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- The laplace transform
- The laplace transform: excercises
Exercises
- Find the Laplace Transform of the following signals, for each case indicate the Laplace transform property that was used:
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- Suppose that two filters having impulse responses
and
are cascaded (i.e. connected in series). Find the transfer function of the equivalent filter assuming
and
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- Find the inverse Laplace transforms of the following:
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- Use partial fraction expansions to find the inverse Laplace transforms of the following:
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- Consider a filter having impulse response
. Use Laplace transforms to find the output of the filter when the input is given by:
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- Indicate whether the following impulse responses correspond to stable or unstable filters:
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- Use Laplace transform tables to find the impulse response of the second-order lowpass filter in terms of
and
for the overdamped, critically damped, and underdamped case.
- Use a series RLC circuit to design a critically damped second-order lowpass filter with a corner frequency of 100 rad/sec. Use a
k
resistor in your design.
- Using a 10 k
resistor, design a critically damped bandpass filter, having a center frequency of 100 rad/sec and indicate the resulting bandwidth of the filter. What is the quality factor of the filter?
- Use bode plots to find the magnitude and phase response of the following filters
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Source:
OpenStax, Signals, systems, and society. OpenStax CNX. Oct 07, 2012 Download for free at http://cnx.org/content/col10965/1.15
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