What is a Signal?A signal can be defined in one of the following ways −Anything that conveys information can be termed as a signal.A signal can also be defined as a single valued function of one or more independent variables which has some information.A signal may also be defined as any physical quantity that varies with time or any other independent variable.A signal may be represented in time domain or frequency domain. Some common examples of a signal are human speech, electric current, electric voltage, etc.By the definition, a signal can be a function of one or more independent variables ... Read More

When a signal gives the constant acceleration distinction of actual input signal, such a signal is known as parabolic signal or parabolic function. It is also known as unit acceleration signal. The unit parabolic signal starts at t = 0.Continuous-Time Unit Parabolic SignalThe continuous-time unit parabolic signal is a unit parabolic signal which is defined for every instant of positive time. It is denoted by p(t). Mathematically, p(t) is given as, $$\mathrm{p(t)=\left\{\begin{matrix} \frac{t^{2}}{2}\; for\: t\geq 0\ 0\; for\; t< 0\ \end{matrix}\right.}$$Also, $$\mathrm{p(t)=\frac{t^{2}}{2}\;u(t)}$$The graphical representation of the continuous-time parabolic signal p(t) is shown in Figure-1.Discrete-Time Unit Parabolic SignalThe discrete-time unit parabolic ... Read More

What is a System?In signals and systems, a system can be defined in a number of ways as −A system is defined as a physical device that can produce an output or response for the given input.A system may also be defined as an entity which works on an input signal and transforms it into an output signal.A system can also be defined as a set of elements which are connected together and generates an output signal corresponding to an input signal.Generally, a system is represented by a block diagram as shown in Figure-1. Here, the arrow entering the box ... Read More

Stable System or BIBO Stable SystemA system is called a BIBO (bounded input bounded output) stable system or simply stable system, if and only if every bounded input produces a bounded output. The output of a stable system does not change unreasonably.The stability of a system indicates the usefulness of the system. The stability of a system can be determined from the impulse response of the system. The impulse response of the system is nothing but the output of the system for a unit impulse input.If the impulse response of the system is absolutely integrable for a continuoustime system or ... Read More

A single valued function of one or more independent variables which contains some information is known as a signal.Basic Types of SignalsThere are several basic signals which play an important role in the study of signals and systems. These basic signals are the basic building blocks for the construction of more complex signals. These elementary signals are also called standard signals.Rectangular SignalA signal that produces a rectangular shaped pulse with a width of τ (where 𝜏 = 1 for the unit rectangular function) centred at 𝑡 = 0 is known as rectangular signal. The rectangular signal pulse also has a ... Read More

What is Amplitude Scaling?The process of rescaling the amplitude of a signal, i.e., the amplitude of the signal is either amplified or attenuated, is known as amplitude scaling. In the amplitude scaling operation on signals, the shape of the resulting signal remains the as that of the original signal but the amplitude is altered (i.e., increased or decreased).Amplitude Scaling of a Continuous-Time SignalThe amplitude scaling of a continuous time signal x(t) is defined as, 𝑦(𝑡) = 𝐴 𝑥(𝑡)Where, A is a constant. If the value of A is greater than 1 (i.e., A > 1), the signal amplitude scaling is ... Read More

Even SignalA signal which is symmetrical about the vertical axis or time origin is known as even signal or even function. Therefore, the even signals are also called the symmetrical signals. Cosine wave is an example of even signal.Continuous-time Even SignalA continuous-time signal x(t) is called the even signal or symmetrical signal if it satisfies the following condition, 𝑥(𝑡) = 𝑥(−𝑡); for − ∞ < 𝑡 < ∞Some examples of continuous-time even signals are shown in Figure-1.Discrete-time Even SignalA discrete-time signal x(n) is said to be even signal or symmetrical signal if it satisfies the condition, 𝑥(𝑛) = 𝑥(−𝑛); for ... Read More

Addition and Subtraction of Continuous-Time SignalsThe sum of two continuous time signals 𝑥1(𝑡) and 𝑥2(𝑡) can be obtained by adding their values at every instant of time. Likewise, the difference of two continuous time signals 𝑥1(𝑡) and 𝑥2(𝑡) can be obtained by subtracting the values of one signal (say 𝑥2(𝑡)) from another signal (say 𝑥1(𝑡)) at every instant of time.Addition of SignalsLet two continuous time signals 𝑥1(𝑡) and 𝑥2(𝑡) as shown in Figure-1. The sum of these two signals 𝑥1(𝑡) + 𝑥2(𝑡) is also shown in Figure-1.ExplanationThe sum of these two signals can be obtained by considering different time intervals ... Read More

Causal SignalA continuous time signal 𝑥(𝑡) is called causal signal if the signal 𝑥(𝑡) = 0 for 𝑡 < 0. Therefore, a causal signal does not exist for negative time. The unit step signal u(t) is an example of causal signal as shown in Figure-1.Similarly, a discrete time sequence x(n) is called the causal sequence if the sequence x(n) = 0 for n < 0.Anti-Causal SignalA continuous-time signal x(t) is called the anti-causal signal if x(t) = 0 for t > 0. Hence, an anti-causal signal does not exist for positive time. The time reversed unit step signal u(-t) is ... Read More

Causal SystemA system whose output or response at any time instant (t) depends only on the present and past values of the input but not on the future values of the input is called the causal system. For a causal system, the output or response does not begin before the input signal is applied. This is why, a causal system is also called a non-anticipated system.The causal systems are real time systems and they can be physically realised. For a causal system, the impulse response of the system is zero for negative time (i.e., t < 0) because the impulse ... Read More