Watching this video http://youtu.be/1JnayXHhjlg?t=5m30s, I understood the ideia the fourier transform, that is a continuous summation of sinusoids. But now If I have amplitude and phase as function of σ and ω, the summation wouldn't be ##\sum_\sigma \sum_\omega A_{\sigma \omega} \exp(i \varphi_{\sigma \omega}) \exp((\sigma + i \omega)t)##? And in its continous form why the inverse laplace transform isn't a double integral wrt sigma and omega? $$\int_{-\infty }^{+\infty} \int_{-\infty }^{+\infty} F(\sigma, \omega) \exp((\sigma + i \omega)t)d\sigma d\omega $$(adsbygoogle = window.adsbygoogle || []).push({});

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# Why inverse laplace is line integral?

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