Signals Important Definitions

 Signals 

Definition Of Signal: 

A Signal is defined as any physical quantity that will be varying with time, space and any other independent variables. 

Definition of System: 

A System is defined in a way that any physical quantity that will represent a graph or a curve using mathematical modelling is known as a System.

Even (symmetric) and Odd (Anti-symmetric) signal: 

Continuous domain:

Even signal:

A signal that exhibits symmetry with respect to t=0 is called even signal

Even signal satisfies the condition x(t) =x(-t). 

xe(t)=12[x(t)+x(−t)]

Odd signal:

A signal that exhibits anti-symmetry with respect to t=0 is called odd signal

Odd signal satisfies the condition x(t) = -x(-t).

xo(t)=12[x(t)−x(−t)]

Periodic and Aperiodic Signals: 

A Continuous time signal is said to periodic if it satisfies the condition x(t) = x(t+T), where T is fundamental frequency. 

where T is 2pi/omega.

Energy of a Signal: 

    The signal which has finite energy and zero average power is called energy signal. The

non periodic signals like exponential signals will have constant energy and so non periodic

signals are energy signals.

Power of the Signal:

    The signal which has finite average power and infinite energy is called power signal. The

periodic signals like sinusoidal complex exponential signals will have constant power and so

periodic signals are power signals.

Deterministic signal:

    A signal is said to be deterministic if there is no uncertainty over the signal at any

instant of time i.e., its instantaneous value can be predicted. It can be represented by

mathematical equation.

Example: sinusoidal signal

Random signal (Non-Deterministic signal):

A signal is said to be random if there is uncertainty over the signal at any instant of time

i.e., its instantaneous value cannot be predicted. It cannot be represented by mathematical

equation.

Example: noise signal

Causal signal:

A signal is said to be causal if it is defined for t≥0.

i.e, x(t) =0 for t<0

Non-causal signal:

A signal is said to be non-causal, if it is defined for t< 0 or for both

t<0 and t>=0 

        i.e, x(t) ≠ 0 for t<0

When a non-causal signal is defined only for t<0, it is called as anti-causal signal.