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Laplace is a generalisation of Fourier. Fourier can in principle only represent periodic signals. To circumvent this limitation, they invented the windowing of
by nuancebydefault 4y ago
Laplace is a generalisation of Fourier. Fourier can in principle only represent periodic signals. To circumvent this limitation, they invented the windowing of consecuive parts of signals and do the transform on each window. Laplace adds the transient part, that's what makes it more complicated.
- acjohnson55 4y agoThat's not true. The Fourier series represents periodic functions. The Fourier transform applies to all real functions. They need not be periodic, although I'm not sure it's a particularly useful representation of aperiodic functions. It's been a long time since I've thought about the Laplace transform, but IIRC, it has some properties that are preferable the Fourier transform as a math tool. The Fourier transform better maps to an intuitive concept of frequency, which is why it is the basis for the transforms we actual use in practice in engineering, such as the discrete Fourier transform, which is what the famous FFT algorithm computes.