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

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

Expert's answer

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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