Classification of Signals

The signals are classified according to their nature.

1. Continuous time signal and Discrete time signals
2. Deterministic and Random Signals 
3. Even and Odd Signals
4. Periodic and Aperiodic (Non Periodic) Signals
5. Energy and Power Signals

Continuous Time and Discrete Time Signals

In case of continuous time signals, the independent variable is continuous and thus these signals are defined for a continuum of values of the independent variable. The symbol "t" is generally used to denote the continuous time independent variable. Continuous time signals encloses the independent variable in parentheses like (t).

Continuous Time Signal Graphical Representation

Discrete time signals are defined only at discrete times and consequently for these signals, the independent variable takes only a discrete set of values. The discrete time signals are denoted by "n" and are enclosed in brackets like this [n].
Continuous time signals and discrete time signals are further classified, which will be discussed in next post.

Discrete Time Signals Graphical Representation

Deterministic and Random Signal

Deterministic Signal

Any signal that can be uniquely described by an explicit mathematical expression, a table of data or well defined rule is called deterministic signal. It can also be defined as a signal about which there is no uncertainty at any time with respect to its value. The term deterministic emphasizes that all past, present and future values of the signal are known precisely without any uncertainty and are completely specified functions of times. 

Examples : x(t) = Ae^-2t
                  x[n] = 2ⁿ
Random Signal
It is defined as a signal about which there is uncertainty before its actual occurrence. Random signals take on random values at any given time instant and must be modelled probabilistically. They cannot be described to any reasonable degree of accuracy by explicit mathematical formulas.
Examples : Seismic signal, speech signal.

Even and Odd Signal

Even signal 
If the time reversal of x(t) or x[n] is identical to it that is with its reflection about the origin, then the signal is referred to as an even signal. in continuous time a signal is even if

x(-t)=x(t)     ....... for all t 

A discrete time signal is even if

(-n)=x[n]     ....... for all n

Odd signal-

A signal x(t) or x[n] is to odd signal if x(-t)= -x(t) an odd signal must necessarily be at 0 at t=0 or n=0 since x(0)= -x(0) and x[0]= -x[0]

Examples-
Functional form :- Even signal - cosω₀t
                               Odd signal - sinω₀t

Fig(b): Odd continuous time signal

Graphical representation :

Fig(a): Even time  continuous signal

Periodic and Non Periodic(Aperiodic) Signal

Periodic Signal

Any signal whose amplitude values repeat after certain time interval is called a periodic continuous signal x(t) has the property that there is a positive value of T for which 

x(t) = x(t + T)          .......for all values of t

The above equation holds for the smallest positive values of T which is the fundamental time period T₀ of x(t). The fundamental period T₀ is the amount of time taken by the signal x(t) to complete its one cycle. The fundamental frequency of signal is the reciprocal of fundamental time period T₀.

ƒ = ¹/_T0...........Hertz or cycles/second

The fundamental angular frequency is given by 

ω = 2ϖƒ = ^2ϖ/_T0

Periodic Continuous Time Signal

Note:- Sinusoidal signals are periodic signals. 

           Asinω₀t , Acosω₀t ..............................................with period ^2ϖ/_T0

Periodic Signal are defined analogously in discrete time. A discrete time signal x[n] is said to be periodic if it satisfies the condition,

x[n] = x[n +N]        ............for all N

where N is a positive integer, if it is unchanged by time shift of N. The smallest value of N which satisfies the condition is called as fundamental period N₀ of x[n]. The fundamental angular frequency of x[n] is given by,

Ω = ^2ϖ/_N0.......... radians

A discrete time periodic signals

Non Periodic Signal (Aperiodic Signal)

Any continuous time signal x(t) which does not satisfy the condition,

x(t) ≠ x(t + T)

is called non periodic or aperiodic signal. There is no value of T which satisfies the above condition.

Any discrete time signal x[n] which does not satisfy the condition, 

 x[n] ≠ x[n +N]

is called non periodic or aperiodic discrete time signal.

Examples :- Exponential signals like e^-αt, parabolic signals are non periodic signals.