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Problem 1: a) Given is the following circuit. Find analytically the impulse response h(t) of the system where and .

V_in(t)=1 for 0 <= t <= 1sec. and 0 otherwise.

b) We obtain by convolving the impulse response and the given input signal. Find the analytical expression for .

Problem 2: Convolution and Causality

In this part, we want to investigate how convolution affects causality. A signal will be considered causal if it is zero for time t<0 and non-causal otherwise.

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• (a) causal rectangular and non causal rectangular (Take the screenshot and label the graph as graph1)
• (b) causal rectangular and causal rectangular (Take the screenshot and label the graph as graph2)
• (c) non causal rectangular and non causal sinc (Take the screenshot and label the graph as graph3)

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