Γ
Home
Jobs
Tools
Coding Ground
Current Affairs
UPSC Notes
Online Tutors
Whiteboard
Tutorix
Login
Categories
Java
JSP
iOS
HTML
Android
Python
C Programming
C++ Programming
C#
PHP
CSS
Javascript
jQuery
SAP
SAP HANA
Data Structure
RDBMS
MySQL
Mathematics
8085 Microprocessor
Operating System
Digital Electronics
Analysis of Algorithms
Mobile Development
Front End
Web Development
Selenium
MongoDB
Computer Network
General Topics
Q/A
Library
eBooks
Courses
Trending Categories
Data Structure
Networking
RDBMS
Operating System
Java
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Selected Reading
UPSC IAS Exams Notes
Developer's Best Practices
Questions and Answers
Effective Resume Writing
HR Interview Questions
Computer Glossary
Who is Who
Manish Kumar Saini
has Published
506
Answers
Linearity and Frequency Shifting Property of Fourier Transform
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 02-Dec-2021 12:09:14
Fourier TransformFor a continuous-time function $x(t)$, the Fourier transform can be defined as, $$\mathrm{X(\omega)=\int_{−\infty}^{\infty}x(t)e^{-j\omega t}dt}$$Linearity Property of Fourier TransformStatement − The linearity property of Fourier transform states that the Fourier transform of a weighted sum of two signals is equal to the weighted sum of their individual Fourier transforms.Therefore, if$$\mathrm{x_{1}(t)\overset{FT}{\leftrightarrow}X_{1}(\omega)\:\:and\:\:x_{2}\overset{FT}{\leftrightarrow}X_{2}(\omega)}$$Then, ...
Read More
Linearity and Conjugation Property of Continuous-Time Fourier Series
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 02-Dec-2021 12:05:59
Fourier SeriesIf $x(t)$ is a periodic function with period $T$, then the continuous-time exponential Fourier series of the function is defined as, $$\mathrm{x(t)=\displaystyle\sum\limits_{n=−\infty}^\infty\:C_{n}\:e^{jn\omega_{0}t}\:\:\:… (1)}$$Where, $C_{n}$ is the exponential Fourier series coefficient, which is given by, $$\mathrm{C_{n}=\frac{1}{T}\int_{t_{0}}^{t_{0}+T}X(t)e^{-jn\omega_{0}t}\:dt\:\:… (2)}$$Linearity Property of Continuous Time Fourier SeriesConsider two periodic signals $x_{1}(t)$ and $x_{2}(t)$ which ...
Read More
GIBBS Phenomenon for Fourier Series
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 02-Dec-2021 12:04:13
What is GIBBS Phenomenon?The GIBBS phenomenon was discovered by Henry Wilbraham in 1848 and then rediscovered by J. Willard Gibbs in 1899.For a periodic signal with discontinuities, if the signal is reconstructed by adding the Fourier series, then overshoots appear around the edges. These overshoots decay outwards in a damped ...
Read More
Frequency Derivative Property of Fourier Transform
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 02-Dec-2021 12:01:25
Fourier TransformThe Fourier transform of a continuous-time function can be defined as, $$\mathrm{X(\omega)=\int_{−\infty }^{\infty}\:X(t)e^{-j\omega t}\:dt}$$Differentiation in Frequency Domain Property of Fourier TransformStatement − The frequency derivative property of Fourier transform states that the multiplication of a function X(t) by in time domain is equivalent to the differentiation of its Fourier ...
Read More
Fourier Transform of Unit Step Function
Signals and Systems
Electronics & Electrical
Digital Electronics
Manish Kumar Saini
Published on 02-Dec-2021 11:58:46
Fourier TransformFor a continuous-time function $x(t)$, the Fourier transform is defined as, $$\mathrm{X(\omega)=\int_{−\infty }^{\infty}x(t)e^{−j\omega t}\:dt}$$Fourier Transform of Unit Step FunctionThe unit step function is defined as, $$\mathrm{u(t)=\begin{cases}1 & for\:t≥ 0\\0 & for\:t< 0\end{cases}}$$Because the unit step function is not absolutely integrable, thus its Fourier transform cannot be found directly.In order ...
Read More
What is Mean Square Error?
Electronics & Electrical
Electron
Digital Electronics
Manish Kumar Saini
Published on 13-Nov-2021 10:34:03
The mean square error (MSE) is defined as mean or average of the square of the difference between actual and estimated values.Mathematically, the mean square error is, $$\mathrm{\varepsilon =\frac{1}{t_{2}-t_{1}}\int_{t_{1}}^{t_{2}}\left [ x(t) -\sum_{r=1}^{n}C_{r}g_{r}(t)\right ]^{2}dt}$$$$\mathrm{\varepsilon =\frac{1}{t_{2}-t_{1}}\left [ \int_{t_{1}}^{t_{2}}x^{2}(t)dt+\sum_{r=1}^{n}C_{r}^{2}\int_{t_{1}}^{t_{2}}g_{r}^{2}(t)dt-2\sum_{r=1}^{n}C_{r}\int_{t_{1}}^{t_{2}}x(t)g_{r}(t)dt\right ]\; ...(1)}$$$$\mathrm{\therefore C_{r}=\frac{\int_{t_{1}}^{t_{2}}x(t)g_{r}(t)dt}{\int_{t_{1}}^{t_{2}}g_{r}^{2}(t)dt}=\frac{1}{K_{r}}\int_{t_{1}}^{t_{2}}x(t)g_{r}(t)dt\; \; ...(2)}$$$$\mathrm{\therefore \int_{t_{1}}^{t_{2}}x(t)g_{r}(t)dt=C_{r}\int_{t_{1}}^{t_{2}}g_{r}^{2}(t)dt=C_{r}K_{r}\; \; ...(3)}$$Using equations (1) and (3), we have, ...
Read More
Signals and Systems: Invertible and Non-Invertible Systems
Electronics & Electrical
Electron
Digital Electronics
Manish Kumar Saini
Published on 13-Nov-2021 10:31:04
Invertible SystemIf a system has a unique relationship between its input and output, the system is called the invertible system. In other words, a system is said to be an invertible system only if an inverse system exists which when cascaded with the original system produces an output equal to ...
Read More
Signals and Systems: Energy and Power Signals
Electronics & Electrical
Electron
Digital Electronics
Manish Kumar Saini
Published on 13-Nov-2021 10:24:47
Energy SignalA signal is said to be an energy signal if and only if its total energy E is finite, i.e., 0 < πΈ < ∞. For an energy signal, the average power P = 0. The nonperiodic signals are the examples of energy signals.Power SignalA signal is said to ...
Read More
Even and Odd Components of a Signal
Electronics & Electrical
Electron
Digital Electronics
Manish Kumar Saini
Published on 13-Nov-2021 10:17:55
Even SignalA signal is said to be an even signal if it is symmetrical about the vertical axis or time origin, i.e., π₯(π‘) = π₯(−π‘); for all π‘ … continuous time signalπ₯(π) = π₯(−π); for all π … discrete time signalOdd SignalA signal is said to ...
Read More
Signals and Systems: BIBO Stability Criterion
Electronics & Electrical
Electron
Digital Electronics
Manish Kumar Saini
Published on 13-Nov-2021 10:08:20
Bounded SignalA signal whose magnitude is a finite value is called the bounded signal. A sine wave is an example of bounded signal.BIBO Stable SystemA system is called BIBO stable (or bounded-input, bounded-output stable) system, if and only if every bounded input to the system produces a bounded output.BIBO Stability ...
Read More
Previous
1
...
11
12
13
14
15
16
17
...
51
Next
Advertisements
Print
Add Notes
Bookmark this page
Report Error
Suggestions
Save
Close
Dashboard
Logout