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inttrans

  

invfourier

  

inverse Fourier transform

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

invfourier(expr, w, t)

Parameters

expr

-

expression, equation, or set of equations and/or expressions to be transformed

w

-

variable expr is transformed with respect to w

t

-

parameter of transform

opt

-

option to run this under (optional)

Description

• 

The invfourier function computes the inverse fourier transform (f(t)) of expr (F(w)) with respect to w, using the definition

ft=FwⅇItwⅆw2π

• 

Expressions involving exponentials, polynomials, trigonometrics (sin, cos) and a variety of functions and other integral transforms can be transformed.

• 

The invfourier function recognizes derivatives (diff or Diff) and integrals (int or Int).

• 

Users can define the transforms of their own functions by using the function addtable.

• 

The program first attempts to classify the function simply, from the lookup table.  Then it considers various cases, including a piecewise decomposition, products, powers, sums, and rational polynomials.  Finally, if all other methods fail, the program will resort to integration.  If the option opt is set to 'NO_INT', then the program will not integrate. This will increase the speed at which the transform will run.

• 

The command with(inttrans,invfourier) allows the use of the abbreviated form of this command.

Examples

withinttrans:

invfourierfourierfx,x,w,w,x2

fx2

(1)

invfourier31+t2,t,w

32ⅇwHeavisidew+32ⅇwHeavisidew

(2)

invfouriertⅇ3tHeavisidet,t,w

12Iw32π

(3)

invfourier14It13,t,w

123Γ23ⅇ4wHeavisideww2/3π

(4)

addtablefourier,myfunct,Myfuncs,t,s:

invfouriermyfuncw,w,t

12Myfunctπ

(5)

See Also

dsolve

inttrans

inttrans[addtable]

inttrans[fourier]

 


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