Sample Solved Problems: Classification of Signals and Systems

Sample Problems:

1.    Determine whether the following systems are: i) Memoryless, ii) Stable iii) Causal iv) Linear and v) Time-invariant.

i)             y(n)= nx(n)

ii)          y(t)= e^x(t)

Solution:-

2.           Determine whether the following systems are time invariant or not. 

i)             Y(t) = tx(t)

ii)          Y(n) = x(2n)

Solution:

i)             Y(t) = tx(t)

Y(t) = T[x(t)] = tx(t)

The output due to delayed input is,

Y(t,T) = T[x(t - T)] = tx(t - t)

If the output is delayed by T, we get

Y(t -T) = (t - T) x( t - T)

The system does not satisfy the condition, y(t,T) = y(t – T).

Then the system is time invariant.

ii)          Y(n) = x(2n)

Y(n) = x(2n)

Y(n) = T[x(n)] = x(2n)

If the input is delayed by K units of time then the output is,

Y(n,k) = T[x(n-k)] = x(2n-k)

The output delayed by k units of time is,

Y(n-k) = x[2(n-k)]

Therefore, y(n,k) is not equal to y(n-k). Then the system is time variant.