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Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Document Description: Basic CT & DT Signals for Electrical Engineering (EE) 2022 is part of Digital Signal Processing preparation. The notes and questions for Basic CT & DT Signals have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Basic CT & DT Signals covers topics like and Basic CT & DT Signals Example, for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Basic CT & DT Signals.

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To test a system, generally, standard or basic signals are used. These signals are the basic building blocks for many complex signals. Hence, they play a very important role in the study of signals and systems.

Unit Impulse or Delta Function

A signal, which satisfies the condition, δ(t)=limϵ→∞x(t) is known as unit impulse signal. This signal tends to infinity when t = 0 and tends to zero when t ≠ 0 such that the area under its curve is always equals to one. The delta function has zero amplitude everywhere excunit_impulse.jpgept at t = 0.

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Properties of Unit Impulse Signal

  • δ(t) is an even signal.
  • δ(t) is an example of neither energy nor power (NENP) signal.
  • Area of unit impulse signal can be written as;

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

  • Weight or strength of the signal can be written as;

    y(t)=Aδ(t)
     
  • Area of the weighted impulse signal can be written as −

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Unit Step Signal

A signal, which satisfies the following two conditions −

  • U(t)=1(whent≥0)and
  • U(t)=0(whent<0)

is known as a unit step signal.

It has the property of showing discontinuity at t = 0. At the point of discontinuity, the signal value is given by the average of signal value. This signal has been taken just before and after the point of discontinuity (according to Gibb’s Phenomena).

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

If we add a step signal to another step signal that is time scaled, then the result will be unity. It is a power type signal and the value of power is 0.5. The RMS (Root mean square) value is 0.707 and its average value is also 0.5

Ramp Signal

Integration of step signal results in a Ramp signal. It is represented by r(t). Ramp signal also satisfies the condition r(t) = ∫t−∞U(t)dt = tU(t)r(t). It is neither energy nor power (NENP) type signal.

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Parabolic Signal

Integration of Ramp signal leads to parabolic signal. It is represented by p(t). Parabolic signal also satisfies he condition  Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)  It is neither energy nor Power (NENP) type signal.

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Signum Function

This function is represented as

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

It is a power type signal. Its power value and RMS (Root mean square) values, both are 1. Average value of signum function is zero.

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Sinc Function

It is also a function of sine and is written as −

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Properties of Sinc function

  • It is an energy type signal.
  • Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)
  • Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE) (Range of sinπ∞ varies between -1 to +1 but anything divided by infinity is equal to zero)
  • Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)
    Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)


Sinusoidal Signal

A signal, which is continuous in nature is known as continuous signal. General format of a sinusoidal signal is

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Here,

A = amplitude of the signal

ω = Angular frequency of the signal (Measured in radians)

φ = Phase angle of the signal (Measured in radians)

The tendency of this signal is to repeat itself after certain period of time, thus is called periodic signal. The time period of signal is given as;

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

The diagrammatic view of sinusoidal signal is shown below.

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Rectangular Function

A signal is said to be rectangular function type if it satisfies the following condition −

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Being symmetrical about Y-axis, this signal is termed as even signal.

Triangular Pulse Signal

Any signal, which satisfies the following condition, is known as triangular signal.

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

This signal is symmetrical about Y-axis. Hence, it is also termed as even signal.

We have seen that how the basic signals can be represented in Continuous time domain. Let us see how the basic signals can be represented in Discrete Time Domain.

Unit Impulse Sequence

It is denoted as δ(n) in discrete time domain and can be defined as;

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Unit Step Signal

Discrete time unit step signal is defined as;

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

The figure above shows the graphical representation of a discrete step function.

Unit Ramp Function

A discrete unit ramp function can be defined as −

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

The figure given above shows the graphical representation of a discrete ramp signal.

Parabolic Function

Discrete unit parabolic function is denoted as p(n) and can be defined as;

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

In terms of unit step function it can be written as;

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

The figure given above shows the graphical representation of a parabolic sequence.

Sinusoidal Signal

All continuous-time signals are periodic. The discrete-time sinusoidal sequences may or may not be periodic. They depend on the value of ω. For a discrete time signal to be periodic, the angular frequency ω must be a rational multiple of 2π.

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

A discrete sinusoidal signal is shown in the figure above.

Discrete form of a sinusoidal signal can be represented in the format −

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Here A,ω and φ have their usual meaning and n is the integer. Time period of the discrete sinusoidal signal is given by −

Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE)

Where, N and m are integers.

The document Basic CT & DT Signals Notes | Study Digital Signal Processing - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Digital Signal Processing.
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