Signals and Systems - Classification of Signals and Systems - 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.

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