# Continuous Time And Discrete Time Signals

A signal is a quantity which contains information. For example, speech, music, the speed of an automobile, etc.

**Continuous time signal**

**Fig. :** Graphical representation of continuous time signal

**Discrete time signal**

**Fig. : **Graphical representation of discrete time signal

# Basic Signals

**Rectangular pulse:**It is given by A = rect(t/2a)

**Fig. : **Rectangular Pulse

**Unit step function:**

**Fig. : **Unit Step

**Ramp function:**

**Fig. : **Ramp Pulse

**Sampling function:**Sa(x) = sinx/X

**Fig. : **Sampling Function

**Exponential function:**Represented by*e*^{x}

^{}^{ }

^{}^{ }

**Fig. : **Exponential Function

**Unit impulse function/Dirac-Delta function**

** **

**Fig. : **Unit Impulse Function

**Signum function:**

** **

**Fig. : **Signum Function

# Categories of Signals

**Energy Signal**{x(t) or x(n)}: Its total energy has a non-zero finite value, i.e. .

The total energy in continuous time is defined as

In discrete time

**Power Signals**: The total power has a non-zero finite value. 0 <*P*< âˆž_{x}

**Three classes of signals:**

**Class 1:** Signals with finite total energy, E_{âˆž} < âˆž and zero average power, (Energy signal)

**
Class 2: **With finite average power P

_{âˆž}. If P

_{âˆž}> 0, then E

_{âˆž}= âˆž. An example is the signal x[n] = 4, it has infinite energy, but has an average power of

P

_{âˆž}= 16 (power signal)

** **

**Class 3: **Signals for which neither P_{âˆž} and E_{âˆž}_{ }are finite. An example of this signal is x(t) = t.

**Even and Odd Signal:**If signal x(t) = x(-t), then it is an even signal, e.g. Cos x

** **

**Fig. : **Even continuous signal

**Fig. : **Odd continuous signal

If signal *x*(*t*) = {â€“*x*(â€“*t*)}, then it is odd, e.g. sin x shown in fig. 13.

**Periodic and Non-periodic Signal :**Periodic signals repeats the same pattern for an infinite time as shown in fig. . Expressions for periodic signals :

whereas, a non-periodic signal has a non-repeating pattern.

** **

**Fig. : **Periodic signal

**Causal and Non-Causal Signals**: If*x*(*t*) = 0, for*t*< 0 & for*n*< 0,*x*(*n*) = 0, then it is a causal signal as shown in fig. 15.

** **

**Fig. : **Causal signal