Transcription of The Scientist and Engineer's Guide to Digital Signal ...
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The Scientist and Engineer's Guide to Digital Signal ...
581 CHAPTER32 The Laplace TransformThe two main techniques in Signal processing , convolution and Fourier analysis, teach that alinear system can be completely understood from its impulse or frequency response. This is avery generalized approach, since the impulse and frequency responses can be of nearly any shapeor form. In fact, it is too general for many applications in science and engineering. Many of theparameters in our universe interact through differential equations. For example, the voltageacross 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.
582 The Scientist and Engineer's Guide to Digital Signal Processing X (T) ’ m 4 &4 x (t) e &jTt d t X (F,T) ’ m 4 &4 [x (t) e &Ft] e &jTt d t case Greek sigma. Likewise, the imaginary axis uses the variable, T, the natural frequency. This coordinate system allows the location of any point to be specified by providing values for F and T ...
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