CLASSIFICATION OF SIGNALS

CLASSIFICATION OF SIGNAL

Signal my be classified in several ways:

1. The signals can be one-dimensional or multidimensional

(a) ONE-Dimensional Signals.

When the function depends on a single variable, the signal is said to be one incision Al Speech signal, whose amplitude varies with time, is one dimensional signal.

(b) MultiDimensional Signals.

When the function depends on a single variable, the signal is said to be one incision Al Speech signal, whose amplitude varies with time, is one dimensional signal.

2. Based upon their nature and characteristics in the time domain, the signals may be broadly classified as given below.

(a) Continuous-Time Signals.

This function is defined continuously in the time domain. A continuous-time

signal is represented by x) where x represents the shape of the signal and shows that the variable is time.

This signal will have some value at every instant of time. show is time singnal fig (a)

(a) A Continuous-Time Signals

(b) Discrete-Time Signals.

A discrete-time signal is defined only at certain time instants. For discrete time signals,

(b) Discrete-Time Signals

the amplitude between two time instant is not defined. It is represented by xem, here time n is the independent variable. Figure (b) shows discrete-time signal. Mathematically, a discrete time signal is denoted as under

Rn) = (.0.0, 1, 3.0, -2, 1,2,0.)

Here arrow indicates the value of n) at n =0.

3. Deterministic and Non-Deterministic (Random) Signals.

Deterministic signals are those signals which can be completely specified in time. The pattern of this type of signal is regular and can be characterized mathematically. Also the nature and amplitude of such a signal at any time can be predicted.

So these signals are called deterministic signals. A non-deterministic signal is one whose occurrence is always random in nature. The pattern of such a signal is quite irregular so these signals are also called random signals. For example, a thermal noise generated in an electric circuit is a

non-deterministic signal.

4. Periodic and Non-Periodic Signals.

(a) Periodic Signal.A signal which repeats itself after a fixed time period is called a periodic signal. It can bedefin mathematically as

x(t)=x(t+To).It is a condition of periodicity

Here To is called as the period of signal x().

Example of these signals are sine wave, cosine wave, square wave etc.

(b) Periodic Discrete-Time Signal. For the discrete-time signal, the condition of periodicity is

xin) = x(n + N)

Here, N is the period of signal and its smallest value is called as fundamental period.

(c) Non-Periodic Signal. A signal which does not repeat itself after a fixed time period or does not repeat at all is

called as non-periodic or aperiodic signal. Mathematical expression for this signal is Sometimes value of period T, = oo then it is an export

x(t) # x(1 + T

tial signal and mathematically can be expressed as

x(n)=x(n+N)

5.Symmetrical(Even) or Anti symmetrical (Odd) Signals.

(a) Symmetrical Continuous Time Signal. A signals x() is symmetrical or even if it satisfies the following condition:

x(t)=x(-t)

Here x(t) is value of signal for positive r and x(-t) is value of signal for negative t.

Cosine wave is an example of symmetrical continuous time signal.

(b) Anti symmetrical Continuous Time Signal.

A signal x(t) is anti symmetrical or odd if it satisfies the following condition:

x(t) = -x(-t)

Sine wave is an example of anti symmetrical continuous time signal.

(C)

(c) Symmetrical Discrete- Time Signal. This type of signal satisfies the following condition and is shown in Fig. D (a)

x(n) = x(-n)

(d) Unsymmetrical Discrete-Time Signal. This type of signal satisfies the following condition and is shown in ko

Fig. D (b)

x(n) =-x(-n)

D Symmetrical and Anti symmetrical Discrete - Time Signal.

6. Energy and Power Signals.

Signals may be classified as energy and power signals. However, there are some signals which can neither be classified as energy signals nor power signals.

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

x(t) is an energy signal if it satisfies following condition:

0<E< and P 0

Here, E is the energy and P is the power of signal x(t).

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

x(1) is a power signal if it satisfies following condition:

0<P<0 and E= 0

7. Signal Channel and Multichannel Signals

Multichannel signals are generated by multiple sources or multiple sensors. The resultant signal is the vector sum of signals from all channels. It is expressed as:

A common example of multichannel signal is ECG waveform.

8. One-Dimensional And Multidimensional Signals.

If a signal is a function of single independent variable, the signal is called as one-dimensional signal. On the other hand, if the signal is a function of multi independent variables then it is called as multidimensional signal.

For example, to locate a pixel on the TV screen, two coordinates X and Y are required and this pixel is a function of time too. This it is a multidimensional signal and can be expressed mathematically as P(x, y, 1).