Basic idea of Signals and Systems

Signals and Systems: It is a collection of tool using which we can solve our engineering problems.

Signals:

-Any waveform that can carry information is signal (for comm. Engg.)

-A signal is a set of information or data. Ex – Telephone or television signal etc.

-Signal is a function of time and therefore signal may be defined as a set of rules to assign a number f(t) for every number t(For electrical engg.)

-Signals are not always function of time, may be function of space Ex – Electrical charge distributed over a surface, the signal is charge density, a function of space (Electrical signal doesn’t have information)

Systems:

-A system is an entity that processes a set of signals (inputs) to yield another set of signals (outputs)

-System processes signals, may modify them or extract additional information from them. -Systems may be made up of physical components as in electrical, mechanical or hydraulic systems (hardware realization) or it may be an algorithm that computes an output from an input signal (software realization).

-Systems convert available signal into desired signal.

-Most complicated system is human body

- Signals can’t be generated automatically.

Classification of Signals:

1. Continuous-time and Discrete-time signals

2. Analog and Digital Signals

3. Energy and power signals

4. Deterministic and probabilistic signals

Continuous-time signal: A signal that is specified for every value of time. Ex- Telephone and video camera outputs.

Discrete-time signals: A signal that is specified only at discrete values of t. Ex – Monthly sales of a corporation, stock market daily averages.

Analog Signal: A signal whose amplitude can take on any value in a continuous range. This means that analog signal amplitude can take on an infinite number of values.

Digital Signal: A signal whose amplitude can take on only a finite number of values.Ex – Signals associated with digital computer are digital (Binary Digital)

The term continuous time and discrete time qualify the nature of a signal along the time (horizontal axis).

The term analog and digital qualify the nature of signal amplitude (vertical axis)

(a) Analog,continuous signal (b) Digital ,continuous signal (c) Analog ,discrete-time signal

(d) Digital, discrete-time signal

Note: It is clear that analog is not necessarily continuous time and digital need not be discrete time.

Periodic Signal: A signal g(t) is said to be periodic if for some positive constant T, g(t)=g(t+T) for all t. Smallest value of T is known as period of g(t)

1. Periodic signal must start at t= -infinite ,because if it starts at some finite instant,say t=0 , the time shifted signal g(t+T) would not be same as g(t).Thus a periodic signal ,by definition must start at t= -infinite and continue forever.

2. g(t) can be generated by periodic extension of any segment of g(t) of duration T(period)

Aperiodic signal: A signal is aperiodic if it is not periodic.

Energy Signals: A signal with finite energy is an energy signal. Mathematically

Power signals: A signal with a finite and nonzero power (mean square value) is a power signal. Mathematically

Power is the time average of the energy. Since the averaging is over an infinitely large interval, a signal with finite energy has zero power and signal with finite power has infinite energy. Therefore a signal can’t be an energy and power signal. Note: There are signals that are neither energy nor power signals. Ex – Ramp signal Every signal observed in real life is an energy signal A power signal, on the other hand, must necessarily have an infinite duration otherwise its power which is its average energy (averaged over an infinitely large interval) will not approach a (non zero) limit. Obviously it is impossible to generate a true power signal in practice.

Note: All periodic signals are power signals however not all power signals are periodic.

Random Signals: All message signals are random signals because to convey information a signal must have uncertainty about it.