Determine the Fourier transform of f(x) = sin (x), pi/2 > x > -pi/2 ; 0 otherwise(adsbygoogle = window.adsbygoogle || []).push({});

To do this,

i) express f(x) as a complex exponential,

ii) write down the Fourier integral,

iii) solve the integral, and

iv) replace the complex exponentials by simple trigonometric functions.

Attempt at answer

To start with i get stuck when deciding if i substitute the complex exponential term of sin (x);

see attachment

then substitute this into the fourier integral and try and evaluate. Im not sure what to do from this point, presuming of course its correct up to this.

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# Fourier transformation

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