Question

How to prove that the output of a Linear Constant Coefficient Differential Equation (LCCDE) is Linear Time-Invariant (LTI)?

a) Analyze the frequency response
b) Apply the superposition principle
c) Check for time-invariance
d) Perform Laplace transform

Answer 1

To prove that the output of a Linear Constant Coefficient Differential Equation (LCCDE) is Linear Time-Invariant (LTI), you can analyze the frequency response, apply the superposition principle, check for time-invariance, and perform a Laplace transform.

Step-by-step explanation:

To prove that the output of a Linear Constant Coefficient Differential Equation (LCCDE) is Linear Time-Invariant (LTI), you can follow these steps:

1. Analyze the frequency response to determine if the system is linear by applying input signals of different frequencies and observing the output.
2. Apply the superposition principle by summing the responses to individual input signals to determine if the system is linear.
3. Check for time-invariance by shifting the input signal in time and observing if the output shifts correspondingly.
4. Perform a Laplace transform to convert the LCCDE into an algebraic equation, which can help analyze the linearity and time-invariance of the system.