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| {{merge to|Sampling (signal processing)|discuss=Talk:Sampling rate#Merge to Sampling (signal processing)|date=September 2013}}
| | NFL- Tennessee Titans Beat The Houston Texans 20-17<br><br> |
| [[File:Analog digital series.svg|thumb|Analog signal (light blue) with a sampled signal (red) with a fixed spacing or ''sampling rate''.]]
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| The '''sampling rate''', '''sample rate''', or '''sampling frequency''' (<math>f_\mathrm{s}</math>) defines the number of [[sample (signal)|samples]] per unit of [[time]] (usually [[second]]s) taken from a [[continuous signal]] to make a [[discrete signal]]. For [[time-domain]] signals, the unit for sampling rate is [[hertz]] (inverse seconds, 1/s, s<sup>−1</sup>), sometimes noted as Sa/s or S/s (samples per second). The reciprocal of the sampling frequency is the '''sampling period''' or '''sampling interval''', which is the time between samples.<ref>{{cite book | title = Communications Standard Dictionary | author = Martin H. Weik | publisher = Springer | year = 1996 | isbn = 0412083914 | url = http://books.google.ca/books?id=jxXDQgAACAAJ&dq=Communications+Standard+Dictionary&hl=en&sa=X&ei=3t71T6KdKIOyqAHQ2OiKCQ&ved=0CDQQ6AEwAA }}</ref> | | The stone of choice is River Rock for Xeriscaping. Any copayments and also maximum coverage rewardsthree. It's obtainable in two sorts, 24 hour cure and seventy-two hour cure. The environment of the reservoir creates a prime environment for the fish to develop, generating eight pound Walleyes not unusual. Attendance for Oilers games was beneath par although they played in the Liberty Bowl in Memphis. We ordered the Household Dinner meal for two. So, who is the correct coach to replace Fulmer to resurrect Tennessee football?<br><br>They have an proper selection of the most current styles that are certain to please your teenager. The coaching system involves physical fitness tests and teaches you all of the safety information you require to know while in the air. She earned quick accolades as Sofia, the distraught housewife. Once this is accomplished, they may possibly have the whole case expunged. Average wages are primarily based on 2010 - 2012 averages. The climate of Johnson City is like that of most of Tennessee - typical higher temperatures reach around 85ºF in the summer time months, and average low temperatures attain down to 25ºF in the winter.<br><br>Preparation, product and process are the essential components to a long-lasting finish. These are [http://www.dailymail.co.uk/home/search.html?sel=site&searchPhrase=covered covered] with a layer of skin significantly thicker and tougher than the skin covering the rest of their bodies. A single may possibly not bathe with out wearing 'suitable clothing', ie that which covers 1's body from neck to knee. Certified copies are not accessible in the state. in Wyoming In Cheyenne, residents can't take a shower on Wednesdays. It is important that you commence the approach as quickly as attainable.<br><br>It is against the law to 'frown' at a police officer. It is illegal for a moose to stroll on a sidewalk in Fairbanks. These are the ideal Christmas tree farms closest to Jackson, Tenn., listed in order of proximity. A well-trained expungement lawyer will do a thorough criminal record search with your date of birth and complete name, leaving no stone unturned to ensure that each and every achievable criminal record that can be expunged is fully erased. You can saddle up your horse at a lot of stables all through the region. In Belize, it is illegal for a man to have sex with or marry his personal aunt.<br><br>It is illegal to eat an orange sitting in a [http://Answers.Yahoo.com/search/search_result?p=bathtub&submit-go=Search+Y!+Answers bathtub]. This could aid you in saving thousands of dollars as interest. In addition, it is also estimated that rural web expansion could generate an extra 49,000 jobs. A semi-computerized holds its rounds in a easy gadget identified as a magazine (it is achievable to offend some [https://www.behance.net/gallery/19295165/Terry-Bandy-Secrets-Of-Generating-Real-Estate-Income Terry Bandy] hard-line gun lovers by calling a publication a clip). Then they return north in the spring. Research done shows and proves that when checkpoints are made public and are frequently done, it reduces injuries as well as death due to alcohol.<br><br> |
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| ==Sampling theorem==
| | Debtors are needed to spend off the income rent out and accrued interest, in the predetermined time. It will be achievable to use soft scrub and a white 3M cleaning pad with out injuring the surface region. Any individual caught eating peanuts in church may possibly be jailed for up to a single year. In the end, a crematory operation should spend a wonderful deal of time searching at the peaks and valleys of fuel costs of any source and determine the volatility of each compared to the value. It is illegal to challenge someone to a duel, or accept a duel, even if it is by no means truly fought. They run the Homebuyer Assistance Plan which provides help in the variety of $2000 which can be utilized as down payment and other expenses. |
| The [[Nyquist–Shannon sampling theorem]] states that perfect reconstruction of a signal is possible when the sampling frequency is greater than twice the maximum frequency of the signal being sampled, or equivalently, when the [[Nyquist frequency]] (half the sample rate) exceeds the highest frequency of the signal being sampled. If lower sampling rates are used, the original signal's information may not be completely recoverable from the sampled signal.<ref>[[Claude E. Shannon|C. E. Shannon]], "Communication in the presence of noise", [[Proc. Institute of Radio Engineers]], vol. 37, no.1, pp. 10–21, Jan. 1949. [http://www.stanford.edu/class/ee104/shannonpaper.pdf Reprint as classic paper in: ''Proc. IEEE'', Vol. 86, No. 2, (Feb 1998)]</ref> For example, if a signal has an upper [[Bandwidth (signal processing)|band limit]] of 100 Hz, a sampling frequency greater than 200 Hz will avoid [[aliasing]] and would theoretically allow perfect reconstruction.
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| The full range of [[human hearing]] is between 20 Hz and 20 kHz.<ref>{{cite web | url = http://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml | title = Frequency Range of Human Hearing | work = The Physics Factbook}}</ref> The minimum sampling rate that satisfies the sampling theorem for this full bandwidth is 40 kHz. The 44.1 kHz sampling rate used for [[Compact Disc]] was chosen for this and other technical reasons.
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| ==Oversampling==
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| {{Main|Oversampling}}
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| In some cases it is desirable to have a sampling frequency more than twice the desired system bandwidth so that a steep [[digital filter]] and a less steep analog [[anti-aliasing filter]] can be used in exchange for a steep analog [[anti-aliasing filter]]. The reason for wanting a less steep analog [[anti-aliasing filter]] is that the digital filter is not subject to any component variations thus always giving the filter response ([[filtering function]]) that the designer has chosen. This process is known as [[oversampling]].<ref>{{cite book|title=Signals, Sound, and Sensation|author=William Morris Hartmann|publisher=Springer|year=1997|isbn=1563962837|url=http://books.google.com/books?id=3N72rIoTHiEC&pg=PA485}}</ref>
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| ==Undersampling==
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| {{Main|Undersampling}}
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| Conversely, one may sample below the Nyquist rate. For a [[baseband]] signal (one that has components from 0 to the band limit), this introduces aliasing, but for a [[passband]] signal (one that does not have low frequency components), there are no low frequency signals for the aliases of high frequency signals to collide with, and thus one can sample a high frequency (but narrow bandwidth) signal at a much lower sample rate than the Nyquist rate.
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| ==Audio==<!--[[Audio sampling rate]] redirects here-->
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| In [[digital audio]] the most common sampling rates are 44.1 kHz, 48 kHz, 88.2 kHz, 96 kHz and 192 kHz.<ref>{{cite book |url=http://books.google.com/books?id=WzYm1hGnCn4C&pg=PT200&lpg=PT200 |pages=200, 446 |last=Self |first=Douglas |title=Audio Engineering Explained |publisher=Taylor & Francis US |year=2012 |isbn=0240812735}}</ref> Lower sampling rates have the benefit of smaller data size and easier storage and transport. Because of the Nyquist–Shannon sampling theorem, sampling rates higher than about 50 kHz to 60 kHz cannot supply more usable information for human listeners. Early [[professional audio]] equipment manufacturers chose sampling rates in the region of 50 kHz for this reason. 88.2 kHz and 96 kHz are often used in modern professional audio equipment, along with 44.1 kHz and 48 kHz. Higher rates such as 192 kHz are prone to ultrasonic artifacts causing audible [[intermodulation distortion]], and inaccurate sampling caused by too much speed.<ref>{{cite journal |url=http://trustmeimascientist.com/2013/02/04/the-science-of-sample-rates-when-higher-is-better-and-when-it-isnt/ |title=The Science of Sample Rates (When Higher Is Better—And When It Isn’t) |last=Colletti |first=Justin |journal=Trust Me I'm A Scientist |date=February 4, 2013 |accessdate=February 6, 2013}}</ref> The [[Audio Engineering Society]] recommends 48 kHz sample rate for most applications but gives recognition to 44.1 kHz for [[Compact Disc]] and other consumer uses, 32 kHz for transmission-related application and 96 kHz for higher bandwidth or relaxed [[anti-aliasing filter]]ing.<ref name=AES5/>
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| A more complete list of common audio sample rates is:
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| {| class="wikitable"
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| ! Sampling rate
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| | 8,000 Hz
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| | [[Telephone]] and encrypted [[walkie-talkie]], [[wireless intercom]]<ref>[http://www.hme.com/proDX200.cfm HME DX200 encrypted wireless intercom]{{dead link|date=January 2011}}</ref><ref>{{cite web|url=http://www.telexradiocom.com/product.php?id=71897XX |title=Telex BTR-1 encrypted wireless intercom |publisher=Telexradiocom.com |accessdate=2011-01-18}}</ref> and [[wireless microphone]]<ref>{{cite web|url=http://www.telex.com/wirelessmicrophones/Product.aspx?MarketID=14&CategoryID=59&ProductID=141 |title=Telex SAFE-1000 wireless microphone |publisher=Telex.com |accessdate=2011-01-18}}</ref> transmission; adequate for human speech but without [[sibilance]]; ''ess'' sounds like ''eff'' ({{IPAslink|s}}, {{IPAslink|f}}).
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| | 11,025 Hz
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| | One quarter the sampling rate of audio CDs; used for lower-quality PCM, MPEG audio and for audio analysis of subwoofer bandpasses.{{Citation needed|date=January 2011}}
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| | 16,000 Hz
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| | [[Wideband]] frequency extension over standard [[telephone]] [[narrowband]] 8,000 Hz. Used in most modern [[VoIP]] and [[VVoIP]] communication products.<ref>http://www.voipsupply.com/cisco-hd-voice{{rs|date=September 2013}}</ref>
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| | 22,050 Hz
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| | One half the sampling rate of audio CDs; used for lower-quality PCM and MPEG audio and for audio analysis of low frequency energy. Suitable for digitizing early 20th century audio formats such as [[78 rpm|78s]].<ref>{{cite web|url=http://www.restoring78s.co.uk/Procedure%20Part%201.htm |title=The restoration procedure - part 1 |publisher=Restoring78s.co.uk |accessdate=2011-01-18|archiveurl=http://web.archive.org/web/20090914133005/http://www.restoring78s.co.uk/Procedure%20Part%201.htm|archivedate=2009-09-14|quote=For most records a sample rate of 22050 in stereo is adequate. An exception is likely to be recordings made in the second half of the century, which may need a sample rate of 44100.}}</ref>
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| | 32,000 Hz
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| | [[miniDV]] digital video [[camcorder]], video tapes with extra channels of audio (e.g. [[DVCAM]] with 4 Channels of audio), [[Digital Audio Tape|DAT]] (LP mode), Germany's [[:de:Digitales Satellitenradio|Digitales Satellitenradio]], [[NICAM]] digital audio, used alongside analogue television sound in some countries. High-quality digital [[wireless microphone]]s.<ref>{{cite web|url=http://www.zaxcom.com/transmitters.htm |title=Zaxcom digital wireless transmitters |publisher=Zaxcom.com |accessdate=2011-01-18}}</ref> Suitable for digitizing [[FM broadcasting|FM radio]].{{Citation needed|date=September 2011}}
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| | 44,056 Hz
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| | Used by digital audio locked to [[NTSC]] ''color'' video signals (245 lines by 3 samples by 59.94 fields per second = 29.97 [[frames per second]]).
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| | [[44,100 Hz]]
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| | [[Compact Disc|Audio CD]], also most commonly used with [[MPEG-1]] audio ([[VCD]], [[SVCD]], [[MP3]]). Originally chosen by [[Sony]] because it could be recorded on modified video equipment running at either 25 frames per second (PAL) or 30 frame/s (using an NTSC ''monochrome'' video recorder) and cover the 20 kHz bandwidth thought necessary to match professional analog recording equipment of the time. A [[PCM adaptor]] would fit digital audio samples into the analog video channel of, for example, [[PAL]] video tapes using 588 lines by 3 samples by 25 frames per second.
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| | 47,250 Hz
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| | world's first commercial [[Pulse-code modulation|PCM]] sound recorder by [[Nippon Columbia]] (Denon)
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| | 48,000 Hz
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| | The standard audio sampling rate used by professional digital video equipment such as tape recorders, video servers, vision mixers and so on. This rate was chosen because it could deliver a 22 kHz frequency response and work with 29.97 frames per second NTSC video - as well as 25 frame/s, 30 frame/s and 24 frame/s systems. With 29.97 frame/s systems it is necessary to handle 1601.6 audio samples per frame delivering an integer number of audio samples only every fifth video frame.<ref name=AES5>{{citation |url=http://www.aes.org/publications/standards/search.cfm?docID=14 |title=AES5-2008: AES recommended practice for professional digital audio - Preferred sampling frequencies for applications employing pulse-code modulation |publisher=Audio Engineering Society |year=2008 |accessdate=2010-01-18}}</ref> Also used for sound with consumer video formats like DV, [[digital TV]], [[DVD]], and films. The professional Serial Digital Interface [[Serial Digital Interface|(SDI)]] and High-definition Serial Digital Interface [[Serial Digital Interface|(HD-SDI)]] used to connect broadcast television equipment together uses this audio sampling frequency. Most professional audio gear uses 48 kHz sampling, including [[mixing console]]s, and [[digital recording]] devices.
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| | 50,000 Hz
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| | First commercial digital audio recorders from the late 70s from [[3M]] and [[Soundstream]].
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| | 50,400 Hz
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| | Sampling rate used by the [[X-80|Mitsubishi X-80]] digital audio recorder.
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| | 88,200 Hz
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| | Sampling rate used by some professional recording equipment when the destination is CD (multiples of 44,100 Hz). Some pro audio gear uses (or is able to select) 88.2 kHz sampling, including mixers, EQs, compressors, reverb, crossovers and recording devices.
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| | 96,000 Hz
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| | [[DVD-Audio]], some [[LPCM]] DVD tracks, [[BD-ROM]] (Blu-ray Disc) audio tracks, [[HD DVD]] (High-Definition DVD) audio tracks. Some professional recording and production gear is able to select 96 kHz sampling. This sampling frequency is twice the 48 kHz standard commonly used with audio on professional equipment.
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| | 176,400 Hz
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| | Sampling rate used by [[HDCD]] recorders and other professional applications for CD production.
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| | 192,000 Hz
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| | [[DVD-Audio]], some [[LPCM]] DVD tracks, [[BD-ROM]] (Blu-ray Disc) audio tracks, and [[HD DVD]] (High-Definition DVD) audio tracks, High-Definition audio recording devices and audio editing software. This sampling frequency is four times the 48 kHz standard commonly used with audio on professional video equipment.
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| | 352,800 Hz
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| | [[Digital eXtreme Definition]], used for recording and editing [[Super Audio CD]]s, as 1-bit DSD is not suited for editing. Eight times the frequency of 44.1 kHz.
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| | 2,822,400 Hz
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| | [[Super Audio CD|SACD]], 1-bit [[delta-sigma modulation]] process known as [[Direct Stream Digital]], co-developed by [[Sony]] and [[Philips]].
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| | 5,644,800 Hz
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| | Double-Rate DSD, 1-bit [[Direct Stream Digital]] at 2x the rate of the SACD. Used in some professional DSD recorders.
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| ==Video systems==
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| {{Refimprove section|date=June 2007}}
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| In [[digital video]], the temporal sampling rate is defined the [[frame rate]] – or rather the [[field rate]] – rather than the notional [[pixel clock]]. The image sampling frequency is the repetition rate of the sensor integration period. Since the integration period may be significantly shorter than the time between repetitions, the sampling frequency can be different from the inverse of the sample time:
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| * 50 Hz – [[PAL]] video
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| * 60 / 1.001 Hz ~= 59.94 Hz – [[NTSC]] video
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| Video [[digital-to-analog converter]]s operate in the megahertz range (from ~3 MHz for low quality composite video scalers in early games consoles, to 250 MHz or more for the highest-resolution VGA output).
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| When analog video is converted to [[digital video]], a different sampling process occurs, this time at the pixel frequency, corresponding to a spatial sampling rate along [[scan line]]s. A common [[pixel]] sampling rate is:
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| * 13.5 MHz – [[CCIR 601]], [[D1 video]]
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| Spatial sampling in the other direction is determined by the spacing of scan lines in the [[raster graphics|raster]]. The sampling rates and resolutions in both spatial directions can be measured in units of lines per picture height.
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| Spatial [[aliasing]] of high-frequency [[luma (video)|luma]] or [[chrominance|chroma]] video components shows up as a [[moiré pattern]].
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| ==See also==
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| * [[Bit rate]]
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| * [[Digital control]]
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| * [[Normalized frequency (digital signal processing)|Normalized frequency]]
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| * [[Sample and hold]]
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| * [[Sample rate conversion]]
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| * [[Signal (electronics)]]
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| * [[Sampling (signal processing)|Sampling]]
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| ==References==
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| {{Reflist}}
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| {{DSP}}
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| {{DEFAULTSORT:Sampling Rate}}
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| [[Category:Digital signal processing]]
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| [[Category:Signal processing]]
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| {{Link FA|es}}
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NFL- Tennessee Titans Beat The Houston Texans 20-17
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