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Determine the Fourier transform of f(x) = sin (x), pi/2 > x > pi/2 ; 0 otherwise
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.
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.
Attachments

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