Engineering Signal & System CTFT: Find x(t) from X(ω)

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The discussion revolves around finding the continuous-time signal x(t) from its continuous-time Fourier transform (CTFT) X(ω). Participants express difficulty in determining the limits and seek hints from Fourier transform tables. One user mentions that their approach did not align with the solution provided by their professor, prompting them to seek clarification. The conversation highlights the challenges in applying Fourier transform concepts and the importance of referencing established tables for assistance. Ultimately, the need for collaborative problem-solving in understanding CTFT is emphasized.
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Homework Statement
Find the CT signal associated with CTFT:
Relevant Equations
.
Given the CTFT X(ω): 1638042527872.png
1638042702750.png

and here are my solution to find CT signal x(t) associated with the given CTFT , but i got stuck at the limit part
 
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BvU said:
FInd any hints in a table of FTs ?

##\ ##
Oh, my professor never mention this, i will check this and see
Thank you
 
##\exp(n(jt-1/2))-1\to -1## as ##n\to \infty## since ##\exp(jtn)=\cos(tn)+j\sin(tn)## and ##\exp(-n/2)\to 0## as ##n\to \infty##.
 
MathematicalPhysicist said:
##\exp(n(jt-1/2))-1\to -1## as ##n\to \infty## since ##\exp(jtn)=\cos(tn)+j\sin(tn)## and ##\exp(-n/2)\to 0## as ##n\to \infty##.
Yes i have tried this before, but it didn't match the solution that my professor gave, that's why i ask in here to check
1638093425950.png
 

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