**What is Signal, Classification of Signals and the role of Signals in Digital Communication**

Table of Contents

**What Is Signal?**

A

signalis defined as anyphysicalorvirtual quantitythat varies withtimeorspaceor any other independent variable or variables.

Graphically, the **independent variable** is represented by **horizontal axis** or x-axis. And the **dependent variable** is represented by **vertical axis** or y-axis.

Mathematically, a signal is a function of one or more than one independent variables.

**Single Variable Signal**

It depends on a single independent variable. It either varies linearly or non-linearly depending on the expression of the signal. Examples of single variable signal are:

**S(x) = x+5**

**S(x) = x ^{2}+5** Where

**x**is the variable

**S(t) = cos(wt+ϴ)** Where **t** is the variable

**Two Variables Signal**

A **two variable signal** varies with the change in the two independent variables. Example of a two variable signal is

**S(x,y) = 2x+ 5y**

**Characteristics Of Signal**

A signal is defined by its characteristics. It shows the nature of the signal. These characteristic are given below:

**Amplitude**

Amplitude is the **strength **or** height** of the signal waveform. Visually, it is the height of the waveform from its center line or x-axis. The y-axis of a signal’s waveform shows the amplitude of a signal. The amplitude of a signal varies with time.

For example, the amplitude of a sine wave is the maximum height of the waveform on Y-axis.

The signal’s strength is usually measured in **decibels db**.

**Frequency**

Frequency is the rate of repetitions of a signal’s waveform in a second.

Periodic signals repeat its cycle after some time. The number of cycles in a second is known as **Frequency**. The unit of Frequency is **hertz (Hz)** and **one hertz** is equal to **one cycle** per second. It is measured along the x-axis of the waveform.

For example, a sine wave of **5 hertz** will complete its **5 cycles** in a **one second**.

**Time** **Period**

The time period of a signal is the time in which it completes its one full cycle. The unit of the time period is **Second**. The time period is denoted by **‘T’** and it is the **inverse** of **frequency**. I.e.

**T=1/F**

For example, a sine wave of time period **10 sec** will complete its **one full cycle** in **10 seconds**.

**Phase**

The phase of a sinusoidal signal is the **shift** or **offset** in its origin or starting point. The phase shift can be **lagging** or **leading**. Usually, the **original** sinusoidal signals have **0°** degree phase and start at 0 amplitude but an offset in phase will shift its starting amplitude to other than 0.

An example of **45°** phase shift is given below. The signal remains same but its origin is shifted to **45°**.

The phase shift can be from **0° to 360°** in **degrees** or **0 to 2π** in **radians**. 360° degree or 2π radians is one complete period.

**Signal Size**

The size of a signal is a number that shows the **strength** or largeness of that signal. As we know, a signal’s amplitude varies with respect to time. Because of this variation, we cannot say that its amplitude can be its size. To measure the signal size, we have to take into account the **area covered** by the amplitude of the signal within the time duration.

According to the size of the signal, there are two parameters.

**Signal Energy**

The energy of the signal is the area of the signal under its curve. But the signal can be in both positive and negative region. Due to which, it will cancel each other’s effect resulting in a smaller signal. To eradicate this problem, we take the **square of the signal’s amplitude** which is always positive.

For a signal g(t), the area under the **g ^{2}(t)** is known as the

**Energy of the signal**.

**Unit Of Energy Of Signal**

This energy is not taken as in its conventional sense, but it shows the signal size. Therefore, its unit is not joule. The unit of energy **depends on the signal**. If it is a **voltage signal** then its unit will be **volts ^{2}/second**.

**Limitation**

The energy of a signal can be measured only if the **signal** is **finite.** The **infinite signal** will have **infinite energy**, which is absurd. A **finite signal’s** amplitude **goes to 0** as the time (t) approaches to **infinity** (∞).

So it is **necessary** that the signal is a **finite** **signal** if you want to measure its energy.

**Signal Power**

If the signal is an **infinite signal** i.e. its **amplitude** does not go to **0** as time t approaches to **∞**, we cannot measure its energy. In such case, we take the time average (**Time period**) of the energy of the signal as the power of the signal.

**Unit Of Power**

Similar to Energy of the signal, this power is also not taken in the conventional sense. It will also **depend** on the **signal to be measured**. If the signal is **voltage signal**, then the power will be in **volts ^{2}**.

**Limitation**

Just like the energy of signal, the measurement of the power of a signal also has some limitation that the signal **must** be of a **periodic nature**. An **infinite** and **non-periodic** signal neither have **energy nor power**.

**Classification Of Signals**

Signals are classified into different categories based on their characteristics. Some of these categories are given below.

**Analog Vs. Digital Signal**

The signal can be classified into analog or digital category base on their **amplitude**. This classification is based on only **vertical-axis** (amplitude) of the signal. And it does not have any relation with horizontal-axis (time axis).

The amplitude of an **analog signal** can have **any value** (including fractions) at any point in time. That means analog signal have **infinite values**.

However, the **digital signal’s** amplitude can only have **finite** and **discrete** values.

The **special case** of Digital signal having **two discrete** values is known as **Binary signal**. However, the number of values for amplitude in a digital signal is **not limited** to **only two**.

Analog signal is converted into Digital signal using **A to D converter (ADC)**.

**Continuous-Time And Discrete-Time Signal**

This classification is based on the **horizontal axis** (time axis) of the signal.

Continuous and discrete time signals should not be confused with analog and digital signal respectively.

A **continuous time** signal is a signal whose value (amplitude) exists for **every fraction** of **time** t.

A **discrete time** signal exists only for a **discrete value** of **time t**.

**Remember**, there is **no limitation** on the **amplitude** of the signal. That is why it should not be confused with the analog or digital signal.

**Energy Vs. Power Signal**

A signal is **Energy signal** if its **amplitude** goes to **0** as **time** approaches **∞**. Energy signals have finite energy.

Similarly, a signal with finite power is known as Power signal. A **power signal** is a **periodic signal** i.e. it has a time period.

An **Energy signal** has **finite Energy** but **zero power**. And a **Power signal** has **finite Power** but **infinite Energy**. So a signal can be **either energy signal** or **power signal** but it **cannot** be **both**.

An **infinite signal** that has **no periodic nature** is neither **Energy nor Power signal**.

**Periodic Vs. Aperiodic Signal**

A **periodic signal** is a signal which keeps **repeating** its pattern after a **minimum fixed time**. That time is known as **Time period ‘T’** of that signal. Periodic signal does not change if it is time-shifted by any multiple of Time period “T”.

The mathematical expression for periodic signal **g(t)** is:

**T _{0 }**is the Time period of signal

**g(t)**.

**Periodic signal** starts from **t=-∞** and continues to **t=+∞**. A signal which starts at **t=0** will not be the same signal if it is time-shifted by +T because it did not exist for negative **t.**

The **aperiodic** or **non-periodic** signal is a signal which does **not repeat** itself after a specific time. These signals have **no repetitions** of any pattern.

**Deterministic And Random Signal**

A signal which can be represented in **mathematical** or **graphical form** is called **deterministic signal**. Deterministic signals have **specified amplitude, frequency** etc. They are easy to process as they are defined over a long period of time and we can **Evaluate** its **outcome** if they are applied to a specific system based on its expression.

The **random** or **non-deterministic** signal is a signal which can only be represented in **probabilistic expression** rather than its full mathematical expression. Every signal that has some kind of **uncertainty** is a **random signal**. **Noise signal** is the best example of random signal.

Generally, every message signal is a random signal because we are uncertain of the information to be conveyed to the other side.

**Operation Of Signal**

Some basic operation of signals are given below

**Time Shifting**

**Time-shifting** means **movement** of the signal across the **time axis** (**horizontal axis**). A time shift in a signal does not change the signal itself but only shifts the origin of the signal from its original point along time-axis.

Basically, **addition in time** is time shifting. To time-shift a signal **g(t)**, **t** should be replaced with **(t-T)**, where **T** is the seconds of **time-shift**. Therefore, **g(t-T)** is the time-shifted signal by **T** seconds.

Time shift can be **right-shift** (delay) or **left-shift** (advance).

If the time-shift **T** is **positive** than the signal will shift to the **right** (delay). For example, the signal **g(t-4)** is the shifted version of **g(t)** with **4** seconds **delay**.

If the time-shift **T** is **negative** than the signal will shift to the **left** (advance). The signal **g(t+4)** is the shifted version of **g(t)** with **4** seconds to the **left**.

**Time Scaling**

**Time scaling** of a signal means to **compress** or **expand** the signal. It is achieved by **multiplying** the **time variable** of the signal by a **factor**. The signal expands or compresses depending on the factor.

Suppose a signal **g(t)** than its scaled version is **g(at)**.

If the factor **a>1** then the signal will **compress**. And the operation is called **signal compression**. Compressing a signal will make the signal **fast** as it becomes smaller and its time duration become less.

If **a<1** then the signal will **expand**. And the operation is called **signal dilation**.

After scaling, the **origin** of the signal remains unchanged. Expanding the signal will make the signal **slow** as it becomes wider and covers more time duration.

**Time Inversion**

In **time inversion**, the signal is **flipped** about the **y-axis** (vertical axis). The resultant signal is the **mirror image** of the original signal.

Time inversion is a special case of **time-scaling** in which the **factor a=-1**. Therefore to invert a * signal*, we replace it’s

**(t)**with

**(-t)**.

Mathematically, the time-invert of signal g(t) is g(-t).

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