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The product of two continuous-time signals can be obtained by multiplying their values at every instant of time. Consider two continuous time signals 𝑥_{1}(𝑡) and 𝑥_{2}(𝑡) as shown in the figure.

The multiplication of the two signals can be performed by considering different time intervals as follows −

**For 𝟎 ≤ 𝒕 ≤ 𝟏**: 𝑥_{1}(𝑡) = 3 and 𝑥_{2}(𝑡) = 2, thus𝑥

_{1}(𝑡)𝑥_{2}(𝑡) = 3 × 2 = 6**For 1≤ 𝒕 ≤ 𝟐**: 𝑥_{1}(𝑡) = 2 and 𝑥_{2}(𝑡) = 2 + (𝑡 − 1), hence,𝑥

_{1}(𝑡)𝑥_{2}(𝑡) = 2[2 + (𝑡 − 1)] = 4 + 4(𝑡 − 1)**For 2≤ 𝒕 ≤ 𝟑**: 𝑥_{1}(𝑡) = 2 − (𝑡 − 2) and 𝑥_{2}(𝑡) = 3, hence,𝑥

_{1}(𝑡)𝑥_{2}(𝑡) = [2 − (𝑡 − 2)]3 = 6 − 3(𝑡 − 2)

The multiplication of the signals (i.e., 𝑥_{1}(𝑡)𝑥_{2}(𝑡)) is shown in the figure.

The multiplication of two discrete-time signals 𝑥_{1}(𝑛) and 𝑥_{2}(𝑛) can be
performed by multiplying the corresponding sample values.

Consider two discrete time sequences 𝑥_{1}(𝑛) and 𝑥_{2}(𝑛) as follows −

𝑥_{1}(𝑛) = {−3, 1, 5, 1, 2}

𝑥_{2}(𝑛) = {2, −1, 1, 3, −3}

Then, the product of these two signal is given by,

𝑥_{1}(𝑡)𝑥_{2}(𝑡) = {−3 × 2, 1 × (−1), 5 × 1, 1 × 3, 2 × (−3)}

⟹ 𝑥_{1}(𝑡)𝑥_{2}(𝑡) = {−6, −1, 5, 3, −6}

- Related Questions & Answers
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