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Digital Signal Processing: A Practical Guide for Engineers and Scientists by Steven Smith

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CHAPTER 32

The Laplace Transform

The two main techniques in signal processing, convolution and Fourier analysis, teach that a linear system can be completely understood from its impulse or frequency response. This is a very generalized approach, since the impulse and frequency responses can be of nearly any shape or form. In fact, it is too general for many applications in science and engineering. Many of the parameters in our universe interact through differential equations. For example, the voltage across an inductor is proportional to the derivative of the current through the device. Likewise, the force applied to a mass is proportional to the derivative of its velocity. Physics is filled with these kinds of relations. The frequency and ...

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