- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Signals and Systems: Multiplication of Signals

## Multiplication of Continuous-Time Signals

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.

## Explanation

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.

## Multiplication of Discrete-Time Signals

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 Articles
- Signals and Systems – Multiplication Property of Fourier Transform
- Signals and Systems – Classification of Signals
- Signals and Systems: Amplitude Scaling of Signals
- Signals and Systems – Time Scaling of Signals
- Signals and Systems: Addition and Subtraction of Signals
- Signals and Systems: Even and Odd Signals
- Signals and Systems: Periodic and Aperiodic Signals
- Signals and Systems: Energy and Power Signals
- Signals and Systems – Fourier Transform of Periodic Signals
- Signals and Systems – Properties of Even and Odd Signals
- Signals and Systems: Classification of Systems
- Signals and Systems: Real and Complex Exponential Signals
- Signals and Systems – Z-Transform of Sine and Cosine Signals
- Signals and Systems: Causal, Non-Causal, and Anti-Causal Signals
- Signals and Systems – Filter Characteristics of Linear Systems