In a previous post we explored some relationships between the Laplace and the Fourier transforms. In this post we address a common question: “when is the Fourier transform of a signal, $X(j\omega)$, equal to its Laplace transform, $X(s)$, evaluated at $s = j \omega$?” The short answer is: when the region of convergence of the corresponding Laplace transform contains the imaginary axis.

Continue reading “More on the Fourier transform”# Tag: convolution

## The impulse response

So you wonder how impulse responses are born? They are born out of linearity.

Continue reading “The impulse response”## Is that a constant? Or is it a delta?

This might be a stupid question.. but oh well. So the inverse laplace of a constant is the dirac delta function times the constant.

With a proportional controller, K(s) = Kp, the inverse laplace of the controller would be the delta function. Is the delta function asymptotically stable?

Anonymous

As it turns out, this is not a stupid question at all! It hits right at the heart of what is and how to represent a dynamic system.

Continue reading “Is that a constant? Or is it a delta?”