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In Matlab, I would like to compute the inverse Fourier transform symbolically of the following function :

cf=1/(1 - beta*t*1i)^N

But impossible to get a result with :

>> ifourier(cf,t,x)

ans =

fourier(1/(1 - beta*t*1i)^N, t, -x)/(2*pi)

Isn't there really no explicit formula for the inverse Fourier transform of this function cf

Edit

I try to use sum and product with log to express in other form the cf function :

cf=exp(-A(k)*symsum((1-1i*beta*t),k,1,N)

with N=60 and A=ones(1,N).

But when I apply FT, I get :

cf=exp(-A(k)*symsum((1-1i*beta*t),k,1,N))
Error using message
In 'symbolic:sym:symsum:InvalidSummationIndex', parameter {0} must be a real scalar.

Error in sym/symsum (line 54)
    error(message('symbolic:sym:symsum:InvalidSummationIndex', char(x)));

What's wrong here?

halfer
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  • Are you trying to take the inverse fourier transform of a time domain function? I'm trying to understand the first function `cf = 1 / (1 - beta*t*1i)^N`. Which values are constants and which are symbolic? – Matt Aug 13 '21 at 14:20
  • @Matt the symbolic variable are `t` (time variable), `beta` and `N` . If the computation cannot be done symbolically with symbolic variable `N`, I can take it as a numerical value equal to `N=60`. Regards –  Aug 13 '21 at 19:44
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    Your equation appears to some form of exponential which doesn't have periodic properties. From the `doc ifourier` documentation "If ifourier cannot find an explicit representation of the inverse Fourier transform, then it returns results in terms of the Fourier transform." In other words `cf / 2pi` is expected. Normally one uses the inverse fourier transform to go from frequency domain to the time domain. I could be missing the point of your question though. – Matt Aug 13 '21 at 23:18

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