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SEO Keyword summary for en.wikipedia.org/wiki/lti_system_theory
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle system infty |
long Tail Keywords (2 words) mathrm d -infty infty stackrel textdef d tau impulse response |
long Tail Keywords (3 words) mathrm d tau mathrm d lambda int -infty infty systems impulse response exponentials as eigenfunctions move to sidebar infty xtau cdot |
en.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a en.wikipedia.org/wiki/lti_system_theory page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
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linear timeinvariant system wikipedia
Meta description
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Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
Emphasis (bold and italic)
Emphasis SEO impact
Images
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Image alt descriptions
Images SEO impact
wikipedia free encyclopedia displaystyle axt ayt xtxt ytyt xtt ytt yixihi asest bsest bsas ytxht mathrel stackrel mathrm def int limits infty xttau cdot htau tau xtau httau textstyle delta xutau ytmathrel textdef otx otleftint ctau umathrm urightint underbrace ytau otxtau beginalignedotxutau umathrel quad yttau ottau xendaligned htmathrel otdelta utau beginalignedxhtint ptint endaligned udelta beginalignedxhtotleftint uright ptotleftxu urightmathrel ytendaligned mathcal hflambda lambda aest asin mathbb xtaest aestau beginalignedoverbrace aesttau hfint aestestau ptaestint estau ptoverbrace textinput foverbrace textscalar hsmathrel htestmathrm vteiomega vateiomega hvateiomega ahvt eiomega hvathvta hvtaeiomega hvtau lhtmathrel ejomega omega jmathrel sqrt hjomega fht ythxtmathrel hsxs frac tleftc trightc txttau lleftfrac txtrightsxs aleftxtrightmathrel tataxlambda beginalignedmathcal tint tatac tatax tendaligned aleftxttau rightint ttau attau axxi axttau aleftxtrightint leftfrac arightxlambda tmathrel begincases textif tfrac endcases forall xtinfty ytinfty htmathrm tinfty sjomega xnmathrel xntqquad nin xmk xmktext all integer values ynmathrel onx xmdelta hnmathrel ondelta onleftsum kinfty ckcdot xkm mrightsum onxk beginalignedonxmk mmathrel ynkmathrel onkxendaligned xmequiv sum xkcdot beginalignedynonxonleftsum mendaligned ckxk xkmdelta beginalignedondelta onkdelta hnkendaligned hnk xnkcdot znestn tin zest zsin xnzn minfty hnmzm hmznmznsum hmzmznhz hzmathrel hmzm hzmathcal zhnsum ninfty hnzn zejomega hejomega fhn ynhxnsum hnmxmmathcal hzxz dxnmathrel dleftc nrightc dxnmxnm mdxnm zleftdxnrightz aleftxnrightmathrel knanaxk aleftc nrightsum knanaleftc krightc knanax aleftx nrightendaligned aleftxnmrightsum knanaxkmsum knmanmaxkmathcal aleftxrightnmendaligned xninfty yninfty hninfty edit wikidata wikimedia foundation powered mediawiki
Mobile SEO en.wikipedia.org/wiki/lti_system_theory
Mobile rendering
Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
Marketing / lead generation for en.wikipedia.org/wiki/lti_system_theory
Social Media
Facebook shares | Facebook likes | ||
Facebook comments | Tweets | ||
Google +1 |
Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
lti found in path !
system found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
Sitemap found?
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
statistics
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en.m.wikipedia.org |
en.wikipedia.org wikimedia foundation inc
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w httpsenwikipediaorgwindexphptitlelineartimeinvariantsystemoldid1243525871
page information
printable version
lti system theory
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wiki block diagram
superposition principle
system analysis
system
linearity
timeinvariance
convolution
impulse response
electrical circuit
resistors
capacitors
inductors
linear amplifiers
image processing
discretetime
sampled
applied mathematics
electrical circuit analysis and design
signal processing
filter design
control theory
mechanical engineering
measuring instruments
nmr spectroscopy
ordinary differential equations
continuous time
discrete time
sequences
frequency domain
transfer function
onesided laplace transform
z transform
eigenfunction
complex
exponential functions
sinusoids
amplitude
phase
nonlinear
differential equation
electrical circuits
filter banks
vectors
green function
impulse
causal system
eigenvalue
linear
timeinvariant
fourier transform
bilateral laplace transform
square integrable
wienerkhinchin theorem
derivative
boxcar function
twosided laplace transform
bibo stability
maximum absolute values
l1
region of convergence
lowpass filter
sinc function
cutoff frequency
sampling circuit
analogtodigital converter
sampling period
nyquist filter
nyquist frequency
aliased
kronecker delta function
discretetime fourier transform
fourier series
unit circle
locus
isbn
circulant matrix
frequency response
signalflow graph
riskin ea
bibcode
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SEO Advice for en.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 65% | A title should reflect the contents of a site. This site has a 50 % match | |
Title Length | 100% | Limit your title to anywhere between 40 and 70 characters. Your title was 41 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 50% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 166 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 6 folders above or in the first level of navigation. | |
Headings | 58% | Headers should reflect the contents of a site. This site has a 25 % match | |
Links | 12% | Link anchors should to some degree reflect the contents of a site. This site has a 6 % match | |
Image alt tags | 22% | Image alt tags should to some degree reflect the contents of a site. This site has a 8 % match | |
Bold and italic | 66% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 22 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 97% | 97.46192893401 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 6179 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 93.34% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 100% | There are important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 413 inline style declarations ( <a style="color:green">) with a size of 14577 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (2) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 40% | We dit not font a normalized heading structure. A heading 2 (h2) for example should be followed by a heading of an equal level (h2), a child heading (h3) or even a aprent heading (h1). |
How would you like to have SEO advice for all your pages ?? Start your SEO Dashboard and optimize your website!
en.wikipedia.org images and descriptions
156 images found at en.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
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https://wikimedia.org/api/rest_v1/media/math/render/svg/843d6fba7804c7ee7099d1be0d7f0619e56326e6 height: height attribute not set width: width attribute not set description: {\displaystyle \int _{-\infty }^{\infty }h(t-\tau )ae^{s\tau }\,\mathrm {d} \tau } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bcddc6f695993370f7c7509114ed2f3d0580675d height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\overbrace {\int _{-\infty }^{\infty }h(\tau )\,ae^{s(t-\tau )}\,\mathrm {d} \tau } ^{{\mathcal {h}}f}&=\int _{-\infty }^{\infty }h(\tau )\,ae^{st}e^{-s\tau }\,\mathrm {d} \tau \\[4pt]&=ae^{st}\int _{-\infty }^{\infty }h(\tau )\,e^{-s\tau }\,\mathrm {d} \tau \\[4pt]&=\overbrace {\underbrace {ae^{st}} _{\text{input}}} ^{f}\overbrace {\underbrace {h(s)} _{\text{scalar}}} ^{\lambda },\\\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/80be7cd364241cc8b0af96a26a06042722501dfa height: height attribute not set width: width attribute not set description: {\displaystyle h(s)\mathrel {\stackrel {\text{def}}{=}} \int _{-\infty }^{\infty }h(t)e^{-st}\,\mathrm {d} t} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f1b91390324fc9c33ec00fe57e3924ad7118cc1e height: height attribute not set width: width attribute not set description: {\displaystyle h(s)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/395df90d70385a448d0c2434b9042f6fff5d2b5b height: height attribute not set width: width attribute not set description: {\displaystyle v(t)=e^{i\omega t}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/398eea781bb625970b6c9b11d42c70b6e32754ac height: height attribute not set width: width attribute not set description: {\displaystyle v_{a}(t)=e^{i\omega (t+a)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/028bc8c112a60a2c038e1318c3984670ece6f3ff height: height attribute not set width: width attribute not set description: {\displaystyle h[v_{a}](t)=e^{i\omega a}h[v](t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e0894140733fa51fadafdec3c99fa1305889de74 height: height attribute not set width: width attribute not set description: {\displaystyle e^{i\omega a}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b83ef94c53fd62b051c30489848de02b7ca690fb height: height attribute not set width: width attribute not set description: {\displaystyle h[v_{a}](t)=h[v](t+a)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b height: height attribute not set width: width attribute not set description: {\displaystyle h} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a9f94f406bff0281e34cdae10b27c0e406fe1494 height: height attribute not set width: width attribute not set description: {\displaystyle h[v](t+a)=e^{i\omega a}h[v](t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/43469ec032d858feae5aa87029e22eaaf0109e9c height: height attribute not set width: width attribute not set description: {\displaystyle t=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/051d559b68e53a40841ddd44e6478d00a33d38a9 height: height attribute not set width: width attribute not set description: {\displaystyle h[v](\tau )=e^{i\omega \tau }h[v](0)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a72750d46710bf82e1f436f8fb19da8d1a65cd29 height: height attribute not set width: width attribute not set description: {\displaystyle e^{i\omega \tau }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1230f304e6efdcbee5bf4bdb66061ebb524bfd28 height: height attribute not set width: width attribute not set description: {\displaystyle h(s)\mathrel {\stackrel {\text{def}}{=}} {\mathcal {l}}\{h(t)\}\mathrel {\stackrel {\text{def}}{=}} \int _{0}^{\infty }h(t)e^{-st}\,\mathrm {d} t} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84f8673593e85aacbb2741a859a596219082cb46 height: height attribute not set width: width attribute not set description: {\displaystyle e^{j\omega t}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/89e8c2b65efd16235f21240e5585a0b9ceaf56d9 height: height attribute not set width: width attribute not set description: {\displaystyle \omega \in \mathbb {r} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3aded4ecec8fbeb55f6c7825c927a9c233093e6c height: height attribute not set width: width attribute not set description: {\displaystyle j\mathrel {\stackrel {\text{def}}{=}} {\sqrt {-1}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8243cf79c3eccf125bb67646e818c2f70e18ad17 height: height attribute not set width: width attribute not set description: {\displaystyle h(j\omega )={\mathcal {f}}\{h(t)\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/54b9cf918573394f5d6d888c7c8519bfc73eb7a7 height: height attribute not set width: width attribute not set description: {\displaystyle h(j\omega )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6890f3b832d3444b4cac7a9dabdb20b8bb8a528e height: height attribute not set width: width attribute not set description: {\displaystyle y(t)=(h*x)(t)\mathrel {\stackrel {\text{def}}{=}} \int _{-\infty }^{\infty }h(t-\tau )x(\tau )\,\mathrm {d} \tau \mathrel {\stackrel {\text{def}}{=}} {\mathcal {l}}^{-1}\{h(s)x(s)\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fe439b424a94433cc5cc5ebe99ac04bf2145aba9 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left(c_{1}x_{1}(t)+c_{2}x_{2}(t)\right)=c_{1}x'_{1}(t)+c_{2}x'_{2}(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0243b3cb9f1fd4f69b31b01696cffa56d9c38bd9 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}x(t-\tau )=x'(t-\tau )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/58d3a54aab93e29cd231d6c0bd97d42719b14565 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {l}}\left\{{\frac {\mathrm {d} }{\mathrm {d} t}}x(t)\right\}=sx(s)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1418664a674c192643f68c68df6aacd9cdb948f9 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {a}}\left\{x(t)\right\}\mathrel {\stackrel {\text{def}}{=}} \int _{t-a}^{t+a}x(\lambda )\,\mathrm {d} \lambda .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/38b1f7cf3262aeda4109c791eba2e660632fdfe2 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}{\mathcal {a}}\{c_{1}x_{1}(t)+c_{2}x_{2}(t)\}&=\int _{t-a}^{t+a}(c_{1}x_{1}(\lambda )+c_{2}x_{2}(\lambda ))\,\mathrm {d} \lambda \\&=c_{1}\int _{t-a}^{t+a}x_{1}(\lambda )\,\mathrm {d} \lambda +c_{2}\int _{t-a}^{t+a}x_{2}(\lambda )\,\mathrm {d} \lambda \\&=c_{1}{\mathcal {a}}\{x_{1}(t)\}+c_{2}{\mathcal {a}}\{x_{2}(t)\},\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e49016a6b58595821ed6f24b635f322f150e2e04 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}{\mathcal {a}}\left\{x(t-\tau )\right\}&=\int _{t-a}^{t+a}x(\lambda -\tau )\,\mathrm {d} \lambda \\&=\int _{(t-\tau )-a}^{(t-\tau )+a}x(\xi )\,\mathrm {d} \xi \\&={\mathcal {a}}\{x\}(t-\tau ),\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/280ae03440942ab348c2ca9b8db6b56ffa9618f8 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {a}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1e4e2bfab2678273fc9e71442acc41a6da4ebada height: height attribute not set width: width attribute not set description: {\displaystyle \pi (t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b654e4eaabad6a81ec78efcf5f144c528401691b height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {a}}\left\{x(t)\right\}=\int _{-\infty }^{\infty }\pi \left({\frac {\lambda -t}{2a}}\right)x(\lambda )\,\mathrm {d} \lambda ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/57b66c3840465f877c14bc3aec3efc2ec01f3f65 height: height attribute not set width: width attribute not set description: {\displaystyle \pi (t)\mathrel {\stackrel {\text{def}}{=}} {\begin{cases}1&{\text{if }}|t|<{\frac {1}{2}},\\0&{\text{if }}|t|>{\frac {1}{2}}.\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4a3f8e3389da4df9edc7175a5d97eb38a22245ef height: height attribute not set width: width attribute not set description: {\displaystyle h(t)=0\quad \forall t<0,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d5908a8849de74171518929ae19615aab503d9d1 height: height attribute not set width: width attribute not set description: {\displaystyle \ \|x(t)\|_{\infty }<\infty } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/26015a0cfe0310878f91f8c6acc1e5f15676b5c8 height: height attribute not set width: width attribute not set description: {\displaystyle \ \|y(t)\|_{\infty }<\infty } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e65ab566ad6c922f5c27a30bc6b81ab8cb43d0e5 height: height attribute not set width: width attribute not set description: {\displaystyle \|h(t)\|_{1}=\int _{-\infty }^{\infty }|h(t)|\,\mathrm {d} t<\infty .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/114e5dcfb07325a06ed4329e3690d8225eadf422 height: height attribute not set width: width attribute not set description: {\displaystyle s=j\omega } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9c8875f14d87cb6daa44307512a91eceb5f34d87 height: height attribute not set width: width attribute not set description: {\displaystyle t<0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/29a2960e88369263fe3cfe00ccbfeb83daee212a height: height attribute not set width: width attribute not set description: {\displaystyle t>0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e3ef43ca3fc4fbed405d4ef06a875a9bb2545cfe height: height attribute not set width: width attribute not set description: {\displaystyle x_{n}\mathrel {\stackrel {\text{def}}{=}} x(nt)\qquad \forall \,n\in \mathbb {z} ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a59aaa5ef2de37e72f08f058bb47018dbf71b41d height: height attribute not set width: width attribute not set description: {\displaystyle \{x[m-k];\ m\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f94e37f7f04b5567c6798d215c5b219c3db12630 height: height attribute not set width: width attribute not set description: {\displaystyle \{x[m-k];{\text{ for all integer values of }}m\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a120eeb8a091b516595765bd08b306f2394e7721 height: height attribute not set width: width attribute not set description: {\displaystyle \{x\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/373d34e017c034f0e5bf06a7f50b93dcf3245c97 height: height attribute not set width: width attribute not set description: {\displaystyle \{x[m];\ m\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b49a0e849cf0c994af2f0914a0c095259c4d5a6e height: height attribute not set width: width attribute not set description: {\displaystyle \{y\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc height: height attribute not set width: width attribute not set description: {\displaystyle o} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/28bc1024cf958d3bb61b992d50dca65be2d8ef80 height: height attribute not set width: width attribute not set description: {\displaystyle y[n]\mathrel {\stackrel {\text{def}}{=}} o_{n}\{x\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d7a9c5f6dd10da1a2ab4c6b691277229ef14a0d9 height: height attribute not set width: width attribute not set description: {\displaystyle x[m]=\delta [m],} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/60cf4bc1fb844dde951ed0ec6030476ec37362ef height: height attribute not set width: width attribute not set description: {\displaystyle h[n]\mathrel {\stackrel {\text{def}}{=}} o_{n}\{\delta [m];\ m\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d755d801592991facc3af20e28cdf53b751ccaaf height: height attribute not set width: width attribute not set description: {\displaystyle o_{n}\left\{\sum _{k=-\infty }^{\infty }c_{k}\cdot x_{k}[m];\ m\right\}=\sum _{k=-\infty }^{\infty }c_{k}\cdot o_{n}\{x_{k}\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3260c759b66184ad44082e9b88d96da4e67707cf height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}o_{n}\{x[m-k];\ m\}&\mathrel {\stackrel {\quad }{=}} y[n-k]\\&\mathrel {\stackrel {\text{def}}{=}} o_{n-k}\{x\}.\,\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e6c2dfb15f99ef96c45a79bec37b94612e959683 height: height attribute not set width: width attribute not set description: {\displaystyle \{h\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/efe176cbaffc71d23545a592a87051d63f636ec7 height: height attribute not set width: width attribute not set description: {\displaystyle x[m]\equiv \sum _{k=-\infty }^{\infty }x[k]\cdot \delta [m-k],} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/64a0b0f4e35b39262dee1eef9df0259d8a976b68 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}y[n]=o_{n}\{x\}&=o_{n}\left\{\sum _{k=-\infty }^{\infty }x[k]\cdot \delta [m-k];\ m\right\}\\&=\sum _{k=-\infty }^{\infty }x[k]\cdot o_{n}\{\delta [m-k];\ m\},\,\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3262f2d9a48e648243906dc7bc9e8eb79f4575c8 height: height attribute not set width: width attribute not set description: {\displaystyle c_{k}=x[k]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dc0b4ae024d43ef8c4d2da79b48850099eddb1a6 height: height attribute not set width: width attribute not set description: {\displaystyle x_{k}[m]=\delta [m-k]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de95b7bf0ed896eaa9181a15a1eb71e7746cd9bf height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}o_{n}\{\delta [m-k];\ m\}&\mathrel {\stackrel {\quad }{=}} o_{n-k}\{\delta [m];\ m\}\\&\mathrel {\stackrel {\text{def}}{=}} h[n-k].\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/305428e6d1fb59cd0163a7a96ace52292a262afa height: height attribute not set width: width attribute not set description: {\displaystyle y[n]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8978a74a4e9ee231c1640862e44e6131703bd75f height: height attribute not set width: width attribute not set description: {\displaystyle =\sum _{k=-\infty }^{\infty }x[k]\cdot h[n-k]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/900174f73fd3472b8c093083993b05ae1dae54b1 height: height attribute not set width: width attribute not set description: {\displaystyle =\sum _{k=-\infty }^{\infty }x[n-k]\cdot h[k],} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4430e805a5f519b46eea4ec0d2dc04fc2fd19028 height: height attribute not set width: width attribute not set description: {\displaystyle o_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d4a6b2e1adce167c74509815ea30bc068f3a75a height: height attribute not set width: width attribute not set description: {\displaystyle z^{n}=e^{stn}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3c1cf6a513f2062531d95dbb198944936f312982 height: height attribute not set width: width attribute not set description: {\displaystyle n\in \mathbb {z} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1dc942013c1e7b6ace10ca49d838176c318b6abf height: height attribute not set width: width attribute not set description: {\displaystyle t\in \mathbb {r} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0c1cd01768652d0636434d9b0f361c8334eaffad height: height attribute not set width: width attribute not set description: {\displaystyle z=e^{st},\ z,s\in \mathbb {c} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0a1aaab3eda38d84f0850c910008e6abb8bb28f9 height: height attribute not set width: width attribute not set description: {\displaystyle x[n]=z^{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/89981bbbb05ffd469eeadb828c18359965985e46 height: height attribute not set width: width attribute not set description: {\displaystyle h[n]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a9c4df90ddb44d22aba287928e1d64d5ec9c984b height: height attribute not set width: width attribute not set description: {\displaystyle \sum _{m=-\infty }^{\infty }h[n-m]\,z^{m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2436df7fc69ec8e54781a4d531ec7d7d9f0b2542 height: height attribute not set width: width attribute not set description: {\displaystyle \sum _{m=-\infty }^{\infty }h[m]\,z^{(n-m)}=z^{n}\sum _{m=-\infty }^{\infty }h[m]\,z^{-m}=z^{n}h(z)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/003eedc6cc469292df931c7ac50df49bcbc48e29 height: height attribute not set width: width attribute not set description: {\displaystyle h(z)\mathrel {\stackrel {\text{def}}{=}} \sum _{m=-\infty }^{\infty }h[m]z^{-m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5b1a8cdd7ee39054e510deeb38ee551cc7616ae1 height: height attribute not set width: width attribute not set description: {\displaystyle z^{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3c5a542a7eaa29c58fb64cbeb5133ce98ac4f4b height: height attribute not set width: width attribute not set description: {\displaystyle h(z)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bec710d5f878067627c1d84fcc58812b84af7f14 height: height attribute not set width: width attribute not set description: {\displaystyle h(z)={\mathcal {z}}\{h[n]\}=\sum _{n=-\infty }^{\infty }h[n]z^{-n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3f09515e56b631e2e4106f7ab7ab09fa65b73be6 height: height attribute not set width: width attribute not set description: {\displaystyle e^{j\omega n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e38263aebb505f6e3125c67a9c0776db679dfb02 height: height attribute not set width: width attribute not set description: {\displaystyle z=e^{j\omega }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a482380e11e77f6522d702d69e02ae097539b43f height: height attribute not set width: width attribute not set description: {\displaystyle h(e^{j\omega })={\mathcal {f}}\{h[n]\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6d097c693531afa19239fd9387f5bb199494cdca height: height attribute not set width: width attribute not set description: {\displaystyle h(e^{j\omega })} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fad368d07cec1e332668528b21d27386d80f12aa height: height attribute not set width: width attribute not set description: {\displaystyle y[n]=(h*x)[n]=\sum _{m=-\infty }^{\infty }h[n-m]x[m]={\mathcal {z}}^{-1}\{h(z)x(z)\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bb20ff4361d05961823f3f29849748d8ae458067 height: height attribute not set width: width attribute not set description: {\displaystyle d\{x[n]\}\mathrel {\stackrel {\text{def}}{=}} x[n-1]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4b5883ac9970f573dd544c075a593104f30ad550 height: height attribute not set width: width attribute not set description: {\displaystyle d\left(c_{1}\cdot x_{1}[n]+c_{2}\cdot x_{2}[n]\right)=c_{1}\cdot x_{1}[n-1]+c_{2}\cdot x_{2}[n-1]=c_{1}\cdot dx_{1}[n]+c_{2}\cdot dx_{2}[n]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/62b1900ef2f37f5a24a9bb157880ec31383b107d height: height attribute not set width: width attribute not set description: {\displaystyle d\{x[n-m]\}=x[n-m-1]=x[(n-1)-m]=d\{x\}[n-m]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/26d3be8cf91a6a89461ed80ab025671cae29d5d1 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {z}}\left\{dx[n]\right\}=z^{-1}x(z).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e2dbee2877e06aa38c016b997355b869ecd00643 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {a}}\left\{x[n]\right\}\mathrel {\stackrel {\text{def}}{=}} \sum _{k=n-a}^{n+a}x[k].} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7edfb8033760b16754671bd579790578a5a9b381 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}{\mathcal {a}}\left\{c_{1}x_{1}[n]+c_{2}x_{2}[n]\right\}&=\sum _{k=n-a}^{n+a}\left(c_{1}x_{1}[k]+c_{2}x_{2}[k]\right)\\&=c_{1}\sum _{k=n-a}^{n+a}x_{1}[k]+c_{2}\sum _{k=n-a}^{n+a}x_{2}[k]\\&=c_{1}{\mathcal {a}}\left\{x_{1}[n]\right\}+c_{2}{\mathcal {a}}\left\{x_{2}[n]\right\},\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/26d18c14e6ad4a27e6dcb23d65fb07824c35f32e height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}{\mathcal {a}}\left\{x[n-m]\right\}&=\sum _{k=n-a}^{n+a}x[k-m]\\&=\sum _{k'=(n-m)-a}^{(n-m)+a}x[k']\\&={\mathcal {a}}\left\{x\right\}[n-m],\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/55e598ad76163467d521d27fd36872677740d338 height: height attribute not set width: width attribute not set description: {\displaystyle h[n]=0\ \forall n<0,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/beaec54893163f4ca4fc6ff2731dbfeb2282501c height: height attribute not set width: width attribute not set description: {\displaystyle \|x[n]\|_{\infty }<\infty } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3ab0a3137b9f47e17a643996e681857b3807a509 height: height attribute not set width: width attribute not set description: {\displaystyle \|y[n]\|_{\infty }<\infty } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/864cbbefbdcb55af4d9390911de1bf70167c4a3d height: height attribute not set width: width attribute not set description: {\displaystyle x[n]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/13a3ea009355e856627f3d2d8efb163218175841 height: height attribute not set width: width attribute not set description: {\displaystyle \|h[n]\|_{1}\mathrel {\stackrel {\text{def}}{=}} \sum _{n=-\infty }^{\infty }|h[n]|<\infty .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3749e5cd50ee274eb73aea2ade8441687140a66 height: height attribute not set width: width attribute not set description: {\displaystyle |z|=1} |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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