Overview
This lecture explains how to add two or more continuous-time signals by summing their amplitudes at each point in time, demonstrated through a step-by-step example.
Addition of Continuous-Time Signals
- To add continuous-time signals, sum their amplitudes at every instant of time.
- Let the given signals be ( X_1(t) ) and ( X_2(t) ).
- The resulting signal is ( X_3(t) = X_1(t) + X_2(t) ).
Step-by-Step Example
- For ( t \leq 2 ) and ( t > 1 ): ( X_1(t) = 0 ), ( X_2(t) = 2 ), so ( X_3(t) = 2 ).
- For ( t \leq 1 ) and ( t > 0 ): ( X_1(t) = 2 ), ( X_2(t) = 1 ), so ( X_3(t) = 3 ).
- For ( t \leq 0 ) and ( t > -1 ): ( X_1(t) = 2 ), ( X_2(t) = -1 ), so ( X_3(t) = 1 ).
- For ( t \leq -1 ) and ( t > -2 ): ( X_1(t) = 1 ), ( X_2(t) = -1 ), so ( X_3(t) = 0 ).
- For ( t \leq -2 ) and ( t > -3 ): ( X_1(t) = 0 ), ( X_2(t) = 2 ), so ( X_3(t) = 2 ).
Resulting Waveform Summary
- ( X_3(t) = 2 ) for ( t ) from 1 to 2.
- ( X_3(t) = 3 ) for ( t ) from 0 to 1.
- ( X_3(t) = 1 ) for ( t ) from -1 to 0.
- ( X_3(t) = 0 ) for ( t ) from -2 to -1.
- ( X_3(t) = 2 ) for ( t ) from -3 to -2.
Key Terms & Definitions
- Continuous-Time Signal — A signal defined for every value of time.
- Amplitude — The value of a signal at a specific time point.
- Signal Addition — The process of summing the amplitudes of two or more signals at each instant.
Action Items / Next Steps
- Review the plotted waveform of ( X_3(t) ) as described.
- Prepare for the next lecture on multiplying continuous-time signals.