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Matching of time waveforms using inverse Laplace transforms

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The waveforms of FIGURE 2 were produced by the circuit of FIGURE 3. In FIGURE 3, LAP1 is a Laplace block transfer function.

Match each waveform A, B, C and D with its causing transfer function (1), (2), (3) and (4) given in TABLE A.

The filter responses to be matched with the waveform options are

a) 1/{s*2 + 2s + 2}

b) 1/{s^2 + s + 2}

c) 1/{s^2 + 0.5s + 2}

d) 1/{s^2 + 0.4s + 4}

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Please see mathematical analysis showing the steps in the attachments. You may need to consult both the attachments in tandem as I have separated some of ...

Solution Summary

A filter response is matched to its correct time domain waveform (from a number of options given) by carrying out the inverse Laplace transform analysis on each option response