[TI-92][TI-89] Fourier Transform Library

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https://helpcalculator.forumfree.it/?t=7760484

 

파일 다운로드 : https://digilander.libero.it/fpirozzi/fourier.zip

 

Readme.txt

 

fourier
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Fourier version 3.20 for TI-92/TI-92II and TI-89/TI-92+

This packet contains functions to perform Fourier-/inverse Fourier-
transformation. A function, which can rewrite the output of Fourier/
iFourie to a form that, can be evaluated numerical. A function to 
graph the output.

Keep the functions together in a separate folder with the name 
"FOURIER" and do not create any variable in it. 

Before using iFourier or Fourier set TI-92 MODE
  Complex Format to RECTANGULAR
  Angle to RADIAN
  Exact/Approx to AUTO

You have to do these settings yourself because; the functions cannot 
change the mode setting on the calculator. 

The package include following programs/functions:
 Help              online help to programs.
 Fourier           Fourier transformation
 iFourier          inverse Fourier transformation
 Plot              graph expression 
 eval              evaluate expression
 Menu              custom menu

Other files in the package are all sub functions or data for above functions.

--------------------- Archiving on TI-89 and TI-92+ -------------------------

All variables can be archived on the TI-89 and TI-92+. Functions and programs can also be archived, but first after they have been used one time each. If
the programs have not been run before archiving, the calculator has to 
compile them each time they are used, this will slow down the execution time
of the programs.

Before archiving the programs execute following commands from the command
line in the "fourier" folder:

Help()  and  press 'x'
ifourier(1/w,w)
fourier(1,t)
eval(1)
plot(1,t,0)

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Help

This program will give online information about and demonstrate the 
use of functions in this package. When you do not need this program 
any longer just delete it and the data file "hlp".

Syntax: Help()

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Function: Fourier(f(var), var ,mode)

 

Transforms the expression "f(var)" from time domain to frequency domain (Fourier). This function has the ability in the most occasions to perform symbolical transformations, but not in all. It depends on the type of transform.

 

f(var): can be any expression, which have a Fourier transform.

 

var   : is  the name of the variable to transform normally 't', but can be any name.

 

mode  : decide the format of the result.

Mode can be 1 or 2.

In mode 1 the result will be in Ti-92's complex format (exp(i*w) will be rewritten to cos(w)+i*sin(w)). Mode 2 is a special format, where the calculators complex 'i' will be replaced with the letter 'i'.

The results in mode 2 will be exponential functions instead of sine and cosine. The letter 'i' in the results of Fourier is the same as the complex 'i' and can always be replaced with it. 

The letter 'i' and 'complex i' will be interpreted as equal.

The expression may contain constants of any kind except constants 
containing the letter 's'.
       
Special transforms:
Unit step function (Heaviside function):
Definition:    u(t-a) = 1 for t>=a else 0

      Fourier(u(t - a),t,2) = pi*'Delta'(w)-i*exp(-a*i*w)/w

Dirac delta function:
Definition:  'delta'(t - a) = 1 for t=a else 0

      fourier('delta'(t - a),t,2) = exp(-a*i*w)

You can get 'delta' by pressing 'green diamond' + G + D on TI-92.

signum function:
Definition: signum(t-a) = 1 for t>=a else -1

      Fourier(signum(t - a),t,2) = -i*2*exp(-a*i*w)/w

Some examples:

Fourier(cos(5*t),t,1) = pi*'delta'(w-5)+pi*'delta'(w+5)

Fourier(cos(5*t)*u(t),t,1) = 
  i*(-1/2*(w+5))-1/(2*(w-5))+pi*'delta'(w-5)+pi*'delta'(w+5)

Fourier(1/(t-i),t,2) = 2*pi*i*exp(w)*u(-w)

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Function: iFourier(F(var), var ,mode)

 

Transforms the expression "F(var)" from frequency domain to time domain
(inverse Fourier).

F(var): can be any expression, which have an inverse Fourier transform.

var   : is  the name of the variable to transform normally 'w', but can 
be any name. This function has the ability in the most occasions to 
perform symbolical transformations, but not in all. It depends on the 
type of transform.

mode  : decide the format of the result. Mode can be 1 or 2. In mode 1 
the result will be in Ti-92's complex format (exp(i*w) will be rewritten 
to cos(w)+i*sin(w)). Mode 2 is a special format, where the calculators 
complex 'i' will be replaced with the letter 'i'. The results in mode 2 
will be exponential functions instead of sine and cosine. The letter 'i' 
in the results of iFourier is the same as the complex 'i' and can always 
be replaced with it. 

The letter 'i' and 'complex i' will be interpreted as equal.

The expression may contain constants of any kind except constants containing the letter 's'.
       
Special transforms:
Unit step function (Heaviside function):
Definition:    u(w-a) = 1 for w>=a else 0
      iFourier(u(w - a),w,2) = 'Delta'(-t)/2+i*exp(a*i*t)/(2*pi*t)

Dirac delta function:
Definition:  'delta'(w - a) = 1 for w=a else 0

      Fourier('delta'(w - a),w,2) = exp(a*i*t)/(2*pi)

You can get 'delta' by pressing 'green diamond' + G + D on TI-92.

signum function:
Definition: signum(w - a) = 1 for w>=a else -1

      Fourier(signum(w - a),w,2) = i*exp(a*i*t)/(pi*t)

Some examples:

iFourier(u(w+1)-u(w-1),w,1) = sin(t)/(pi*t)

iFourier(1/(w+1)^2,w,2) = 2*t*exp(-i*t)*(2*u(-t)-1)

iFourier('delta'(w+5)+'delta'(w-5),t,1) = sin(5*t)/pi

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Function: eval(f(var))

 

f(var) any function containing Heaviside, dirac delta or signum

This function will replace u(var), 'delta'(var), signum(var) with a
equivalent when-functions. The letter 'i' will be replaced with the 
'complex i'.

Example: eval(u(t-a))=when(t-a>=0, 1,0)

To get a numerical result out of a function containing special 
functions

eval(f(var))|var=value

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Program: Plot(f(var),var,type)

 

This program will graph functions containing Heaviside, dirac delta or
signum. It will not change the setting of the calculator and it is 
therefore up to you to manage the window settings.

f(var) any function containing Heaviside, dirac delta or signum

var     variable to plot

type=0    plot the function       f(var)
type=1    plot the amplitude        abs(f(var))
type=2    plot phase           angle(f(var))

Example:

 Plot(u(t)-u(t-4),t,0)      plots a pulse

Example:
 Plot the amplitude of a complex function

  plot(f(war),var,1)

Plot the phase 

  plot(f(war),war,2)

 

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Author: Lars Frederiksen
E-mail: LTF@POST8.TELE.DK

PS. Please do not ask for more programs.