Classification of Continuous and Discrete Time Signals

CLASSIFICATION OF CONTINUOUS TIME AND DISCRETE TIME SIGNALS

Continuous time and discrete time signals are classified according to their properties as follows.

1. Periodic and aperiodic signals

2. Energy and power signals

3. Deterministic and random signals.

Periodic and Aperiodic (Non-Periodic) Signals (CT & DT)

i. A signal is said to be periodic, if it repeats at regular interval of time.

ii. A signal is said to be non periodic (Aperiodic) if it does not repeats at regular interval of time.

Condition for periodic signal and Aperiodic signal:

T₀ > 0, ⇒ period of the signal. : f₀ = 1/T₀ → frequency of the signal.

N ⇒ period of x(n) in samples.

Periodicity of the Signal x(t) = x₁(t) + x₂(t)

Here K and l are integers

Periodicity of DT signal x(n)

Let us consider the signal 

x(n) is periodic if x(n) = x(n + N)

Replace n by n + N in. (1)

Here K is integer.

Periodicity of DT signal x(n) = x₁(n) + x₂(n)

Let us consider the signal

Then x (n) is periodic if

Examples on Periodicity (Continuous Time Signal)

1. Find the periodicity of x(t) = sin 10 π t + sin 5 π t

Solution:

2. Find the periodicity of x(t)

Solution:

3. Determine the periodicity of following signal. If periodic obtain its fundamental period.

Solution:

4. Determine whether the following signals are periodic or not. If periodic determine the fundamental period.

Solution :

(ii) 

Solution :

(iii) 

Solution :

(iv) 

Solution :

Hence the fundamental time period

(v) 

Solution :

5) Determine the periodicity of the following signal x(t) = 5 cos(4t) + sin(πt)

Solution:

Hence the given signal is non periodic signal.

Examples on Periodicity for Discrete Time Signal

(1) Check the periodicity of following signal. If periodic determine its fundamental period.

Solution:

 which is rational. Hence the given signal is periodic signal.

Fundamental period N = 2.

Solution :

, 

which is rational. Hence the given signal periodic signal with period N = 12

Solution :

Hence the given signal is periodic signal with period N = 100

Solution :

Solution :

Solution :

4. Determine whether the following signal is periodic (or) not. If periodic find the fundamental period.

Solution:

This is rational. Hence the given signal is periodic signal with fundamental period N = 8.

5. Determine whether the following signal is periodic (or) not. x(n) = cos2n.

Solution:

This is not rational. Hence the given signal is nonperiodic signal.

6. Determine whether the following signal is periodic (or) not. 

Solution :

This is not rational. Hence the given signal is nonperiodic signal.