Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) PDF Download

Conjugate Signals

Signals, which satisfies the condition x(t) = x∗(−t) are called conjugate signals.

Let x(t) = a(t) + jb(t)        ...eqn. 1

So,  x(−t) = a(−t) + jb(−t)x

And  x∗(−t) = a(−t) − jb(−t)         ...eqn. 2

By Condition, x(t) = x∗(−t)

If we compare both the derived equations 1 and 2, we can see that the real part is even, whereas the imaginary part is odd. This is the condition for a signal to be a conjugate type.

Conjugate Anti-Symmetric Signals

Signals, which satisfy the condition x(t) = −x∗(−t) are called conjugate anti-symmetric signal

Let x(t) = a(t) + jb(t)     ...eqn. 1

So x(−t) = a(−t) + jb(−t)

And x∗(−t) = a(−t) − jb(−t)

−x∗(−t) = −a(−t) + jb(−t)     ...eqn. 2

By Condition x(t) = −x∗(−t)

Now, again compare, both the equations just as we did for conjugate signals. Here, we will find that the real part is odd and the imaginary part is even. This is the condition for a signal to become conjugate anti-symmetric type.

Example

Let the signal given be x(t) = sint + jt2.

Here, the real part being sint is odd and the imaginary part being t2 is even. So, this signal can be classified as conjugate anti-symmetric signal.

Any function can be divided into two parts. One part being Conjugate symmetry and other part being conjugate anti-symmetric. So any signal x(t) can be written as

x(t) = xcs(t) + xcas(t)

Where xcs(t) is conjugate symmetric signal and xcas(t) is conjugate anti symmetric signal

Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

And

Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Half Wave Symmetric Signals

When a signal satisfies the condition Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) it is called half wave symmetric signal. Here, amplitude reversal and time shifting of the signal takes place by half time. For half wave symmetric signal, average value will be zero but this is not the case when the situation is reversed.

Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Consider a signal x(t) as shown in figure A above. The first step is to time shift the signal and make it Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) So, the new signal is changed as shown in figure B. Next, we reverse the amplitude of the signal, i.e. make it Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) as shown in figure C. Since, this signal repeats itself after half-time shifting and reversal of amplitude, it is a half wave symmetric signal.

Orthogonal Signal

Two signals x(t) and y(t) are said to be orthogonal if they satisfy the following two conditions.

Condition 1 Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) [for non-periodic signal]
Condition 2 Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) [For periodic Signal]

The signals, which contain odd harmonics (3rd, 5th, 7th ...etc.) and have different frequencies, are mutually orthogonal to each other.

In trigonometric type signals, sine functions and cosine functions are also orthogonal to each other; provided, they have same frequency and are in same phase. In the same manner DC (Direct current signals) and sinusoidal signals are also orthogonal to each other. If x(t) and y(t) are two orthogonal signals and Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) then the power and energy of z(t) can be written as ;

Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Example

Analyze the signal:Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

Here, the signal comprises of a DC signal (3) and one sine function. So, by property this signal is an orthogonal signal and the two sub-signals in it are mutually orthogonal to each other.

The document Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE) is a part of the Electronics and Communication Engineering (ECE) Course Digital Signal Processing.
All you need of Electronics and Communication Engineering (ECE) at this link: Electronics and Communication Engineering (ECE)
3 videos|50 docs|54 tests

Top Courses for Electronics and Communication Engineering (ECE)

FAQs on Miscellaneous Signals - Digital Signal Processing - Electronics and Communication Engineering (ECE)

1. What are the different types of signals in electrical engineering?
Ans. In electrical engineering, there are various types of signals, including analog signals, digital signals, periodic signals, non-periodic signals, and deterministic signals. Analog signals are continuous and can have any value within a range. Digital signals, on the other hand, are discrete and can only have specific values. Periodic signals repeat themselves after a certain time period, while non-periodic signals do not have any repeating pattern. Deterministic signals can be precisely defined by a mathematical equation or formula.
2. What is the difference between analog and digital signals?
Ans. The main difference between analog and digital signals lies in their representation. Analog signals are continuous and can have infinite values within a range, while digital signals are discrete and can only have specific values, usually represented as binary digits (0s and 1s). Analog signals are susceptible to noise and distortion, whereas digital signals are more immune to these interferences. Additionally, analog signals are used to represent real-world phenomena, while digital signals are commonly used in computer systems and communication networks.
3. How are periodic signals characterized in electrical engineering?
Ans. Periodic signals in electrical engineering are characterized by their period, frequency, amplitude, and phase. The period of a periodic signal is the time it takes for one complete cycle to occur. Frequency represents the number of cycles per unit of time and is the inverse of the period. Amplitude refers to the maximum value of the signal, and phase indicates the position of the signal in its cycle at a particular time. These characteristics are essential for analyzing and processing periodic signals in various electrical engineering applications.
4. What are deterministic signals in electrical engineering?
Ans. Deterministic signals in electrical engineering are signals that can be precisely defined by a mathematical equation or formula. Unlike stochastic signals, which are random and unpredictable, deterministic signals follow a known pattern or function. Deterministic signals are often used in mathematical modeling, simulations, and control systems. Examples of deterministic signals include sine waves, square waves, and triangular waves.
5. How are digital signals transmitted over long distances without loss of quality?
Ans. Digital signals can be transmitted over long distances without significant loss of quality through various techniques. One common approach is to encode the digital signal using techniques such as pulse code modulation (PCM) or differential pulse code modulation (DPCM). These techniques convert the digital signal into a series of pulses or differential values that can be easily transmitted and reconstructed at the receiver end. Additionally, error detection and correction codes, such as forward error correction (FEC) or cyclic redundancy check (CRC), can be implemented to detect and correct any errors that may occur during transmission.
3 videos|50 docs|54 tests
Download as PDF
Explore Courses for Electronics and Communication Engineering (ECE) exam

Top Courses for Electronics and Communication Engineering (ECE)

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Sample Paper

,

Extra Questions

,

Free

,

study material

,

MCQs

,

past year papers

,

pdf

,

Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

,

Exam

,

mock tests for examination

,

Objective type Questions

,

video lectures

,

Semester Notes

,

Viva Questions

,

Important questions

,

Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

,

Miscellaneous Signals | Digital Signal Processing - Electronics and Communication Engineering (ECE)

,

practice quizzes

,

shortcuts and tricks

,

ppt

,

Summary

,

Previous Year Questions with Solutions

;