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> a more powerful superset What do you mean? How is integral over half R more powerful than integral over whole R?
by posix_me_less 7y ago
> a more powerful superset
What do you mean? How is integral over half R more powerful than integral over whole R?
- danaos 7y agoParent is right. The Laplace transform is a generalization of Fourier's. There are two types of Laplace tranforms, the two-sided and the one-sided. The two-sided is defined in all of R. The s variable is a complex frequency in the form s = σ + jw. Setting σ = 0 in yields the Fourier tranform. The single-sided LT transform is equivalent to the one-sided if the signal is causal. A causal signal f(t) is zero for all t < 0. All of the signals in the real world are causal. This is convenient as the exponential e^(-st) = e^(-(σ + jw)t) gets really big for values of σ close to minus infinity something the renders the whole integral non convergent. We can avoid that if we make sure the signal is causal.