Transcription of Topic 3 The -function & convolution. Impulse response ...
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Topic 3 The -function & convolution. Impulse response ...
Topic 3 The -function & response & Transfer functionIn this lecture we will described the mathematic operation of theconvolutionoftwo continuous functions . As the name suggests, two functions are blended orfolded will then discuss theimpulse responseof a system, and show how it is relatedto the transfer function of the though we will define a special function called the -function or unit is, like the Heaviside step functionu(t), a generalized function or distribution and is best defined by considering another function in conjunction with The -functionConsider a functiong(t) ={1/w0< t < w0otherwiseOne thing of note aboutg(t) is that w0 g(t)dt= lower limit 0 is a infinitesimally small amount less than zero. Now, supposethat the widthwgets very small, indeed as small at 0+, an number an infinitesimalamount bigger than zero.}
In the time domain, a system is described by its Impulse Response Function h(t). This function literally describes the response of system at time tto an unit impulse or -function input administered at time t= 0. Suppose that \now" is time t, and you administered an impulse to the system at time ˝in the past. The response now is y(t) = h(t ...
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