Here is one of my early videos I did using Camtasia discussing the topic about Laplace Transforms. I planned to redo this video in a future post.

An important concept in engineering concerns the Laplace Transform. Applying this important concept in electrical engineering, the Laplace Transform takes a function described in the time domain and converts it into the frequency domain or Laplace Domain. Loosely speaking, the Laplace Transform is a more general case to the Fourier Transform.

When dealing with undamped sinusoidal signals, then the Fourier Transform is used to analyze signal and system behavior. On the other hand, when dealing with exponentially-damping sinuoidal signals, then the Laplace Transform is used.

Why convert from the time domain to the frequency domain? The answer lies in the described problem. Sometimes it’s easier to analyze a signal in one domain or the other. For example, the interaction between the input signal and the system is described by the convolution integral when analyzing this in the time domain. However, the more complicated integral problem can be transformed into a simpler algebraic problem when analyzing the problem in the frequency domain first. Then, after finding the solution in the frequency or Laplace domain, then you can transform back into the time domain to get the final solution of the problem.

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