Answer to Question #140412 in Electrical Engineering for ahmet

Question #140412
A discrete-time system is described by the following rule
y(n)=(-1)^n x(n) + 2x(n -1)
where x is the input signal, and y the output signal.

Classify the system as:
i. causal/non-causal
ii. linear/nonlinear
iii. time-invariant/time-varying
1
Expert's answer
2020-10-29T08:23:47-0400

The function is ,


(i) Causal/Non Causal:

The impulse response of the system can be written as,



The impulse response is zero zero for all which implies the system is Causal.


ii) Linear/Non Linear:


For input let output be

For input let output be


We have,


If the input was ,out put is



Thus we observe the system satisfy the superposition principle,hence it is Linear.


iii) Time invariant/Time varying:


For a delayed input the output is


......................(1)

For a delayed time , The output equation is,


.............(2)


We observe that equation (1) and (2) are not equal. Which implies it is Time varying.




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