In a **data communication** system a signal is basically a physical form of data. The physical layer of the **OSI model** converts the data in the form of signals. Two nodes in a communication system exchange data in the form of signals.

For example in wireless communication the signal propagation is done via electromagnetic waves also known as **radio waves**, in optical fiber system the signal is a light wave. Similarly in a computer system signal is an **electric current** that takes the data from one point to another.

In this signal and systems lecture I will discuss classification of signals**.** In addition to this I will discuss signal characteristics

**Types of Signals in Communication**

Mathematically the signal is represented as a function of time (t). Time is an independent variable. Now let’s try to understand how dependency on time results many types of signals in data communication.

**1. Continuous Time Signal **

According to continuous-time signal definition, if a signal y(t) varies continuously with respect to time, this is called continuous time signal. In other words a continuous time signal can take any value within a specified time interval (a,b). Interval can be from – ∞ to + ∞. Another name of this signal is analogue signal. The following figures shows graphical representation of analogue signal.

**Fig-1: Continuous Time Signal Graph**

**Continuous time signal examples **

- Audio signal
- Sine and cosine waves
- Wireless communication signal

**2. Discrete Time Signal**

If the signal is not continuous, means its values exist on discrete time intervals. Then its a discrete time signal. **(See Fig-2). **

**Fig-2: Discrete Time Signal Graph**

The discrete signal representing the sequence of values. That is why another name of discrete-time signal is digital signal.

We can get a digital signal by sampling the continuous-time signal. Sampling means we are taking the values of analogue signal at discrete intervals of time. **(See Fig-3). **Using the method of sampling we can convert an analogue signal into digital signal.

**Fig-3: Sampling of Analogue Signal**

In the above figure **{n1, n2, n3,..}** are the samples. So **y(t1) = y[n1], y(t2) = y[n2], y(t3) = y[n3]** and so on. Where **y[n1]** and **y[n2]** are the amplitudes of samples** n1** and **n2** at time **t1** and **t2** respectively.

#### Discrete Time Signal Example

- Noting the temperature values after every 1 hour
- The closing points of a stock exchange at the end of the working day

**3. Deterministic Signal**

Deterministic signals are those signals which can be represented in the form of precise mathematical equation or function of time. In other words we can find the values of the signal using that equation at any instant of time.

** Deterministic Signal Examples**

- Sinusoidal wave with some period
- Cosine wave
- Square wave

**4. Random signal**

Signals which are not deterministic in nature. They can take any value at any moment of time. They cannot be packed in the form of a precise mathematical equations because they are random in nature. Their amplitude and frequency can change at any instant. We can only predict their values Using some probabilistic model but cannot find exact values at any time.

**Fig-4: A Random Signal in Graphic Form**

** Random Signal Examples**

- Additive white Gaussian noise in communication channels
- Thermal noise created by the random motion of electrons in a conductor

**5. Even Signal **

If a signal is reversed in time such that the new signal is just a mirror image of the original signal (**See fig-5)**. The amplitude remains the same. This is called an even signal. Mathematically it can be written as

**Continuous time: **y(t) = y(-t)

**Discrete Time: **y[tn] = y[-tn] and n = 0,1,2,3,…

**Fig-5: Even Signal in Graphic form**

**6. Odd signal**

Even and Odd signals are almost same except in odd signal the time as well as the amplitude is also reversed. Mathematically it can be represented as

**Continuous time: **y(t) = -y(-t)

**Discrete Time: **y[tn] = – y[-tn] and n = 0,1,2,3,…

**Fig-6: Odd Signal in Graphic Form**

**7. Periodic signal **

The word periodic explaining the periodic signal definition. A signal which repeats its pattern or wave shape in equal intervals of time is the periodic signal **(See Fig-7). **In one complete cycle or time period (T) only one pattern or wave completes.

**Fig-7: Periodic Signal Examples**

### 8. Non Periodic or Aperiodic Signal

If a continuous time or discrete time signal which is not periodic is known as aperiodic signal. Non periodic signal does not follow any definite sequence in equal intervals of time. In **figure-4** above the random signal is also an example of non-periodic signal.

**9. Real and Complex Signals**

A signal is a real signal is it has real number values. Similarly complex signal is that which has complex values**. **Mathematically a general complex signal is written as a function of time and take the following form.

**z(t) = x(t) +jy(t)**

x(t) and y(t) are real signals and j = sqrt(-1)

**10. Energy Signal**

Energy signal and power signal are often discussed together. Here i will try to teach both of them one by one so you can understand easily.

A signal is said to be an energy signal if its energy (E) is always finite i.e 0 < E < ∞. Remember the power of energy signal is always zero. (see some solved examples below to understand this point).

Energy of a signal can be calculated by using the following formula

** Energy of Continuous-time Signal: **

**Energy of Discrete-time Signal:**

**11. Power signal**

If a signal has finite power then its a power signal i.e 0 < P < ∞. Here also remember that the energy of the power signal is infinite. The power of a signal can be calculated by using the following

**Power of Continuous-time Signal:**

**Power of Discrete-time Signal:**

**Example 1:**

**Calculate the energy and power of signal s(t) = 2 e^(-2t) u(t)**

Using equation (1)

As signal is multiplying with unit step function u(t), so it is zero from – ∞.to 0. Hence

Now calculate power using equation (3)

As energy is finite i.e 0 < E < ∞ and power is infinite. this fulfills the condition of an energy signal. So we can say this is an energy signal but not the power signal.

**Example 2:**

**Calculate the energy and power of signal s(t) = 2 u(t)**

Using equation (1)

As signal is multiplying with unit step function u(t), so it is zero from – ∞.to 0. Hence

Now calculate power using equation (3)

Now see the power is finite and energy is infinite. This is the condition of a power signal. Hence we can say this is a power signal but not the energy signal.

**Example 3:**

**Calculate the energy and power of signal s(t) = sint**

Using equation (1)

As signal is multiplying with unit step function u(t), so it is zero from – ∞.to 0. Hence

Now calculate power using equation (3)

From above discussion on energy and power signals we can conclude some important results which would be very important if we are solving signal and system problems

- The power of an energy signal is zero.
- The energy of a power signal is infinite.
- The periodic signal is always a power signal. But all power signals are not periodic.
- The signal with finite duration and finite amplitude is always an energy signal.

**Characteristics of Signal**

Signal characteristics describe the nature and features of a signal. In data communication the signal is represented by using the following four characteristics

**1. Frequency of a Signal**

Frequency is the rate at which a signal repeats in one second**. **It is my measured in Hertz (Hz). Frequency is basically the number of waves passing through a point in one second. **(See Fig-8)**

**Fig-8: (a) Sine wave (b) Saw-tooth Wave**

If one wave is passing through a point in one second then frequency is 1 Hz. If 10 waves are passing then frequency is 10 Hz.

A random signal can have more than one frequencies because it is not following a particular pattern. So it is usually described in terms of bandwidth.

**2. Amplitude of a signal**

Amplitude of a wave basically explains how strong is the signal. If you observe above figures the amplitude is equivalent to the height of the signal. It basically represents fluctuation or displacement of a signal above and below the reference point or mean value.

If it’s a voice signal then amplitude may be loudness of the voice. If it’s an electric signal amplitude could be the voltage level.

**3. Time Period of a Signal**

Time period is the time of completion of one wave. Refer figure-7 above to understand this. Time period and frequency are reciprocal to each other i.e T = 1/f.

If a signal has small time period then its frequency is high. Because the length of a wave is small. So more waves will pass through a point in one second. Signal with large time period has low frequency. Because less number of waves will pass through a point in one second

**Fig-9: (a) large time period, (b) small time period**

**4. Phase of a Signal**

Phase is basically the starting point of a signal. Phase difference brings the concept of leading and lagging between the two waves. We can distinguish the two signals on the same channel by their phase difference. **(See Fig-10)**

Another meaning of the phase is that how much a signal has been shifted from the reference point. A signal starting before the reference is lagging behind a signal starting on the reference or beyond the reference point by some phase angle measured in radians.

**Fig-10: Phase Difference between two waves**

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