3 ms·

Interesting, Fourier transform has never been an issue for me but Laplace never clicked. I know it's kind of similar (convolution, exponential and all that) but

• dannymi 4y ago
  The frequency is the imaginary part of the Laplace parameter s (and the attenuation is the real part of the Laplace parameter s). Laplace transforms work on systems with attenuation—that’s the main advantage. Because the kind of transform was swapped out anyway, people used the chance to often only define one-sided Laplace transforms that only work for t > 0 (because as an engineer, thats the systems you want anyway). There’s a direct correspondence between the (usual) one-sided Laplace transform and the (unusual) one-sided Fourier transform for that reason. Since you usually have systems where f(t) = 0 for all t < 0 anyway, the distinction one-sided or not is not so important in practice for understanding.