Math Problem Statement
An analog LTI system with impulse response function h(t) = u(2-t) + u(t-2) is presented with an input x(t) = t[u(t-2) -u(t-3)].a) Determine and plot the system output y(t) = x(t) * h(t).
Solution
The plot shows the output of the LTI system, where:
- for the interval .
- for and .
This output reflects the result of convolving the input with the impulse response .
Would you like more details on any specific part, or do you have any questions?
Related Questions:
- How would the output change if the impulse response function were different?
- Can you explain the significance of convolution in LTI systems?
- What is the effect of the unit step functions in defining the input and impulse response?
- How would you compute the convolution if the input were a more complex function?
- How does the convolution property relate to the frequency domain?
Tip:
Convolution in time domain corresponds to multiplication in the frequency domain, which can simplify the analysis of LTI systems.
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Math Problem Analysis
Mathematical Concepts
Linear Time-Invariant (LTI) Systems
Convolution
Unit Step Function
Formulas
-
Theorems
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Suitable Grade Level
Undergraduate Level
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