Question

For each part of this problem, you are given the description of a continuous-time system. Determine if the given system is: (i) Linear (iv) Causal (ii) Time-Invariant (v) Stable (iii) Memoryless (vi) Invertible

Answer 1

Hello, you haven't provided any continuous-time system, therefore, I am going to explain to you how to solve this problem in general and you can apply this to your system or any continuous-time system.

Answer step-by-step explanation:

• Linear: A system is linear if it obeys the principle of superposition Z{aX1(t)+bX2(t)}=aZ{X1(t)}+bZ{X2(t)}=aY1(t)+bY2(t), where Z is an operator which maps the input into output (Z is the system itself)
• Causal: A system is causal if it doesn't depend on future inputs Y(t)=Z(x(t)) up to time t
• Time-Invariant: A system is time-invariant if a time-shift on the input causes a equivalent shift on the output, if Y(t)=Z(x(t)) then Y(t-t0)=Z(x(t-t0))
• Stable: A system is stable if every bounded input produces a bounded output, abs(Y(t))<B if abs(X(t))<A / abs(A) < inf and abs(B) < inf
• Memoryless: A system is memoryless if its output at time t is dependent only on the input at that time, Y(t) at time t depends only on X(t) at time t
• Invertible: A system is invertible if we can get back the input by passing the output through another system (No information loss)