Is e^(2t)u(t-1) causal or anti-causal?
Understand the Problem
The question is about determining whether the signal e^(2t)u(t-1) is causal or anti-causal. The key is understanding the properties of the unit step function u(t-1) and how it affects the signal's behavior for different values of time, t. A causal signal is one that is zero for t < 0, and an anti-causal signal is one that is zero for t > 0.
Answer
The signal e^(2t)u(t-1) is causal.
The signal e^(2t)u(t-1) is causal because it is zero for t < 1. The unit step function u(t-1) ensures that the signal is only defined for t greater than or equal to 1.
Answer for screen readers
The signal e^(2t)u(t-1) is causal because it is zero for t < 1. The unit step function u(t-1) ensures that the signal is only defined for t greater than or equal to 1.
More Information
A causal signal is one that is zero for all negative time. The given signal is zero for t < 1, therefore it is causal.
Tips
A common mistake is to only consider e^(2t) and assume that it is defined for all t, but u(t-1) restricts the domain.
Sources
- Causal, Non-Causal, and Anti-Causal Signals - Tutorialspoint - tutorialspoint.com
AI-generated content may contain errors. Please verify critical information
