Introduction to Some Simple Signal

7/30/2019 Introduction to Some Simple Signal

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Introduction to some simple signalDefinition of Signal:Any time varying physical phenomenon that can convey information is called signal.

Some examples of signals are human voice, electrocardiogram, sign language, videos

etc. There are several classification of signals such as Continuous time signal, discretetime signal and digital signal, random signals and non-random signals .

Continuous-time Signal:

A continuous-time signal is a signal that can be defined at every instant of time. Acontinuous-time signal contains values for all real numbers along the X-axis. It is

denoted byx(t). Figure 1(a) shows continuous-time signal.

Fig.1(a) Continuous-time signal 1(b) Discrete-time signal

Discrete-time Signal:

Signals that can be defined at discrete instant of time is called discrete time signal.

Basically discrete time signals can be obtained by sampling a continuous-time signal. Itis denoted asx(n).Figure 1(b) shows discrete-time signal.

Digital Signal:

The signals that are discrete in time and quantized in amplitude are called digital signal.The term "digital signal" applies to the transmission of a sequence of values of a

discrete-time signal in the form of some digits in the encoded form.

Periodic and Aperiodic Signal:

A signal is said to be periodic if it repeats itself after some amount of time x(t+T)=x(t),for some value ofT. The period of the signal is the minimum value of time for which it

exactly repeats itself.


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Fig.2(a) Periodic signal Fig.2(b) Aperiodic signal

Signal which does not repeat itself after a certain period of time is called aperiodic

signal. The periodic and aperiodic signals are shown in Figure 2(a) and 2(b) respectively.

Random and Deterministic Signal:

A random signal cannot be described by any mathematical function, where as adeterministic signal is one that can be described mathematically. A common example of

random signal is noise. Random signal and deterministic signal are shown in the Figure3(a) and 3(b) respectively.

Fig.3(a) Random signal Fig.3(b) Deterministic signal

Causal, Non-causal and Anti-causal Signal:

Signal that are zero for all negative time, that type of signals are called causal signals,

while the signals that are zero for all positive value of time are called anti-causal signal.A non-causal signal is one that has non zero values in both positive and negative time.

Causal, non-causal and anti-causal signals are shown below in the Figure 4(a), 4(b) and

4(c) respectively.

Fig.4(a)Causal

signal

Fig.4(b)Non-

caual

signal

Fig.4(c)Anti-

causal

signal


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Even and Odd Signal:

An even signal is any signal 'x' such that x(t) = x(-t). On the other hand, an odd signa

is a signal 'x'for whichx(t) = -x(-t). Even signals are symmetric around the verticalaxis, so that they can easily spotted.

Fig.5(a) Odd signal Fig.5(b) Even signal

An even signal is one that is invariant under the time scaling t - tand an odd signal isone that is invariant under the amplitude and time scaling x(t) - x(-t).

A simple way of visualizing even and odd signal is to imazine that the

ordinate [x(t)] axis is a mirror. For even signals, the part ofx(t) for t > 0 and the partofx(t) for t < 0 are mirror images of each other. In case of an odd signal, the same two

parts of the signals are negative mirror images of each other. Some signals are odd,some signals are even and some signals are neither odd nor even. But any

signalx(t) can be expressed as a sum of its even and odd parts such asx(t) = xe(t) +

xo(t) or we can say that every signal is composed of the addition of an even part and

odd part. The even and odd parts of a signalx(t) are

and

Herexe(t) denotes the even part of signalx(t) andxo(t) denotes the odd part of

signalx(t). Figure 5(a) and 5(b) shows the odd signal and even signarespectively.Impulse Signal:

The Dirac delta function or unit impulse or often referred to as the delta function, is the function that

defines the idea of a unit impulse in continuous-time. Informally, this function is one that is infinitesimally

narrow, infinitely tall, yet integrates to one. Perhaps the simplest way to visualize this as a rectangular

pulse from a -D/2 to a +D/2 with a height of 1/D. As we take the limit of this setup as D approaches 0, we

see that the width tends to zero and the height tends to infinity as the total area remains constant at one.

The impulse function is often written as


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Fig.9(a) Dirac delta functoin Fig.9(b) Unit impulse

Since it is quite difficult to draw something that is infinitely tall, we represent the Dirac with an arrow

centered at the point it is applied. The dirac delta function and unit impulse are shown in Figure 9(a) and

9(b) respectively.

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Introduction to Some Simple Signal