- #1

Jncik

- 103

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## Homework Statement

[PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP19019g3i9ie1bib5d9c00005gh8i4ce0eiab01f?MSPStoreType=image/gif&s=39&w=291&h=54

the link from wolfamalpha: http://www.wolframalpha.com/input/?...t)+)*(sin(pi*t)/t)+from+-infinity+to+infinity

**3. the attempt at a solution**

I tried using the rectangular function and we know that

p

_{T}(t) is 1 for |t|<=T and 0 otherwise

hence for T = π

I get

p

_{T}(t) is 1 for |t|<=π and 0 otherwise

now also using the Fourier transform I get that

sin(π*t)

_______ <----> π*p

_{π}(-ω)

tnow I said that

sin(π*(1/2-t))

____________ <----------> π*p

_{π}(ω-1/2)

1/2 - t

is this correct?

after using the Parseval theorem, I get for some reason π^2 and not 2π

[URL]http://latex.codecogs.com/gif.latex?x%20=%20\frac{1}{2%20\pi}\int_{-oo}^{+oo}%20\pi%20p_{\pi}%28\omega%29%20\pi%20p_{\pi}%28\omega%20-%201/2%29%20=%20\frac{pi}{2}%20\int_{-oo}^{+oo}%20p_{\pi}%28\omega%29%20p_{\pi}%28\omega%20-%201/2%29[/URL]

now since the set of all values in [-pi + 1/2, pi] are within [-pi, pi] and also from [pi,pi+1/2] all values in the integration will give 0

I will have to integrate 1 from -pi to pi and this way I get 2*pi which will give me π^2

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