Calculate using the definition of the Fourier transform

[joseph_93]

Hello people,

I have a problem to calculate this exercise using the definition of the Fourier transform:

\(\displaystyle \mbox{(a) }\, f(x)\, =\, \begin{cases}0,&\mbox{ for se}\, |\, x\, |\, >\, \pi\\-1,&\mbox{ for se}\, -\pi\, <\, x\, <\, 0\\1,&\mbox{ for se}\, 0\, <\, x\, <\, \pi \end{cases}\)

\(\displaystyle \mbox{(b) }\, f(x)\, =\, \begin{cases}e^{-|x|},&\mbox{ for se}\, |\, x\, |\, >\, 10\\-x,&\mbox{ for se}\, -10\, <\, x\, <\, 0\\x,&\mbox{ for se}\, 0\, <\, x\, <\, 10 \end{cases}\)

Thanks.

Att.

Joseph F.

 

[Deleted member 4993]

Hello people,

I have a problem to calculate this exercise using the definition of the Fourier transform:

\(\displaystyle \mbox{(a) }\, f(x)\, =\, \begin{cases}0,&\mbox{ for se}\, |\, x\, |\, >\, \pi\\-1,&\mbox{ for se}\, -\pi\, <\, x\, <\, 0\\1,&\mbox{ for se}\, 0\, <\, x\, <\, \pi \end{cases}\)

\(\displaystyle \mbox{(b) }\, f(x)\, =\, \begin{cases}e^{-|x|},&\mbox{ for se}\, |\, x\, |\, >\, 10\\-x,&\mbox{ for se}\, -10\, <\, x\, <\, 0\\x,&\mbox{ for se}\, 0\, <\, x\, <\, 10 \end{cases}\)

Thanks.

Att.

Joseph F.

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