Determine the Laplace transform, F(s), of the following time signal..pdf
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The document explains the determination of the Laplace transform, f(s), of a time signal defined for t ≥ 0. It details the integral formula for calculating the Laplace transform and describes the variables involved, namely the complex frequency variable s and the time variable t. The notation convention is also mentioned, where lower case letters represent signals and capital letters represent their Laplace transforms.
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Determine the Laplace transform, F(s), of the following time signal..pdf
- 1. Determine the Laplace transform, F(s), of the following time signal. Solution we'll be interested in signals de¯ned for t ¸ 0 the Laplace transform of a signal (function) f is the function F = L(f) de¯ned by F(s) = Z 1 0 f(t)e¡st dt for those s 2 C for which the integral makes sense ² F is a complex-valued function of complex numbers ² s is called the (complex) frequency variable, with units sec¡1; t is called the time variable (in sec); st is unitless ² for now, we assume f contains no impulses at t = 0 common notation convention: lower case letter denotes signal; capital letter denotes its Laplace transform, e.g., U denotes L(u), Vin denotes L(vin), etc.