Classification of Signals and Systems

CLASSIFICATION OF SIGNALS AND SYSTEMS

SIGNAL

Signal is a physical quantity that carries some information and it depends upon one or more independent variable.

(Time, spatial co-ordinates, temperature etc., are independent variable)

Example

TV signal, radio signal, speech signal

Classifications of Signals:

Signals are basically classified in to two types.

i. Continuous time signals (CT signals)

ii. Discrete time signals (DT signals)

Continuous Time Signals: (CT Signals)

Continuous time signal is defined for all values of time "t" and it is represented by x(t). Magnitude of CT signal is continuous in the specified range of time.

Discrete Time Signals: (DT Signals)

Discrete time signal is defined only at regular time interval. It is represented by x (n). Here "n" denotes discrete interval of time. "n" ranges from - ∞ to +∞.

Example:

Figure 1.1 shows an example of CT signal and DT signal

ELEMENTARY SIGNALS

Elementary (or) standard signals are used for the analysis of continuous time and discrete time systems.

Elementary signals are listed as follows.

i. Unit step signal

ii. Unit impulse signal

iii. Unit ramp signal

iv. Sinusoidal signal

v. Exponential signal

Unit Step Signal

i. Unit step signal has amplitude "1" for the positive values of "t" (or) "n".

ii. Unit step signal has amplitude "o" for the negative values of "t" or "n".

Representation:-

Unit Impulse (or) Delta Function

Unit impulse signal δ(t) (or) unit sample signal δ(n) has unit amplitude at t = 0 (or) at n = 0.

Representation:

Waveform:

Shifting property of unit impulse signal

Shifting property of unit sample signal.

Unit Ramp Signal

Unit ramp signal is linearly growing function for positive values of "t" (or) positive values of "n".

Representation

Exponential Signal

Exponential signal is exponentially growing (or) decaying signal.

Representation:

Waveform:

Complex exponential signal

If the exponent of a signal is imaginary then the signal is known as complex exponential signal.

Continuous time (CT) complex exponential signal

Discrete time (DT) complex exponential signal.

Sinusoidal Signal

Continuous time sinusoidal signal:

Discrete time sinusoidal signal:

Comparision of continuous and discrete time signal