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Question: How to verify Fourier transform property?

Question:How to verify Fourier transform property?

Test007 50 Maple 2020
transform fourier inttrans
August 15 2020
0

Is there a way to verify the following Fourier transform property: F[f(x) exp(i b x)](k) = F[f(x)](k − b)? This is what I tried:
 

> 

restart
> 

with(inttrans)
> 

constants := constants, b

false, gamma, infinity, true, Catalan, FAIL, Pi, b

 (1)
> 

left := fourier(f(x)*exp(I*b*x), x, k)/sqrt(2*Pi)

(1/2)*2^(1/2)*fourier(f(x)*exp(I*b*x), x, k)/Pi^(1/2)

 (2)
> 

right := fourier(f(x), x, k-b)/sqrt(2*Pi)

(1/2)*2^(1/2)*fourier(f(x), x, k-b)/Pi^(1/2)

 (3)
> 

simplify(left-right)

(1/2)*2^(1/2)*(fourier(f(x)*exp(I*b*x), x, k)-fourier(f(x), x, k-b))/Pi^(1/2)

 (4)
> 

NULL


 

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