Table of Contents

**Classification of Signal:**

In the communication we had seen the basic block diagram of the communication system and the first block of this communication is the message signal. So if the message signal is in non-electric form then using the transducer. It is converted into the electrical signal. So in communication first of all we should aware about what type of signal we are dealing with that means whether the signal is analog or digital or is it periodic order aperiodic. So for the communication perspective the signal can be classified in the following categories.

**Continuous time signal VS Discrete time signal:**

So let us see this classification one by one so first is continuous time and discrete time signal. So if the signal is specified for every value in the time then it is known as the continuous time signal and these are the some of the examples of the continuous time signal.

So as you can see over here for each value in the time the signal has some finite value and this is the another example of the continuous time signal.

On the other end if the signal is specified only for the discrete time instances then it is called the discrete time signal. So this is the example of the discrete time signal so this graph shows the daily average temperature of the particular city and as you can see the values are available on the daily basis that means in between values are missing over here. So that is the example of the discrete time signal.

**Analog signal VS Digital signal:**

The next classification is whether the signal is analog or the digital signal. So a signal whose amplitude can take any value in the continuous range then it is known as the analog signal for example this signal over here is the example of the analog signal because here its amplitude can take any value on the y-axis and even the discrete time signal can also be an analog signal for example this signal is a discrete signal.

Yet it is the analog signal because here on the y-axis the values that but there could be any value on the other end the digital signal is the one whose amplitude can take only finite number of values for example this signal is the digital signal whose amplitude can take only two different values. So here just do not get confused with the digital signal and the discrete-time signal the digital signal can take only finite values on the y-axis.

While the discrete-time signal can have a values only at the discrete-time intervals similarly you don’t get confused with the continuous-time signal and the analog signal. So as I said the analog signal can take any finite values on the y-axis. While the continuous-time signal shows the continuity of the signal on the time axis so this analog signal could be continuous or the discrete-time signal. For example this signal is the continuous in time yet it can have any finite value on the y-axis so it is the continuous as well as the analog signal on the other end this signal is analog in the discrete time signal because this signal is available at the discreet time intervals but on the y-axis it can have any finite value. Similarly the digital signal could be continuous or the discrete signal for example this signal is continuous in time but it is varying between the two finite values that means this signal is a digital signal as well as the continuous time signal on the other end this signal is a digital signal as well as the discrete time signal. So that is all about the analog and the digital signals.

**Periodic signal VS Aperiodic Signal:**

The next classification is the periodic and the aperiodic signals so if the signal repeats itself after some finite time then it is called the periodic signal. For example this signal over here is the periodic signal because it is repeating itself after some finite time period and the minimum time after which the signal repeat itself is known as the time period of the signal and mathematically the signal is said to be a periodic if:

f (t) = f (t+T)

It means that if we shift this signal by one time period then also it remains the same.

On the other end the signal which is not periodic is known as the aperiodic signal means that a signal which does not repeat itself .

**Energy Signal VS Power Signal: **

Then the next classification is the energy and the power signal. Now whenever we are talking about any type of signal then one thing which we need to ask is what is the strength of the signal and the strength of the signal is measured in terms of the energy of the signal and this energy of the signal can be given by the following expression. Now to measure the energy of the signal the energy of the signal has to be a finite that means as T tends to infinity then the amplitude of the signal has to go to zero like for this signal has the T approaches to infinity then the amplitude of the signal goes to zero.

So if the amplitude does not go to zero then the energy of the signal is infinite and in that case the more meaningful measure is the time average of the energy or in other words we can find the average power of the particular signal so the average power of the signal can be given by the following expression for example if you look this signal then the energy of this signal is infinite because s time T approaches to infinity then the amplitude of the signal does not go to zero that means if you find the energy of such signal then it will be equal to infinite but for such signal we can find the average power.

So if the signal is periodic or has some statistical reputation then we can find the average power. Now since the time average is taken over the infinitely large interval the signal which has a finite energy will have a zero power that means if we take the time average of the signal which has a finite energy then its average power will come out as zero on the other end if we find the energy of the signal which has a finite power then it will be equal to infinite that means the signal can be either an energy signal or the power signal but it can’t be both at the same time but the some signals for which we cannot find the energy or the power for example if you take the example of the ramp signal then we cannot find the energy or the power. So such signals are neither energy signal or the power signals. So in short the signal which has a finite energy is known as the energy signal and the signal which has a finite power is known as the power signal so let us quickly find the energy in the power for few signals. So let’s say this signal can be expressed as 2 times e to the power minus T by 2 that means at T is equal to 0 the amplitude of the signal is equal to 2.

Now if you see where here this signal exists for the time T greater than or equal to 0 so for this signal the energy will be equal to:

if you calculate the energy then the energy of this signal will come out as 4 Joule.

Similarly let us find out the average power of this signal so as you can see this signal is the periodic signal and the time period of this signal is equal to 2 seconds that means this signal repeat itself after the 2 seconds that means instead of everything this time signal over the infinitely large time interval we can average this time signal over the single time period that means the average power of the signal can be given as:

if you calculate the value then it will come out as 1 by 3 that means we can see that the average power of the given signal is equal to 1 by 3 watt so in this way we can find the energy or the power of the particular signal.

**Deterministic VS Random signal:**

The next classification is whether the signal is deterministic or the and end up signal so a signal is said to be a deterministic signal if its physical description is not completely either in the mathematical form or in the graphical form for examples the signal which we have discussed so far can be expressed either in the mathematical form or in the graphical form so they were the example of the deterministic signals on the other end if the signal is known only in terms of the probabilistic description like a mean value the mean square value and the distribution of the signal then such type of signals are known as the random signal. So most of the noise signals which are found practically are the examples of the random signal so that is the brief classification of the different types of signals. Now in the communication apart from this classification sometimes we need the more information about the particular signal like what is the frequency of the signal or if the signal contains more than one frequency then what is the range of the frequencies in the particular signal so let’s take the example of this signal so in the time domain and this signal does not give us much information but if you see the frequency spectra then we can see that it contains the frequencies from 0 to 3 kilo Hertz so from this we can predict the bandwidth of the signal and we can also know how the signal will behave whenever it will pass through the particular medium let’s take the another example so just by looking at the signal we can tell that it is the periodic signal and at the most we can also find the amplitude but on the other end if we represent this signal in the frequency domain then we can tell that it contains the three frequency components so many times my representing the signal in the frequency domain can gives us the more information so using the Fourier analysis we can find the different frequency components in the particular signal.