput}" | bc 
echo "Result as rounded integer:"
echo $userinput | bc 

18. Redirections

18.1. STDOUT from bash script to STDERR

#!/bin/bash
 
 echo "Redirect this STDOUT to STDERR" 1>&2 

To prove that STDOUT is redirected to STDERR we can redirect script's output to file:

18.2. STDERR from bash script to STDOUT

#!/bin/bash
 
 cat $1 2>&1 

To prove that STDERR is redirected to STDOUT we can redirect script's output to file:

18.3. stdout to screen

The simple way to redirect a standard output ( stdout ) is to simply use any command, because by default stdout is automatically redirected to screen. First create a file "file1":

$ touch file1
$ ls file1 
file1

As you can see from the example above execution of ls command produces STDOUT which by default is redirected to screen.

18.4. stdout to file

The override the default behavior of STDOUT we can use ">" to redirect this output to file:

$ ls file1 > STDOUT
$ cat STDOUT 
file1

18.5. stderr to file

By default STDERR is displayed on the screen:

$ ls
file1  STDOUT
$ ls file2
ls: cannot access file2: No such file or directory

In the following example we will redirect the standard error ( stderr ) to a file and stdout to a screen as default. Please note that STDOUT is displayed on the screen, however STDERR is redirected to a file called STDERR:

$ ls
file1  STDOUT
$ ls file1 file2 2> STDERR
file1
$ cat STDERR 
ls: cannot access file2: No such file or directory

18.6. stdout to stderr

It is also possible to redirect STDOUT and STDERR to the same file. In the next example we will redirect STDOUT to the same descriptor as STDERR. Both STDOUT and STDERR will be redirected to file "STDERR_STDOUT".

$ ls
file1  STDERR  STDOUT
$ ls file1 file2 2> STDERR_STDOUT 1>&2
$ cat STDERR_STDOUT
ls: cannot access file2: No such file or directory
file1

File STDERR_STDOUT now contains STDOUT and STDERR.

18.7. stderr to stdout

The above example can be reversed by redirecting STDERR to the same descriptor as SDTOUT:

$ ls
file1  STDERR  STDOUT
$ ls file1 file2 > STDERR_STDOUT 2>&1
$ cat STDERR_STDOUT 
ls: cannot access file2: No such file or directory
file1

18.8. stderr and stdout to file

Previous two examples redirected both STDOUT and STDERR to a file. Another way to achieve the same effect is illustrated below:

$ ls
file1  STDERR  STDOUT
$ ls file1 file2 &> STDERR_STDOUT
$ cat STDERR_STDOUT 
ls: cannot access file2: No such file or directory
file1

or

ls file1 file2 >& STDERR_STDOUT
$ cat STDERR_STDOUT 
ls: cannot access file2: No such file or directory
file1

Writing Sheel Scripts Linux Unix

http://linuxcommand.org/writing_shell_scripts.php

LinuxCommand Learning the shell Writing shell scripts Script library SuperMan pages Who, What, Where, Why Tips, News And Rants	Previous | Contents | Next Here is where the fun begins With the thousands of commands available for the command line user, how can you remember them all? The answer is, you don't. The real power of the computer is its ability to do the work for you. To get it to do that, we use the power of the shell to automate things. We write scripts. Scripts are collections of commands that are stored in a file. The shell can read this file and act on the commands as if they were typed at the keyboard. In addition to the things you have learned so far, the shell also provides a variety of useful programming features to make your scripts truly powerful. What are scripts good for? A wide range of tasks can be automated. Here are some of the things I automate with scripts: A script gathers up all the files (over 2200) in this site on my computer and transmits them to my web server. The SuperMan pages are built entirely by a script. Every Friday night, all my computers copy their files to a "backup server" on my network. This is performed by a script. A script automatically gets the current updates from my Linux vendor and maintains a repository of vital updates. It sends me an email message with a report of tasks that need to be done. As you can see, scripts unlock the power of your Linux machine. So let's have some fun! Contents Writing your first script and getting it to work Writing a script Setting permissions Putting it in your path Editing the scripts you already have Commands, commands, everywhere Aliases Shell functions type .bashrc Here Scripts Writing an HTML file with a script Substitutions - Part 1 Variables How to create a variable Where does the variable's name come from? How does this increase our laziness? Environment Variables Substitutions - Part 2 --help and other tricks Assigning a command's result to a variable Constants Quoting Single and double quotes Quoting a single character Other backslash tricks Shell Functions Keep your scripts working Some Real Work show_uptime drive_space home_space system_info Flow Control - Part 1 if What is a "condition"? Exit status test exit Testing for root Stay Out of Trouble Empty variables Missing quotes Isolating problems Watching your script run Keyboard Input and Arithmetic read Arithmetic Flow Control - Part 2 More branching Loops Building a menu Positional Parameters Detecting command line arguments Command line options Getting an option's argument Integrating the command line processor into the script Adding interactive mode Flow Control - Part 3 Errors and Signals and Traps (Oh My!) - Part 1 Exit status Checking the exit status An error exit function AND and OR lists Improving the error exit function Errors and Signals and Traps (Oh My!) - Part 2 Cleaning up after yourself trap Signal 9 From Outer Space A clean_up function Creating safe temporary files Previous | Contents | Top | Next
	© 2000-2012, William E. Shotts, Jr. Verbatim copying and distribution of this entire article is permitted in any medium, provided this copyright notice is preserved. Linux® is a registered trademark of Linus Torvalds.

http://www.freeos.com/guides/lsst/

Linux Shell Scripting Tutorial v1.05r3 A Beginner's handbook Copyright © 1999-2002 by Vivek G. Gite <vivek@nixcraft.com> (Formally know as vivek-tech.com)

---

Table of Contents

Chapter 1: Quick Introduction to Linux

What Linux is?
Who developed the Linux?
How to get Linux?
How to Install Linux
Where I can use Linux?
What Kernel Is?
What is Linux Shell?
How to use Shell
What is Shell Script ?
Why to Write Shell Script ?
More on Shell...

Chapter 2: Getting started with Shell Programming

How to write shell script
Variables in shell
How to define User defined variables (UDV)
Rules for Naming variable name (Both UDV and System Variable)
How to print or access value of UDV (User defined variables)
echo Command
Shell Arithmetic
More about Quotes
Exit Status
The read Statement
Wild cards (Filename Shorthand or meta Characters)
More commands on one command line
Command Line Processing
Why Command Line arguments required
Redirection of Standard output/input i.e. Input - Output redirection
Pipes
Filter
What is Processes
Why Process required
Linux Command(s) Related with Process

Chapter 3: Shells (bash) structured Language Constructs

Decision making in shell script ( i.e. if command)
test command or [ expr ]
if...else...fi
Nested ifs
Multilevel if-then-else
Loops in Shell Scripts
for loop
Nested for loop
while loop
The case Statement
How to de-bug the shell script?

Chapter 4: Advanced Shell Scripting Commands

/dev/null - to send unwanted output of program
Local and Global Shell variable (export command)
Conditional execution i.e. && and ||
I/O Redirection and file descriptors
Functions
User Interface and dialog utility-Part I
User Interface and dialog utility-Part II
Message Box (msgbox) using dialog utility
Confirmation Box (yesno box) using dialog utility
Input (inputbox) using dialog utility
User Interface using dialog Utility - Putting it all together
trap command
The shift Command
getopts command

Chapter 5: Essential Utilities for Power User

Preparing for Quick Tour of essential utilities
Selecting portion of a file using cut utility
Putting lines together using paste utility
The join utility
Translating range of characters using tr utility
Data manipulation using awk utility
sed utility - Editing file without using editor
Removing duplicate lines from text database file using uniq utility
Finding matching pattern using grep utility

Chapter 6: Learning expressions with ex

Getting started with ex
Printing text on-screen
Deleting lines
Coping lines
Searching the words
Find and Replace (Substituting regular expression)
Replacing word with confirmation from user
Finding words
Using range of characters in regular expressions
Using & as Special replacement character
Converting lowercase character to uppercase

Chapter 7: awk Revisited

Getting Starting with awk
Predefined variables of awk
Doing arithmetic with awk
User Defined variables in awk
Use of printf statement
Use of Format Specification Code
if condition in awk
Loops in awk
Real life examples in awk
awk miscellaneous
sed - Quick Introduction
Redirecting the output of sed command
How to write sed scripts?
More examples of sed

Chapter 8: Examples of Shell Scripts

Logic Development:
Shell script to print given numbers sum of all digit
Shell script to print contains of file from given line number to next given number of lines
Shell script to say Good morning/Afternoon/Evening as you log in to system
Shell script to find whether entered year is Leap or not
Sort the given five number in ascending order (use of array)
Command line (args) handling:
Adding 2 nos. suppiled as command line args
Calculating average of given numbers on command line args
Finding out biggest number from given three nos suppiled as command line args
Shell script to implement getopts statement.
Basic math Calculator (case statement)
Loops using while & for loop:
Print nos. as 5,4,3,2,1 using while loop
Printing the patterns using for loop.
Arithmetic in shell scripting:
Performing real number calculation in shell script
Converting decimal number to hexadecimal number
Calculating factorial of given number
File handling:
Shell script to determine whether given file exist or not.
Screen handling/echo command with escape sequence code:
Shell script to print "Hello World" message, in Bold, Blink effect, and in different colors like red, brown etc.
Background process implementation:
Digital clock using shell script
User interface and Functions in shell script:
Shell script to implements menu based system.
System Administration:
Getting more information about your working environment through shell script
Shell script to gathered useful system information such as CPU, disks, Ram and your environment etc.
Shell script to add DNS Entery to BIND Database with default Nameservers, Mail Servers (MX) and host
Integrating awk script with shell script:
Script to convert file names from UPPERCASE to lowercase file names or vice versa.

Chapter 9: Other Resources

Appendix - A : Linux File Server Tutorial (LFST) version b0.1 Rev. 2
Appendix - B : Linux Command Reference (LCR)
About the author
About this Document

	Home	Next
	Up	Quick Introduction to Linux

Imagenes

http://www6.uniovi.es/vision/intro/node36.html
http://elgva1.usc.es/~mjose/docencia/3ciclo/tema1.htm
http://www.tsc.uc3m.es/imagine/Curso_ProcesadoBasico/Contenido/OperacionesPuntuales/OperacionesPuntuales.html#appletOperacionesPuntuales
http://alojamientos.us.es/gtocoma/pid/tema1-2.pdf
http://www.cs.buap.mx/~iolmos/pdi/Sesion3_Histograma.pdf

Electronic Chillout Voice - Sunlounger-The_Downtempo_Edition-2CD-2010-TGX

http://forum.funkysouls.com/dump/f54t40178n200.html

Sunlounger-The_Downtempo_Edition-2CD-2010-TGX



Artist ............ : Sunlounger
Title ............. : The Downtempo Edition

Genre ............. : Ambient
Label ............. : Armada Music
Catalog Number .... : ARMA232

Source ............ : CD
Quality ........... : 197kbps avg / 44.1KHz / Joint Stereo
Playtime .......... : 02:17:50 (194.MB)
Release Date ...... : 2010-01-20


[Track List]

Disc 1/2
--------
1. Sunlounger - Another Day On The Terrace 8:13
2. Sunlounger - In & Out 5:35
3. Sunlounger - White Sand 4:49
4. Sunlounger - Losing Again 5:14
5. Sunlounger feat. Seis Cuerdas - A Balearic Dinner 5:32
6. Sunlounger feat. Zara - Crawling 6:54
7. Sunlounger - Aguas Blancas 7:25
8. Sunlounger - Keep Our Ring 6:15
9. Sunlounger - Hierbas Ibicencas 5:10
10.Sunlounger - Lounging By The Sea 3:58
11.Sunlounger - Shine On Me 6:16
12.Sunlounger - Lumumba 5:39

Disc 2/2
--------
1. Sunlounger - Sunny Tales 6:01
2. Sunlounger feat. Kyler England - Change Your Mind 6:16
3. Sunlounger - Mediterranean Flower 5:33
4. Sunlounger feat. Zara - Lost 5:38
5. Sunlounger - Spiritual Hideout 5:44
6. Sunlounger feat. Cap & Stephanie Asscher - Heart of the Sun 6:45
7. Sunlounger - Punta Galera 4:29
8. Sunlounger feat. Lorilee - Your Name 4:54
9. Sunlounger - Catwalk 4:57
10.Sunlounger feat. Zara - Talk To me 6:46
11.Sunlounger & Ingsha feat. Simon Binkenborn - One More Day 6:01
12.Sunlounger feat. Seis Cuerdas - A Balearic Breakfast 3:46


[Release Notes]
There's a calmness under the warm waves of Roger Shah's music. Over the
past 4 years, the German music creator has warmed the trance scene with
several strong, Balearic trance productions. Whether played out in their
dance versions for the ten thousands of clubbers, or slipped into the
ears through home speakers or headphones in the chilled out lounge
versions, Shah's tracks have pleased crowds all across the globe.

Shah released some of his biggest productions under the Sunlounger
moniker. The very first Sunlounger track, 'White Sand' turned the heads
and made the trance scene wonder who managed to capture the Balearic
spirit so perfectly. Their need to hear more was fulfilled with two
complete Sunlounger albums, 'Another Day On The Terrace' in 2007,
followed by 'Sunny Tales' in 2008.

'Sunlounger - The Downtempo Edition' is a collection of the chill
versions of the tracks of both albums. 24 guitar-driven, melodic
infusions of pure sunlight captured in beats, synths and the true Shah
sound. Relax, ease your mind and slip this one into your player. Let the
Balearic senses take over completely, with Sunlounger as your guide.

Цитата:

DepositFiles.com LetitBit.net Rapidshare1 Rapidshare2 Rapidshare3 iFolder1 iFolder2 iFolder3

The 'Classic' Non-Recursive DIF FFT Routine.

http://www.engineeringproductivitytools.com/stuff/T0001/PT03.HTM#Head134

The 'Classic' Non-Recursive DIF FFT Routine.

For many processors/languages a recursive routine is not attractive, because of the overhead incurred by a procedure call. Be careful though, in reality an aversion to recursion could cost performance (see the note about cache efficiency). There is also a particular problem with DSP's which often have small hardware stacks, so deeply recursive routines will cause stack overflow. It is fairly easy to see that the above routine can be flattened into nested loops, to yield something resembling the 'classic' (non recursive) DIF FFT. Each DIF uses 2 'half size' DIF's, which in turn will use 4 'quarter size' DIF's, etc.. the last (not trivial) DIF will be for size 2. So, keeping notation consistent with the above recursive DIF, we get 3 nested loops:

• Pass Loop: An N (=2^p ) point transform will perform p 'passes', indexed by P=0..p-1.
• Block Loop: Pass will P operate on B_P (=2^P ) sub-blocks, each of size N_P (=N/B_P=2^p-P), indexed by b=0..B_P-1
• Butterfly Loop: Each sub-block operation will perform N'_P (=N_P/2=2^p-P-1) butterflies, indexed by n=0..N'_P-1.

{Perform in place DIF of 2^p points (=size of f)}
PROCEDURE DIF(p,VAR f);
LOCAL Bp,Np,Np',P,b,n,BaseE,BaseO,e,o;
BEGIN {DIF}
{initialise pass parameters}
Bp:=1;    {No. of blocks}
Np:=1<<p; {No. of points in each block}  
{perform p passes}
FOR P:=0 TO (p-1) DO
  BEGIN {pass loop}
  Np':=Np>>1; {No. of butterflies}
  BaseE:=0;   {Reset even base index}
  FOR b:=0 TO (Bp-1) DO
    BEGIN {block loop}
    BaseO:=BaseE+Np'; {calc odd base index}
    FOR n:=0 TO (Np'-1) DO
      BEGIN {butterfly loop}
      e:= f[BaseE+n]+f[BaseO+n];
      o:=(f[BaseE+n]-f[BaseO+n])*T(Np,n);
      f[BaseE+n]:=e;
      f[BaseO+n]:=o;
      END; {butterfly loop}
    BaseE:=BaseE+Np; {start of next block}
    END; {block loop}
  {calc parameters for next pass}
  Bp:=Bp<<1; {twice as many blocks}
  Np:=Np>>1; {half as many points in each block}
  END; {pass loop}
END; {DIF}

That's as far as we'll go on DIF code. Of course, if you look, there's still plenty of scope for further optimisation of this routine. We won't do it here for fear of obscuring the code even more. The remainder of this section is devoted to a few observations about the practical details of the twiddle factors, which so far have been largely neglected.


Bottom     Previous     Contents

---

The Radix 2 Decimation In Frequency (DIF) Algorithm.

The Maths.

We defined the FFT as:

If N is even, the above sum can be split into 'top' (n=0..N/2-1) and 'bottom' (n=N/2..N-1) halves and re-arranged as follows:

If we now consider the form of this result for even and odd valued k separately, we can see how this result enables us to express an N point FFT in terms of 2 (N/2) point FFT's.
Even k, k=2k' (k'=0..N/2-1):

or equivalently..

Odd k, k=2k'+1 (k'=0..N/2-1):

or equivalently..

The process of dividing the frequency components into even and odd parts is what gives this algorithm its name 'Decimation In Frequency'. If N is a regular power of 2, we can apply this method recursively until we get to the trivial 1 point transform. The factors T_N are conventionally referred to as 'twiddle factors'.

A Recursive DIF FFT Routine.

Given the above results, we can now have a 'first stab' at a recursive routine to implement this algorithm (in a hypothetical Pascal like programming language which supports complex numbers and allows arrays as function arguments and results):

FUNCTION DIF(N,f);
LOCAL N',n,fe,fo,Fe,Fo,k',F;
IF N==1
   THEN RETURN(f); {trivial if N==1}
   ELSE BEGIN      {perform 2 sub-transforms}
        N':=N/2; {size of sub-transforms}
        FOR n:=0 TO (N'-1) DO {perform N' DIF 'butterflies'}
          BEGIN
          fe[n]:= f[n]+f[n+N'];         {even subset}
          fo[n]:=(f[n]-f[n+N'])*T(N,n); {odd  subset}
          END;
        Fe:=DIF(N',fe); {even k}
        Fo:=DIF(N',fo); {odd  k}
        FOR k':=0 TO (N'-1) DO
          BEGIN
          F[2*k'  ]:= Fe[k']; {even k}
          F[2*k'+1]:= Fo[k']; {odd  k}
          END;
        RETURN(F);
        END;

This is simplest form of DIF implementation and directly reflects the mathematical derivation of the algorithm. The process of calculating the fe and fo components is conventionally referred to as a (DIF) 'butterfly', and is the basic primitive operation of the FFT. (Apparently, this name was aquired from certain diagramatic representations of this operation which resemble butterflies.)

DIF FFT Algorithmic Complexity (Why it's fast).

The algorithmic complexity of an FFT is usually quantified in terms of the total number of butterfly operations performed. Let this number be C(p) for a 2^p point transform. Looking at the DIF routine above, it is easy to see that C(p) must satisfy the following recurrence relation:

This has solution:

or, in terms of N (=2^p):

Dropping the constant scaling factors (including the log base) we get an algorithmic complexity of O(N.logN)

A Recursive 'In Place' DIF FFT Routine.

If you coded something like the above routine in a real programming language it would work fine. However, from an efficiency point of view it is somewhat less than ideal. Allocating local arrays on the stack will make this implementation fairly memory hungry, and the last loop in the above routine performs no useful numerical computation, it simply re-arranges values previously calculated.
What if the last loop were somehow replaced by a simple catenation the results of the two sub-transforms? Say we put all the even k samples in the top half of the result and all the odd samples in the bottom half of the result. Treating k as a binary number, the least significant bit of k determines which 'half' of the result array the corresponding value resides in. The least significant bit of k becomes the most significant bit of the corresponding (binary) array index. Because the function is recursive, this bit swapping will occur for each sub-transform etc.. I.E. The array index is determined by bit reversing k. Doing this won't save any time, unless we can arrange that the catenation operation is actually performed implicitly by each sub-transform. This suggests that an 'in place' algorithm should be used (one which performs all necessary operations in a single array, rather than allocating temporary arrays on the stack). Looking at the form of the first loop in the above routine indicates how to do this, put the 'even' subset values back in f[n] (the top half) and put the 'odd' subset values back in f[n+N'] (the bottom half), then perform the DIF operation on each half. Pulling all these ideas together, we get a more efficient (recursive) in-place DIF routine:

{Perform in place DIF of N points starting at position BaseE
 DIF(0,N,f) performs DIF FFT on entire array f, N= size of f
}
PROCEDURE DIF(BaseE,N, VAR f); {f is an external array}
LOCAL N',BaseO,n,e,o;
IF N==1
   THEN {do nothing}
   ELSE BEGIN
        N':=N>>1; {shift right to get size of sub-transforms}
        BaseO:=BaseE+N'; {split block into 2 halves}
        FOR n:=0 TO (N'-1) DO
          BEGIN
          e:= f[BaseE+n]+f[BaseO+n];
          o:=(f[BaseE+n]-f[BaseO+n])*T(N,n);
          f[BaseE+n]:=e;
          f[BaseO+n]:=o;
          END;
        DIF(BaseE,N',f); {even sub-transform}
        DIF(BaseO,N',f); {odd  sub-transform}
        END;

This version of the DIF routine is a little simpler and more efficient than the first, but has the disadvantage that the output is in 'jumbly' (bit reversed) order. This may on may not be a serious problem, depending on what the output is to be used for and whether or not your processor/programming language supports bit reversed addressing (most DSP's do). If bit reversed addressing is not available then you may need to produce a bit reversed index look up table to access the output.
It is worth noting that this is the simplest formulation of the 'in-place' DIF algorithm. It takes normal order input and generates bit reversed order output. However, this is not fundamental to the algorithm, it is merely a consequence of the simplest implementation. It is possible to write a reverse order DIF algorithm FFT which takes bit reversed order input and generates normal order output. This requires the DIF FFT routine to be amended in two ways:

1. Passing an additional parameter which specifies the spacing between elements in each sub-array to be transformed. In the simple code above, this is always 1. In the reverse order FFT, this will start at 1 and double for each sub transform. This parameter is also useful feature for multi-dimensional transforms.
2. Since the input to each sub-transform is now in bit reversed order, the twiddle factors must also used in bit reversed order. This isn't difficult if the twiddle factors are taken from a table in bit reversed order, or if bit reversed addressing is available.

This modified algorithm could be used to implement an inverse DIF FFT, but it's probably simpler to use the DIT algorithm presented in the next section.

The 'Classic' Non-Recursive DIF FFT Routine.

For many processors/languages a recursive routine is not attractive, because of the overhead incurred by a procedure call. Be careful though, in reality an aversion to recursion could cost performance (see the note about cache efficiency). There is also a particular problem with DSP's which often have small hardware stacks, so deeply recursive routines will cause stack overflow. It is fairly easy to see that the above routine can be flattened into nested loops, to yield something resembling the 'classic' (non recursive) DIF FFT. Each DIF uses 2 'half size' DIF's, which in turn will use 4 'quarter size' DIF's, etc.. the last (not trivial) DIF will be for size 2. So, keeping notation consistent with the above recursive DIF, we get 3 nested loops:

• Pass Loop: An N (=2^p ) point transform will perform p 'passes', indexed by P=0..p-1.
• Block Loop: Pass will P operate on B_P (=2^P ) sub-blocks, each of size N_P (=N/B_P=2^p-P), indexed by b=0..B_P-1
• Butterfly Loop: Each sub-block operation will perform N'_P (=N_P/2=2^p-P-1) butterflies, indexed by n=0..N'_P-1.

{Perform in place DIF of 2^p points (=size of f)}
PROCEDURE DIF(p,VAR f);
LOCAL Bp,Np,Np',P,b,n,BaseE,BaseO,e,o;
BEGIN {DIF}
{initialise pass parameters}
Bp:=1;    {No. of blocks}
Np:=1<<p; {No. of points in each block}  
{perform p passes}
FOR P:=0 TO (p-1) DO
  BEGIN {pass loop}
  Np':=Np>>1; {No. of butterflies}
  BaseE:=0;   {Reset even base index}
  FOR b:=0 TO (Bp-1) DO
    BEGIN {block loop}
    BaseO:=BaseE+Np'; {calc odd base index}
    FOR n:=0 TO (Np'-1) DO
      BEGIN {butterfly loop}
      e:= f[BaseE+n]+f[BaseO+n];
      o:=(f[BaseE+n]-f[BaseO+n])*T(Np,n);
      f[BaseE+n]:=e;
      f[BaseO+n]:=o;
      END; {butterfly loop}
    BaseE:=BaseE+Np; {start of next block}
    END; {block loop}
  {calc parameters for next pass}
  Bp:=Bp<<1; {twice as many blocks}
  Np:=Np>>1; {half as many points in each block}
  END; {pass loop}
END; {DIF}

That's as far as we'll go on DIF code. Of course, if you look, there's still plenty of scope for further optimisation of this routine. We won't do it here for fear of obscuring the code even more. The remainder of this section is devoted to a few observations about the practical details of the twiddle factors, which so far have been largely neglected.

Twiddle Factor Tricks.

Recall the form of the twiddle factors:

In practice, calculating these will require time consuming COS's and SIN's, so you certainly don't want to do this for every butterfly (if you do your FFT will be anything but fast). So what you need is a look up table (an array of size N/2) which is calculated just once. The important thing to realise is that you don't need a separate table for each DIF pass (N halves each pass). Instead you use the same table each pass and introduce an additional 'twiddle_step_size' parameter which starts at 1 and doubles after each pass. The twiddle factor used has index n*twiddle_step_size. (The array bounds will never be exceeded, because N halves on each pass and the maximum value of n is N/2-1.)
The next trick is to notice that often the twiddle factor will be either +1 or -j (it will never be -1 or +j). In such cases there is no need to do a full blown complex multiply (remember this requires 4 real multiplies and 2 real adds). Simple addition and subtraction will suffice. We shall call butterflies that use on or other of these twiddle factors 'trivial butterflies'. Specifically:

How often does this occur? Consider the last DIF FFT pass (N=2). In this case T₂(0)=1 is the only twiddle factor used. So the entire last pass consists of trivial butterflies. Similarly, the first butterfly of of any sub-block will use T_N(0)=1. In general, in pass P (P=0..p-1), there are B_P (=2^P) sub-blocks and therefore 2^P butterflies which use a twiddle factor of +1.
In the penultimate (N=4) pass the butterflies will use either T₄(0)=1 or T₄(1)=-j. So this pass also uses only trivial butterflies. As in the above case, in each of the previous (N>4, P<p-2) passes, there are B_P (=2^P) sub-blocks and therefore 2^P butterflies which use a twiddle factor of -j (at n=N/4) .
We can now calculate exactly how many of these trivial butterflies Triv(p) there are in a typical DIF FFT for sizes >4 (p>2). This is the sum of the number of butterflies in the last 2 passes (the easy bit) and the number of trivial butterflies in all the other passes (the hard bit, but the result in Annex B is useful here):

The total number of butterflies was calculated earlier:

So for a 2^p point DIF FFT, the proportion of trivial butterflies is about 3/p. If this shortcut is exploited, then large FFT's benefit less than small FFT's. For example, in a 512 point (p=9) DIF FFT about 1/3 of the butterflies will be trivial.
The non-recursive routine presented above can be modified to exploit trivial butterflies by doing something like this:

• Make the last 2 passes 'specials' which have the appropriate twiddle factors (+1 or -j) 'hard wired' into the code.
• For the remaining passes (N>4, N'_p>2) break the inner butterfly loop into two, each half of which has a 'special' as the first butterfly. The first loop special butterfly should use +1 as the twiddle factor. The second loop special butterfly should use -j as the twiddle factor.

Of course, exactly how much time this will really save in practice is greatly dependent on the processor used.
As a final note, we can observe that there are further opportunities to exploit which we haven't considered:

These aren't quite so trivial (should call them semi-trivial?), but there are still potentially faster ways of using these than full blown complex multiplication.

©1999 - Engineering Productivity Tools Ltd.

---

Next     Top