formulasearchengine - User contributions [en]

Geography of Brazil

2014-03-01T21:12:11Z

99.233.225.212: /* Size and location */

Four or five years ago, a reader of some of my columns bought the domain name jamesaltucher.com and gave it to me as a birthday gift. It was a total surprise to me. I didn't even know the reader. I hope one day we meet. Two years ago a friend of mine, Tim Sykes, insisted I had to have a blog. He set it up for me. He even wrote the "About Me". I didn't want a blog. I had nothing to say. But about 6 or 7 months ago I decided I wanted to take this blog seriously. I kept putting off changing the "About Me" which was no longer really about me and maybe never was. A few weeks ago I did a chapter in one of the books in Seth Godin's "The Domino Project". The book is out and called "No Idling". Mohit Pewar organized it (here's Mohit's blog) and sent me a bunch of questions recently. It's intended to be an interview on his blog but I hope Mohit forgives me because I want to use it as my new "About Me" also. 1. You are a trader, investor, writer, and entrepreneur? Which of these roles you enjoy the most and why? When I first moved to New York [http://www.pcs-systems.co.uk/Images/celinebag.aspx http://www.pcs-systems.co.uk/Images/celinebag.aspx] City in 1994 I wanted to be everything to everyone. I had spent the six years prior to that writing a bunch of unpublished novels and unpublished short stories. I must've sent out 100s of stories to literary journals. I got form rejections from every publisher, journal, and agent I sent my novels and stories to. Now, in 1994, everything was possible. The money was in NYC. Media was here. I lived in my 10�10 room and pulled suits out of a garbage bag every morning but it didn't matter...the internet was revving up and I knew how to build a website. One of the few in the city. My sister warned me though: nobody here is your friend. Everybody wants something 
And I wanted something. I wanted the fleeting feelings of success, for the first time ever, in order to feel better about myself. I wanted a girl next to me. I wanted to build and sell companies and finally prove to everyone I was the smartest. I wanted to do a TV show. I wanted to write books 
But everything involved having a master. Clients. Employers. Investors. Publishers. The market (the deadliest master of all). Employees. I was a slave to everyone for so many years. And the more shackles I had on, the lonelier I got 
Much of the time, even when I had those moments of success, I didn't know how to turn it into a better life. I felt ugly and then later, I felt stupid when I would let the success dribble away down the sink 
I love writing because every now and then that ugliness turns into [http://www.honesty.net honesty]. When I write, I'm only a slave to myself. When I do all of those other things you ask about, I'm a slave to everyone else 
Some links 
33 Unusual Tips to Being a Better Write 
"The Tooth 
(one of my favorite posts on my blog 
2. What inspires you to get up and start working/writing every day 
The other day I had breakfast with a fascinating guy who had just sold a piece of his fund of funds. He told me what "fracking" was and how the US was going to be a major oil player again. We spoke for two hours about a wide range of topics, including what happens when we can finally implant a google chip in our brains 
After that I had to go onto NPR because I firmly believe that in one important respect we are degenerating as a country - we are graduating a generation of indentured servants who will spend 50 years or more paying down their student debt rather than starting companies and curing cancer. So maybe I made a difference 
Then I had lunch with a guy I hadn't seen in ten years. In those ten years he had gone to jail and now I was finally taking the time to forgive him for something he never did to me. I felt bad I hadn't helped him when he was at his low point. Then I came home and watched my kid play clarinet at her school. Then I read until I fell asleep. Today I did nothing but write. Both days inspired me 
It also inspires me that I'm being asked these questions. Whenever anyone asks me to do anything I'm infinitely grateful. Why me? I feel lucky. I like it when someone cares what I think. I'll write and do things as long as anyone cares. I honestly probably wouldn't write if nobody cared. I don't have enough humility for that, I'm ashamed to admit 
3. Your new book "How to be the luckiest person alive" has just come out. What is it about 
When I was a kid I thought I needed certain things: a college education from a great school, a great home, a lot of money, someone who would love me with ease. I wanted people to think I was smart. I wanted people to think I was even special. And as I grew older more and more goals got added to the list: a high chess rating, a published book, perfect weather, good friends, respect in various fields, etc. I lied to myself that I needed these things to be happy. The world was going to work hard to give me these things, I thought. But it turned out the world owed me no favors 
And gradually, over time, I lost everything I had ever gained. Several times. I've paced at night so many times wondering what the hell was I going to do next or trying not to care. The book is about regaining your sanity, regaining your happiness, finding luck in all the little pockets of life that people forget about. It's about turning away from the religion you've been hypnotized into believing into the religion you can find inside yourself every moment of the day 
[Note: in a few days I'm going to do a post on self-publishing and also how to get the ebook for free. The link above is to the paperback. Kindle should be ready soon also. 
Related link: Why I Write Books Even Though I've Lost Money On Every Book I've Ever Writte 
4. Is it possible to accelerate success? If yes, how 
Yes, and it's the only way I know actually to achieve success. It's by following the Daily Practice I outline in this post: 
It's the only way I know to exercise every muscle from the inside of you to the outside of you. I firmly believe that happiness starts with that practice 
5. You say that discipline, persistence and psychology are important if one has to achieve success. How can one work on improving "psychology" part 
Success doesn't really mean anything. People want to be happy in a harsh and unforgiving world. It's very difficult. We're so lucky most of us live in countries without major wars. Our kids aren't getting killed by random gunfire. We all have cell phones. We all can communicate with each other on the Internet. We have Google to catalog every piece of information in history! We are so amazingly lucky already 
How can it be I was so lucky to be born into such a body? In New York City of all places? Just by being born in such a way on this planet was an amazing success 
So what else is there? The fact is that most of us, including me, have a hard time being happy with such ready-made success. We quickly adapt and want so much more out of life. It's not wars or disease that kill us. It's the minor inconveniences that add up in life. It's the times we feel slighted or betrayed. Or even slightly betrayed. Or overcharged. Or we miss a train. Or it's raining today. Or the dishwasher doesn't work. Or the supermarket doesn't have the food we like. We forget how good the snow tasted when we were kids. Now we want gourmet food at every meal 
Taking a step back, doing the Daily Practice I outline in the question above. For me, the results of that bring me happiness. That's success. Today. And hopefully tomorrow 
6. You advocate not sending kids to college. What if kids grow up and then blame their parents about not letting them get a college education 
I went to one of my kid's music recitals yesterday. She was happy to see me. I hugged her afterwards. She played "the star wars theme" on the clarinet. I wish I could've played that for my parents. My other daughter has a dance recital in a few weeks. I tried to give her tips but she laughed at me. I was quite the breakdancer in my youth. The nerdiest breakdancer on the planet. I want to be present for them. To love them. To let them always know that in their own dark moments, they know I will listen to them. I love them. Even when they cry and don't always agree with me. Even when they laugh at me because sometimes I act like a clown 
Later, if they want to blame me for anything at all then I will still love them. That's my "what if" 
Two posts 
I want my daughters to be lesbian 
Advice I want to give my daughter 
7. Four of your favorite posts from The Altucher Confidential 
As soon as I publish a post I get scared to death. Is it good? Will people re-tweet? Will one part of the audience of this blog like it at the expense of another part of the audience. Will I get Facebook Likes? I have to stop clinging to these things but you also need to respect the audience. I don't know. It's a little bit confusing to me. I don't have the confidence of a real writer yet 
Here are four of my favorites 
How I screwed Yasser Arafat out of $2mm (and lost another $100mm in the process 
It's Your Fault 
I'm Guilty of Torturing Wome 
The Girl Whose Name Was a Curs 
Although these three are favorites I really don't post anything unless it's my favorite of that moment 
8. 3 must-read books for aspiring entrepreneurs 
The key in an entrepreneur book: you want to learn business. You want to learn how to honestly communicate with your customers. You want to stand out 
The Essays of Warren Buffett by Lawrence Cunningha 
"The Thank you Economy" by Gary Vaynerchu 
"Purple cow" by Seth Godi 
9. I love your writing, so do so many others out there. Who are your favorite writers 
"Jesus's Son" by Denis Johnson is the best collection of short stories ever written. I'm afraid I really don't like his novels though 
"Tangents" by M. Prado. A beautiful series of graphic stories about relationships 
Other writers: Miranda July, Ariel Leve, Mary Gaitskill, Charles Bukowski, Celine, Sam Lipsyte, William Vollmann, Raymond Carver. Arthur Nersesian. Stephen Dubner 
Many writers are only really good storytellers. Most writers come out of a cardboard factory MFA system and lack a real voice. A real voice is where every word exposes ten levels of hypocrisy in the world and brings us all the way back to see reality. The writers above have their own voices, their own pains, and their unique ways of expressing those pains. Some of them are funny. Some a little more dark. I wish I could write 1/10 as good as any of them 
10. You are a prolific writer. Do you have any hacks that help you write a lot in little time 
Coffee, plus everything else coffee does for you first thing in the morning 
Only write about things you either love or hate. But if you hate something, try to find a tiny gem buried in the bag of dirt so you can reach in when nobody is looking and put that gem in your pocket. Stealing a diamond in all the shit around us and then giving it away for free via writing is a nice little hack, Being fearless precisely when you are most scared is the best hack 
11. I totally get and love your idea about bleeding as a writer, appreciate if you share more with the readers of this blog 
Most people worry about what other people think of them. Most people worry about their health. Most people are at a crossroads and don't know how to take the next step and which road to take it on. Everyone is in a perpetual state of 'where do I put my foot next'. Nobody, including me, can avoid that 
You and I both need to wash our faces in the morning, brush our teeth, shower, shit, eat, fight the weather, fight the colds that want to attack us if we're not ready. Fight loneliness or learn how to love and appreciate the people who want to love you back. And learn how to forgive and love the people who are even more stupid and cruel than we are. We're afraid to tell each other these things because they are all both disgusting and true 
You and I both have the same color blood. If I cut my wrist open you can see the color of my blood. You look at it and see that it's the same color as yours. We have something in common. It doesn't have to be shameful. It's just red. Now we're friends. No matter whom you are or where you are from. I didn't have to lie to you to get you to be my friend 
Related Links 
How to be a Psychic in Ten Easy Lesson 
My New Year's Resolution in 199 
12. What is your advice for young entrepreneurs 
Only build something you really want to use yourself. There's got to be one thing you are completely desperate for and no matter where you look you can't find it. Nobody has invented it yet. So there you go - you invent it. If there's other people like you, you have a business. Else. You fail. Then do it again. Until it works. One day it will 
Follow these 100 Rules 
The 100 Rules for Being a Good Entrepreneur 
And, in particular this 
The Easiest Way to Succeed as an Entrepreneu 
In my just released book I have more [http://Photo.net/gallery/tag-search/search?query_string=chapters chapters] on my experiences as an entrepreneur 
13. I advocate the concept of working at a job while building your business. You have of course lived it. Now as you look back, what is your take on this? Is it possible to make it work while sailing on two boats 
Your boss wants everything out of you. He wants you to work 80 hours a week. He wants to look good taking credit for your work. He wants your infinite loyalty. So you need something back 
Exploit your employer. It's the best way to get good experience, clients, contacts. It's a legal way to steal. It's a fast way to be an entrepreneur because you see what large companies with infinite money are willing to pay for. If you can provide that, you make millions. It's how many great businesses have started and will always start. It's how every exit I've had started 
14. Who is a "person with true moral fiber"? In current times are there any role models who are people with true moral fiber 
I don't really know the answer. I think I know a few people like that. I hope I'm someone like that. And I pray to god the people I'm invested in are like that and my family is like that 
I find most people to be largely mean and stupid, a vile combination. It's not that I'm pessimistic or cynical. I'm very much an optimist. It's just reality. Open the newspaper or turn on the TV and watch these people 
Moral fiber atrophies more quickly than any muscle on the body. An exercise I do every morning is to promise myself that "I'm going to save a life today" and then leave it in the hands of the Universe to direct me how I can best do that. Through that little exercise plus the Daily Practice described above I hope to keep regenerating that fiber 
15. Your message to the readers of this blog 
Skip dinner. But follow me on Twitter. 
Read more posts on The Altucher Confidential �
More from The Altucher Confidentia 
Life is Like a Game. Here�s How You Master ANY Gam 
Step By Step Guide to Make $10 Million And Then Totally Blow 
Can You Do One Page a Day?

Representativeness heuristic

2014-02-10T22:38:22Z

99.233.3.62: /* References */

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Semi-major axis

2014-01-20T15:25:07Z

99.233.63.81:

In [[signal processing]], a '''filter''' is a device or process that removes from a [[Signal (electronics)|signal]] some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some [[frequency|frequencies]] and not others in order to suppress interfering signals and reduce background [[signal noise|noise]]. However, filters do not exclusively act in the [[frequency domain]]; especially in the field of [[image processing]] many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others [[scaled correlation | without having to act in the frequency domain]].

The drawback of filtering is the loss of information associated with it. [[Noise reduction|Signal combination]] in Fourier space is an alternative approach for removal of certain frequencies from the recorded signal.<ref>[http://rsi.aip.org/resource/1/rsinak/v82/i11/p115103_s1?isAuthorized=no Mashaghi et al. Noise reduction by signal combination in Fourier space applied to drift correction in optical tweezers, Rev. Sci. Instrum. 82, 115103 (2011)]</ref>

There are many different bases of classifying filters and these overlap in many different ways; there is no simple hierarchical classification. Filters may be:
*[[linear filter|linear]] or [[non-linear filter|non-linear]]
*[[Time-invariant system|time-invariant]] or [[Time-variant system|time-variant]], also known as shift invariance. If the filter operates in a spatial domain then the characterization is space invariance.
* causal or not-causal: depending if present output depends or not on "future" input; of course, for time related signals processed in real-time all the filters are causal; it is not necessarily so for filters acting on space-related signals or for deferred-time processing of time-related signals.
*[[analogue filter|analog]] or [[digital filter|digital]]
*[[discrete-time]] (sampled) or [[continuous signal|continuous-time]]
*[[passive component|passive]] or [[active filter|active]] type of continuous-time filter
*[[infinite impulse response]] (IIR) or [[finite impulse response]] (FIR) type of discrete-time or digital filter.

==Linear continuous-time filters==

Linear continuous-time circuit is perhaps the most common meaning for filter in the signal processing world, and simply "filter" is often taken to be synonymous. These are [[filter design|filters that are designed]] to remove certain [[frequency|frequencies]] and allow others to pass. Such a filter is, of necessity, a [[linear filter]]. Any non-linearity will result in the output signal containing components of frequency which were not present in the input signal.

The modern design methodology for linear continuous-time filters is called [[network synthesis filters|network synthesis]]. Some important filter families designed in this way are:
*[[Chebyshev filter]], has the best approximation to the ideal response of any filter for a specified order and ripple.
*[[Butterworth filter]], has a maximally flat frequency response.
*[[Bessel filter]], has a maximally flat [[phase delay]].
*[[Elliptic filter]], has the steepest cutoff of any filter for a specified order and ripple.

The difference between these filter families is that they all use a different [[polynomial function]] to approximate to the [[ideal filter]] response. This results in each having a different [[transfer function]].

Another older, less-used methodology is the [[composite image filter|image parameter method]]. Filters designed by this methodology are archaically called "wave filters". Some important filters designed by this method are:
*[[Constant k filter]], the original and simplest form of wave filter.
*[[m-derived filter]], a modification of the constant k with improved cutoff steepness and [[impedance matching]].

===Terminology===
Some terms used to describe and classify linear filters:
[[File:Bandform template.svg|thumb|400px]]
*The frequency response can be classified into a number of different bandforms describing which frequency [[Band (radio)|bands]] the filter passes (the [[passband]]) and which it rejects (the [[stopband]]):
**[[Low-pass filter]] – low frequencies are passed, high frequencies are attenuated.
**[[High-pass filter]] – high frequencies are passed, low frequencies are attenuated.
**[[Band-pass filter]] – only frequencies in a frequency band are passed.
**[[Band-stop filter]] or band-reject filter – only frequencies in a frequency band are attenuated.
**[[Notch filter]] – rejects just one specific frequency - an extreme band-stop filter.
**[[Comb filter]] – has multiple regularly spaced narrow passbands giving the bandform the appearance of a comb.
**[[All-pass filter]] – all frequencies are passed, but the phase of the output is modified.

*[[Cutoff frequency]] is the frequency beyond which the filter will not pass signals. It is usually measured at a specific attenuation such as 3dB.
*[[Roll-off]] is the rate at which attenuation increases beyond the cut-off frequency.
*[[Transition band]], the (usually narrow) band of frequencies between a passband and stopband.
*[[Ripple (electrical)#Frequency domain|Ripple]] is the variation of the filter's [[insertion loss]] in the passband.
*The order of a filter is the [[degree of a polynomial|degree of the approximating polynomial]] and in passive filters corresponds to the number of elements required to build it. Increasing order increases roll-off and brings the filter closer to the ideal response.

==Technologies==

Filters can be built in a number of different technologies. The same transfer function can be realised in several different ways, that is the mathematical properties of the filter are the same but the physical properties are quite different. Often the components in different technologies are directly analogous to each other and fulfill the same role in their respective filters. For instance, the resistors, inductors and capacitors of electronics correspond respectively to dampers, masses and springs in mechanics. Likewise, there are corresponding components in distributed element filters.

*[[Electronic filter]]s were originally entirely passive consisting of resistance, inductance and capacitance. Active technology makes design easier and opens up new possibilities in filter specifications.
*[[Digital filter]]s operate on signals represented in digital form. The essence of a digital filter is that it directly implements a mathematical algorithm, corresponding to the desired filter transfer function, in its programming or microcode.
*[[Mechanical filter]]s are built out of mechanical components. In the vast majority of cases they are used to process an electronic signal and [[transducer]]s are provided to convert this to and from a mechanical vibration. However, examples do exist of filters that have been designed for operation entirely in the mechanical domain.
*[[Distributed element filter]]s are constructed out of components made from small pieces of [[transmission line]] or other [[distributed element model|distributed elements]]. There are structures in distributed element filters that directly correspond to the [[lumped element model|lumped elements]] of electronic filters, and others that are unique to this class of technology.
*[[Waveguide filter]]s consist of waveguide components or components inserted in the waveguide. Waveguides are a class of transmission line and many structures of distributed element filters, for instance the [[stub (electronics)]], can be implemented in waveguides also.
*[[Crystal filter]]s use [[quartz]] crystals as resonators, or some other [[piezoelectric]] material.
*[[Acoustic filter]]s
*[[Filter (optics)|Optical filter]]s were originally developed for purposes other than signal processing such as lighting and photography. With the rise of [[optical fiber]] technology, however, optical filters increasingly find signal processing applications and signal processing filter terminology, such as [[Filter (optics)#Longpass|longpass]] and [[Filter (optics)#Shortpass|shortpass]], are entering the field.

== The transfer function ==
{{Main|transfer function}}
The [[transfer function]] of a filter is most often defined in the domain of the complex frequencies. The back and forth passage to/from this domain is operated by the [[Laplace transform]] and its inverse (therefore, here below, the term "input signal" shall be understood as "the Laplace transform of" (the time representation of) the input signal, and so on).

The [[transfer function]] <math>\ H(s)</math> of a filter is the ratio of the output signal <math>\ Y(s)</math> to that of the input signal <math>\ X(s)</math> as a function of the complex frequency <math>\ s</math>:

:<math>\ H(s)=\frac{Y(s)}{X(s)}</math>
with <math>\ s = \sigma + j \omega</math>.

The transfer function of all linear time-invariant filters generally share certain characteristics:

* For filters which are constructed of discrete components, their transfer function must be the ratio of two polynomials in <math>\ s</math>, i.e. a [[rational function]] of <math>\ s</math>. The order of the transfer function will be the highest power of <math>\ s</math> encountered in either the numerator or the denominator.
* The polynomials of the transfer function will all have real coefficients. Therefore, the poles and zeroes of the transfer function will either be real or occur in complex conjugate pairs.
* Since the filters are assumed to be stable, the real part of all poles (i.e. zeroes of the denominator) will be negative, i.e. they will lie in the left half-plane in complex frequency space.

Distributed element filters do not, in general, produce rational functions but can often approximate to them.

The proper construction of a transfer function involves the [[Laplace transform]], and therefore it is needed to assume null initial conditions, because
:<math>\mathcal{L}\left\{\frac{df}{dt}\right\} = s\cdot\mathcal{L} \left\{ f(t) \right\}-f(0), </math>
And when f(0)=0 we can get rid of the constants and use the usual expression
:<math>\mathcal{L}\left\{\frac{df}{dt}\right\} = s\cdot\mathcal{L} \left\{ f(t) \right\}</math>
An alternative to transfer functions is to give the behavior of the filter as a [[convolution]]. The [[convolution theorem]], which holds for Laplace transforms, guarantees equivalence with transfer functions.

=== Classification ===
{{Main|transfer function}}

Filters may be specified by family and bandform. A filter's family is specified by the approximating polynomial used and each leads to certain characteristics of the transfer function of the filter. Some common filter families and their particular characteristics are:

*[[Butterworth filter]] – no gain [[ripple (filters)|ripple]] in pass band and stop band, slow cutoff
*[[Chebyshev filter|Chebyshev filter (Type I)]] – no gain ripple in stop band, moderate cutoff
*[[Chebyshev filter|Chebyshev filter (Type II)]] – no gain ripple in pass band, moderate cutoff
*[[Bessel filter]] – no [[group delay]] ripple, no gain ripple in both bands, slow gain cutoff
*[[Elliptic filter]] – gain ripple in pass and stop band, fast cutoff
*[[Optimum "L" filter]]
*[[Gaussian filter]] – no ripple in response to step function
*[[Hourglass filter]]
*[[Raised-cosine filter]]

Each family of filters can be specified to a particular order. The higher the order, the more the filter will approach the "ideal" filter; but also the longer the impulse response is and the longer the latency will be. An ideal filter has full transmission in the pass band, complete attenuation in the stop band, and an abrupt transition between the two bands, but this filter has infinite order (i.e., the response cannot be expressed as a [[linear differential equation]] with a finite sum) and infinite latency (i.e., its [[compact support]] in the [[Fourier transform]] forces its time response to be ever lasting).

Here is an image comparing Butterworth, Chebyshev, and elliptic filters. The filters in this illustration are all fifth-order low-pass filters. The particular implementation – analog or digital, passive or active – makes no difference; their output would be the same.

[[Image:Electronic linear filters.svg|500px|center]]

As is clear from the image, elliptic filters are sharper than all the others, but they show ripples on the whole bandwidth.

Any family can be used to implement a particular bandform of which frequencies are transmitted, and which, outside the passband, are more or less attenuated. The transfer function completely specifies the behavior of a linear filter, but not the particular technology used to implement it. In other words, there are a number of different ways of achieving a particular transfer function when designing a circuit. A particular bandform of filter can be obtained by [[transform (mathematics)|transformation]] of a [[prototype filter#Bandform transformation|prototype filter]] of that family.

==Impedance matching==

[[Impedance matching]] structures invariably take on the form of a filter, that is, a network of non-dissipative elements. For instance, in a passive electronics implementation, this would likely take the form of a [[ladder topology]] of inductors and capacitors. The design of matching networks shares much in common with filters and the design invariably will have a filtering action as an incindental consequence. Although the prime purpose of a matching network is not to filter, it is often the case that both functions are combined in the same circuit. The need for impedance matching does not arise while signals are in the digital domain.

Similar comments can be made regarding [[power dividers and directional couplers]]. When implemented in a distributed element format these devices can take the form of a [[distributed element filter]]. There are four ports too be matched and widening the bandwidth requires filter-like structures to achieve this. The inverse is also true, distributed element filters can take the form of coupled lines.

==Some filters for specific purposes==

* [[Audio filter]]
* [[Line filter]]
* [[Texture filtering]]

===Filters for removing noise from data===

* [[Wiener filter]]
* [[Kalman filter]]
* [[Savitzky–Golay smoothing filter]]

== References ==
{{reflist}}
*Miroslav D. Lutovac, Dejan V. Tošić, Brian Lawrence Evans, ''Filter Design for Signal Processing Using MATLAB and Mathematica'', Miroslav Lutovac, 2001 ISBN 0201361302.
*B. A. Shenoi, ''Introduction to Digital Signal Processing and Filter Design'', John Wiley & Sons, 2005 ISBN 0471656380.
*L. D. Paarmann, ''Design and Analysis of Analog Filters: A Signal Processing Perspective'', Springer, 2001 ISBN 0792373731.
*J.S.Chitode, ''Digital Signal Processing'', Technical Publications, 2009 ISBN 8184316461.
*Leland B. Jackson, ''Digital Filters and Signal Processing'', Springer, 1996 ISBN 079239559X.

{{Electronic filters}}

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[[Category:Signal processing]]
[[Category:Telecommunication theory]]
[[Category:Filter theory]]