Intuitively, a filter on a partially ordered set (poset) contains those elements that are large enough to satisfy some criterion. For example, if x is an element of the poset, then the set of elements that are above x is a filter, called the principal filter at x. (Notice that if x and y are incomparable elements of the poset, then neither of the principal filters at x and y is contained in the other one.)
Similarly, a filter on a set contains those subsets that are sufficiently large to contain something. For example, if the set is the real line and x is one of its points, then the family of sets that contain x in their interior is a filter, called the filter of neighbourhoods of x. (Notice that the thing in this case is slightly larger than x, but it still doesn't contain any other specific point of the line.)
Filter is an Americantelevision series on the G4 cable television channel which follows a countdown format. It was canceled in December 2005, resurrected in a re-formatted form, and then once again was canceled in August 2006. It was airing as an interstitial program during commercial breaks prior to May 2012. The show allows registers users (or viewers) to vote in Top Ten lists.
History
Filter was one of the 13 original series to debut with G4. The focus of the show was video games, and each episode covered a different genre, such as sports or role-playing video games. Each week a new theme was chosen and viewers chose the top ten to be featured on the show. The top two games would be put in a Filter Face-off, where the winner was revealed. Shows included the top ten Final Fantasy games, worst games of all time, and all-time top-ten platformers.
After the purchase of TechTV, Filter was revamped to include more pop culture lists such as theatrical and DVDmovie releases, music concerts, and consumer technology. The segment "Tech Toss-up" was added to cover new gadgets such as cellphones and MP3 players. A segment called "Net to Know" showcased correspondent John Walsh's top three websites of the week.
Filter is an American industrial rock group formed in 1993 in Cleveland by singer Richard Patrick and guitarist/programmer Brian Liesegang. The band was formed after Patrick desired to start his own band after leaving Nine Inch Nails as their touring guitarist. Their debut album, Short Bus, was released in 1995, and ended up going platinum, selling over one million copies, largely due to the success of the band's single "Hey Man Nice Shot." After the album, the band would go through the first of many line-up changes, leaving Patrick as the only consistent member across all music releases.
Patrick released the band's follow up album, Title of Record, which also went platinum, off the success of the song "Take a Picture", in 1999, and a third album, The Amalgamut, in 2002, before checking into rehab after years of heavy alcohol and drug abuse. The band went into hiatus while Patrick went to rehab, and then formed a new band, Army of Anyone, which released one self-title album. Filter reformed in 2008 to release Anthems for the Damned, and then The Trouble with Angels in 2010, with Patrick and a revolving door of other musicians. Filter's sixth and most recent studio album, The Sun Comes Out Tonight, was released in 2013. A seventh studio album is scheduled for release in 2016.
Electronic filters are circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both. Electronic filters can be:
The most common types of electronic filters are linear filters, regardless of other aspects of their design. See the article on linear filters for details on their design and analysis.
History
The oldest forms of electronic filters are passive analog linear filters, constructed using only resistors and capacitors or resistors and inductors. These are known as RC and RL single-pole filters respectively.
More complex multipole LC filters have also existed for many years, and their operation is well understood.
Hybrid filters are also possible, typically involving a combination of analog amplifiers with mechanical resonators or delay lines. Other devices such as CCDdelay lines have also been used as discrete-time filters. With the availability of digital signal processing, active digital filters have become common.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Mathematics, also known as Allah Mathematics, (born: Ronald Maurice Bean) is a hip hop producer and DJ for the Wu-Tang Clan and its solo and affiliate projects.
Biography
Born and raised in Jamaica, Queens, New York, Mathematics was introduced to hip hop by his brother who used to bring home recordings of the genre's pioneers like Grandmaster Flash & The Furious Five, Treacherous Three and Cold Crush Brothers. He began his career in 1987 DJing block parties and park jams in Baisley Projects, going by the name Supreme Cut Master. In 1988, he became the full-time DJ for experienced rapper Victor C, doing countless shows in clubs and colleges in New York City.
In 1990, Mathematics linked up with GZA/Genius; he soon became one of the Wu-Tang Clan's founding members, but at the time GZA was struggling to build a career on the Cold Chillin' label. This partnership earned Mathematics a spot on his first official tour, The Cold Chillin Blizzard Tour (with popular acts such as Biz Markie, Big Daddy Kane, Kool G. Rap & DJ Polo and Marley Marl).
"Mathematics" is a b-side single from Mos Def's solo debut album, Black on Both Sides. It contains lyrics about various social issues and asks the listener to add them up and come to conclusions about them. Many references to numbers are found in this song and at times, Mos Def rhymes statistics in numerical order. The song highlights the differences between the White and African-American citizens of the US and uses the lyrics "Do your math..." (from Erykah Badu's "On & On") telling young African-American's to 'do their maths' so they can avoid being part of the numerous degrading statistics he raps about in the opening and third verses of the song. The song is produced by DJ Premier whose famous scratchsamples make up the song's bridge. Premier has called it one of his favorite beats.
The bridge of "Mathematics" contains DJ Premier's signature scratched vocals from various hip hop songs. The lyrics of those samples as well as information about their origin can be found below:
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalization of a point and mention the ultrafilter lemma. Part 2 discusses applications of filters and ultrafilters in topology.
published: 03 Oct 2022
An Introduction to Digital Filters, without the mathematics
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this topic with dense and exhausting mathematics. Although a fair understanding of complex mathematics is required to fully comprehend the science of filter design, understanding the basics of filters and how they fundamentally work is better left to analysis and visualizations, which I try to do in this series.
Find the full playlist here: https://www.youtube.com/watch?v=Qmd685msY-Y&list=PLbqhA-NKGP6Afr_KbPUuy_yIBpPR4jzWo
References:
Designing Audio Effect Plugins in C++, Will C. Pirkle -
https://www.willpirkle.com/about/books/
Introduction to Digital Filters, Julius O. Smith - https://ccrma.stanford.edu/~jos/filters/
If you've got a...
published: 24 Nov 2022
Filter (mathematics)
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.For example, the power set of some set, partially ordered by set inclusion, is a filter.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0
Author-Info: Pgdx
Image Source: https://en.wikipedia.org/wiki/File:Upset.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=eK5446iarck
published: 22 Jan 2016
LftCM2020: Topology and filters - Patrick Massot
published: 17 Jul 2020
Filter (mathematics) | Wikipedia audio article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
00:05:56 3 Filter on a set
00:08:56 3.1 Examples
00:12:01 3.2 Filters in model theory
00:12:58 3.3 Filters in topology
00:14:07 3.3.1 Neighbourhood bases
00:14:56 3.3.2 Convergent filter bases
00:17:02 3.3.3 Clustering
00:18:37 3.3.4 Properties of a topological space
00:19:17 3.3.5 Functions on topological spaces
00:21:07 3.3.6 Cauchy filters
00:23:21 4 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your liste...
published: 15 Jan 2019
Filters-important definitions of filters/topology 2/msc maths
filters - important definitions
topology 2
msc
published: 24 May 2018
state and prove ultra filter principle #topology #importantquestions #mathematics
published: 27 Jun 2023
India vs japan || mathematics challenge || 😅🤣🤣🤭
published: 08 Jun 2021
Bayes theorem, the geometry of changing beliefs
Perhaps the most important formula in probability.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/bayes-thanks
Home page: https://www.3blue1brown.com
The quick proof: https://youtu.be/U_85TaXbeIo
Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/
The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf
You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.
Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probabilit...
published: 22 Dec 2019
2- 4.4.3 VSB Mathematics and Explanation of Complementary Filters
This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The information in this video will help you understand concepts found in "Modern Digital and Analog Communication" by B.P. Lathi and Zhi Ding.
You can purchase this textbook here:
https://www.amazon.com/Digital-Communication-Electrical-Computer-Engineering-dp-0190686847/dp/0190686847/ref=dp_ob_title_bk
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalizati...
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalization of a point and mention the ultrafilter lemma. Part 2 discusses applications of filters and ultrafilters in topology.
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalization of a point and mention the ultrafilter lemma. Part 2 discusses applications of filters and ultrafilters in topology.
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this to...
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this topic with dense and exhausting mathematics. Although a fair understanding of complex mathematics is required to fully comprehend the science of filter design, understanding the basics of filters and how they fundamentally work is better left to analysis and visualizations, which I try to do in this series.
Find the full playlist here: https://www.youtube.com/watch?v=Qmd685msY-Y&list=PLbqhA-NKGP6Afr_KbPUuy_yIBpPR4jzWo
References:
Designing Audio Effect Plugins in C++, Will C. Pirkle -
https://www.willpirkle.com/about/books/
Introduction to Digital Filters, Julius O. Smith - https://ccrma.stanford.edu/~jos/filters/
If you've got any questions, suggestions or recommendations, type them out here, or send me a message on any of my social channels mentioned below.
A lot of time was spent on creating this series, and I plan to do more. So please consider subscribing if you wish to be notified about more releases in the future. And if you feel generous: https://www.patreon.com/akashmurthy
Check out my music here: https://farfetchd-official.bandcamp.com/
Check out the audio track in the intro and outro here: https://soundcloud.com/thrifleganger/tinderbox
Give me a shout here:
Website - https://www.akashmurthy.com/
Facebook - https://www.facebook.com/akash.murthy.319
Instagram - https://www.instagram.com/thrifleganger/
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this topic with dense and exhausting mathematics. Although a fair understanding of complex mathematics is required to fully comprehend the science of filter design, understanding the basics of filters and how they fundamentally work is better left to analysis and visualizations, which I try to do in this series.
Find the full playlist here: https://www.youtube.com/watch?v=Qmd685msY-Y&list=PLbqhA-NKGP6Afr_KbPUuy_yIBpPR4jzWo
References:
Designing Audio Effect Plugins in C++, Will C. Pirkle -
https://www.willpirkle.com/about/books/
Introduction to Digital Filters, Julius O. Smith - https://ccrma.stanford.edu/~jos/filters/
If you've got any questions, suggestions or recommendations, type them out here, or send me a message on any of my social channels mentioned below.
A lot of time was spent on creating this series, and I plan to do more. So please consider subscribing if you wish to be notified about more releases in the future. And if you feel generous: https://www.patreon.com/akashmurthy
Check out my music here: https://farfetchd-official.bandcamp.com/
Check out the audio track in the intro and outro here: https://soundcloud.com/thrifleganger/tinderbox
Give me a shout here:
Website - https://www.akashmurthy.com/
Facebook - https://www.facebook.com/akash.murthy.319
Instagram - https://www.instagram.com/thrifleganger/
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathema...
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.For example, the power set of some set, partially ordered by set inclusion, is a filter.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0
Author-Info: Pgdx
Image Source: https://en.wikipedia.org/wiki/File:Upset.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=eK5446iarck
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.For example, the power set of some set, partially ordered by set inclusion, is a filter.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0
Author-Info: Pgdx
Image Source: https://en.wikipedia.org/wiki/File:Upset.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=eK5446iarck
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
...
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
00:05:56 3 Filter on a set
00:08:56 3.1 Examples
00:12:01 3.2 Filters in model theory
00:12:58 3.3 Filters in topology
00:14:07 3.3.1 Neighbourhood bases
00:14:56 3.3.2 Convergent filter bases
00:17:02 3.3.3 Clustering
00:18:37 3.3.4 Properties of a topological space
00:19:17 3.3.5 Functions on topological spaces
00:21:07 3.3.6 Cauchy filters
00:23:21 4 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9503992225972198
Voice name: en-GB-Wavenet-C
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In mathematics, a filter is a special subset of a partially ordered set. For example, the power set of some set, partially ordered by set inclusion, is a filter. Filters appear in order and lattice theory, but can also be found in topology from where they originate. The dual notion of a filter is an ideal.
Filters were introduced by Henri Cartan in 1937 and subsequently used by Bourbaki in their book Topologie Générale as an alternative to the similar notion of a net developed in 1922 by E. H. Moore and H. L. Smith.
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
00:05:56 3 Filter on a set
00:08:56 3.1 Examples
00:12:01 3.2 Filters in model theory
00:12:58 3.3 Filters in topology
00:14:07 3.3.1 Neighbourhood bases
00:14:56 3.3.2 Convergent filter bases
00:17:02 3.3.3 Clustering
00:18:37 3.3.4 Properties of a topological space
00:19:17 3.3.5 Functions on topological spaces
00:21:07 3.3.6 Cauchy filters
00:23:21 4 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9503992225972198
Voice name: en-GB-Wavenet-C
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In mathematics, a filter is a special subset of a partially ordered set. For example, the power set of some set, partially ordered by set inclusion, is a filter. Filters appear in order and lattice theory, but can also be found in topology from where they originate. The dual notion of a filter is an ideal.
Filters were introduced by Henri Cartan in 1937 and subsequently used by Bourbaki in their book Topologie Générale as an alternative to the similar notion of a net developed in 1922 by E. H. Moore and H. L. Smith.
Perhaps the most important formula in probability.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simp...
Perhaps the most important formula in probability.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/bayes-thanks
Home page: https://www.3blue1brown.com
The quick proof: https://youtu.be/U_85TaXbeIo
Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/
The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf
You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.
Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probability intuitive
13:35 - Issues with the Steve example
Thanks to these viewers for their contributions to translations
Gujarati: Hitesh12358, Pragna1991
Hebrew: Omer Tuchfeld
Italian: @crampaldo
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Perhaps the most important formula in probability.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/bayes-thanks
Home page: https://www.3blue1brown.com
The quick proof: https://youtu.be/U_85TaXbeIo
Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/
The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf
You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.
Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probability intuitive
13:35 - Issues with the Steve example
Thanks to these viewers for their contributions to translations
Gujarati: Hitesh12358, Pragna1991
Hebrew: Omer Tuchfeld
Italian: @crampaldo
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The...
This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The information in this video will help you understand concepts found in "Modern Digital and Analog Communication" by B.P. Lathi and Zhi Ding.
You can purchase this textbook here:
https://www.amazon.com/Digital-Communication-Electrical-Computer-Engineering-dp-0190686847/dp/0190686847/ref=dp_ob_title_bk
This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The information in this video will help you understand concepts found in "Modern Digital and Analog Communication" by B.P. Lathi and Zhi Ding.
You can purchase this textbook here:
https://www.amazon.com/Digital-Communication-Electrical-Computer-Engineering-dp-0190686847/dp/0190686847/ref=dp_ob_title_bk
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalization of a point and mention the ultrafilter lemma. Part 2 discusses applications of filters and ultrafilters in topology.
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this topic with dense and exhausting mathematics. Although a fair understanding of complex mathematics is required to fully comprehend the science of filter design, understanding the basics of filters and how they fundamentally work is better left to analysis and visualizations, which I try to do in this series.
Find the full playlist here: https://www.youtube.com/watch?v=Qmd685msY-Y&list=PLbqhA-NKGP6Afr_KbPUuy_yIBpPR4jzWo
References:
Designing Audio Effect Plugins in C++, Will C. Pirkle -
https://www.willpirkle.com/about/books/
Introduction to Digital Filters, Julius O. Smith - https://ccrma.stanford.edu/~jos/filters/
If you've got any questions, suggestions or recommendations, type them out here, or send me a message on any of my social channels mentioned below.
A lot of time was spent on creating this series, and I plan to do more. So please consider subscribing if you wish to be notified about more releases in the future. And if you feel generous: https://www.patreon.com/akashmurthy
Check out my music here: https://farfetchd-official.bandcamp.com/
Check out the audio track in the intro and outro here: https://soundcloud.com/thrifleganger/tinderbox
Give me a shout here:
Website - https://www.akashmurthy.com/
Facebook - https://www.facebook.com/akash.murthy.319
Instagram - https://www.instagram.com/thrifleganger/
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.For example, the power set of some set, partially ordered by set inclusion, is a filter.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0
Author-Info: Pgdx
Image Source: https://en.wikipedia.org/wiki/File:Upset.svg
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This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
00:05:56 3 Filter on a set
00:08:56 3.1 Examples
00:12:01 3.2 Filters in model theory
00:12:58 3.3 Filters in topology
00:14:07 3.3.1 Neighbourhood bases
00:14:56 3.3.2 Convergent filter bases
00:17:02 3.3.3 Clustering
00:18:37 3.3.4 Properties of a topological space
00:19:17 3.3.5 Functions on topological spaces
00:21:07 3.3.6 Cauchy filters
00:23:21 4 See also
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"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
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In mathematics, a filter is a special subset of a partially ordered set. For example, the power set of some set, partially ordered by set inclusion, is a filter. Filters appear in order and lattice theory, but can also be found in topology from where they originate. The dual notion of a filter is an ideal.
Filters were introduced by Henri Cartan in 1937 and subsequently used by Bourbaki in their book Topologie Générale as an alternative to the similar notion of a net developed in 1922 by E. H. Moore and H. L. Smith.
Perhaps the most important formula in probability.
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The quick proof: https://youtu.be/U_85TaXbeIo
Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/
The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf
You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.
Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probability intuitive
13:35 - Issues with the Steve example
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This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The information in this video will help you understand concepts found in "Modern Digital and Analog Communication" by B.P. Lathi and Zhi Ding.
You can purchase this textbook here:
https://www.amazon.com/Digital-Communication-Electrical-Computer-Engineering-dp-0190686847/dp/0190686847/ref=dp_ob_title_bk
Intuitively, a filter on a partially ordered set (poset) contains those elements that are large enough to satisfy some criterion. For example, if x is an element of the poset, then the set of elements that are above x is a filter, called the principal filter at x. (Notice that if x and y are incomparable elements of the poset, then neither of the principal filters at x and y is contained in the other one.)
Similarly, a filter on a set contains those subsets that are sufficiently large to contain something. For example, if the set is the real line and x is one of its points, then the family of sets that contain x in their interior is a filter, called the filter of neighbourhoods of x. (Notice that the thing in this case is slightly larger than x, but it still doesn't contain any other specific point of the line.)
I live in a double in the Inn on Mass Ave. My name is PatrickBoylston. I’m 19 years old ... The Panopto 2x speed function ... With Panopto, I can filter out everything but the pure, sweet song of rapid mathematics spewing through space and time ... .
He had nothing for them. “They firmly believed that I had some kind of secret knowledge,” said the veteran Democratic strategist ... A whole industry has emerged to parse the data and filter it through complex probabilistic mathematical formulas ... ....
He had nothing for them. “They firmly believed that I had some kind of secret knowledge,” said the veteran Democratic strategist ... A whole industry has emerged to parse the data and filter it through complex probabilistic mathematical formulas ... ....
SoC is typically expressed as a percentage of a battery’s total energy storage capacity ... More advanced techniques, such as Kalman filtering, combine multiple measurement methods and use mathematical models to improve accuracy ... Unique challenges ... ....
Developed by scientists in China, the proposed approach uses mathematical morphologies for image processing, such as image enhancement, sharpening, filtering, and closing operations.
Incoming sensory perceptions generate inferences and in turn used to filter perceptions and direct our actions. Bayesian Statistics, named after mathematician Thomas Bayes, is a mathematical formula ...
More than an hour before the eclipse reached its peak, dozens of people began trickling into the viewing party to make use of the three telescopes and solar filters provided by the School of Mathematics and Science... In fact, it was quite the opposite.
Simon Cohen / Digital Trends. Spatial audio is having a moment ... Contents ... Recommended Videos ... When described mathematically and used to filter incoming sounds to each ear, this audioprint is known as a “head-related transfer function” (HRTF).
Log takes a mathematical approach to video capture and editing ...Think of them as filters, but something far more versatile and one that follows mathematical rules for making color adjustments instead of flat color tone overlaying.
The AI company DeepMind claims it has developed a way to harness the creativity of chatbots to solve mathematical problems while filtering out mistakes ... .
If we do that, eventually scientists could develop filters that we can apply to any extraterrestrial signals we might pick up, using the mathematics of information theory to spot rule structures that could help us translate the message ...Source ... .
The Whale-SETI team has been studying humpback whale communication systems in an effort to develop intelligence filters for the search for extraterrestrial intelligence ... The mathematics of information ...
This includes techniques like input normalization, spatial transformation, or noise injection, which can help detect and filter out potential adversarial perturbations.