summary and formulas for linear convolution of continuous time signals and discrete time signals
Review waiting, please be patient.
This may take 3 months or more, since drafts are reviewed in no specific order. There are 3,285 pending submissions
waiting for review.
If the submission is accepted, then this page will be moved into the article space.
If the submission is declined, then the reason will be posted here.
In the meantime, you can continue to improve this submission by editing normally.
Where to get help
If you need help editing or submitting your draft, please ask us a question at the AfC Help Desk or get live help from experienced editors. These venues are only for help with editing and the submission process, not to get reviews.
If you need feedback on your draft, or if the review is taking a lot of time, you can try asking for help on the
talk page of a
relevant WikiProject. Some WikiProjects are more active than others so a speedy reply is not guaranteed.
To improve your odds of a faster review, tag your draft with relevant
WikiProject tags using the button below. This will let reviewers know a new draft has been submitted in their area of interest. For instance, if you wrote about a female astronomer, you would want to add the Biography, Astronomy, and Women scientists tags.
Linear convolution is a fundamental operation in signal processing and mathematics, essential for understanding the behavior of linear systems and processing signals in various applications such as communication systems, image processing, and audio processing. It involves combining two signals to produce a third signal that represents the mathematical convolution of the original signals.
Definition and Operation
Linear convolution is defined as the integral of the product of two functions, where one of the functions is reflected and shifted across the other function. Mathematically, the linear convolution y(t) of two signals x(t) and h(t) is given by:
In discrete-time signal processing, linear convolution is represented as the sum of the product of discrete samples of two signals. For discrete signals xn] and hn], the linear convolution yn] is calculated as:
Applications
Linear convolution finds applications in various fields:
Digital Signal Processing (DSP): In DSP, linear convolution is used for filtering, system modeling, and signal analysis. For example, it is used in Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters.
Communication Systems: In communication systems, linear convolution is used for channel modeling, equalization, and modulation/demodulation processes.
Image Processing: In image processing, linear convolution is utilized for tasks such as blurring, edge detection, and image enhancement.
Audio Processing: In audio processing, linear convolution is employed for effects processing, such as reverberation and echo generation.
^Oppenheim, Alan V.; Schafer, Ronald W. (2010). Discrete-time signal processing (3rd ed.). Upper Saddle River: Pearson.
ISBN978-0-13-198842-2.
^Proakis, John G.; Manolakis, Dimitris G. (2011). Digital signal processing (4th ed.). New Delhi, India: Prentice Hall.
ISBN978-81-317-1000-5.
^Gonzalez, Rafael C.; Woods, Richard E. (2018). Digital image processing (Fourth edition, india ed.). Uttar Pradesh: Pearson India.
ISBN978-93-5306-298-9.
^Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, N.J: Prentice-Hall.
ISBN978-0-13-914101-0.