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It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br><br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you loved this report and you would like to get additional information about [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC] kindly check out our own web site.
The '''equivalent rectangular bandwidth''' or '''ERB''' is a measure used in [[psychoacoustics]], which gives an approximation to the bandwidths of the filters in [[human hearing]], using the unrealistic but convenient simplification of modeling the filters as rectangular [[band-pass filter]]s.
 
== Approximations ==
 
For moderate sound levels and young listeners, the bandwidth of human auditory filters can be approximated by the [[polynomial]] equation:
 
{{NumBlk|:|<math>
\mathrm{ERB}(f) = 6.23 \cdot f^2 + 93.39 \cdot f + 28.52
</math> <ref name=mooreglasberg/>|{{EquationRef|1|Eq.1}}}}
 
where ''f'' is the center frequency of the filter in kHz and ERB(''f'') is the bandwidth of the filter in Hz. The approximation is based on the results of a number of published [[simultaneous masking]] experiments and is valid from 0.1 to 6.5&nbsp;kHz.<ref name=mooreglasberg>B.C.J. Moore and B.R. Glasberg, "Suggested formulae for calculating auditory-filter bandwidths and excitation patterns" Journal of the Acoustical Society of America 74: 750-753, 1983.</ref>
 
The above approximation was given in 1983 by Moore and Glasberg,<ref name=mooreglasberg/> who in 1990 published another approximation:<ref name=glasbergmoore>B.R. Glasberg and B.C.J. Moore, "Derivation of auditory filter shapes from notched-noise data", Hearing Research, Vol. 47, Issues 1-2, p. 103-138, 1990.</ref>
 
{{NumBlk|:|<math>
\mathrm{ERB}(f) = 24.7 \cdot (4.37 \cdot f + 1)
</math> <ref name=glasbergmoore/>|{{EquationRef|2|Eq.2}}}}
 
where ''f'' is in kHz and ERB(''f'') is in Hz. The approximation is applicable at moderate sound levels and for values of ''f'' between 0.1 and 10&nbsp;kHz.<ref name=glasbergmoore/>
 
== ERB-rate scale==
The '''ERB-rate scale''', or simply '''ERB scale''', can be defined as a function ERBS(''f'') which returns the number of equivalent rectangular bandwidths below the given frequency ''f''. It can be constructed by solving the following [[differential equation|differential]] system of equations:
 
:<math>
\begin{cases}
\mathrm{ERBS}(0) = 0\\
\frac{df}{d\mathrm{ERBS}(f)} = \mathrm{ERB}(f)\\
\end{cases}
</math>
 
The solution for ERBS(''f'') is the integral of the reciprocal of ERB(''f'') with the [[constant of integration]] set in such a way that ERBS(0) = 0.<ref name=mooreglasberg/>
 
Using the second order polynomial approximation ({{EquationNote|Eq.1}}) for ERB(''f'') yields:
 
:<math>
\mathrm{ERBS}(f) = 11.17 \cdot \ln\left(\frac{f+0.312}{f+14.675}\right) + 43.0
</math> <ref name=mooreglasberg/>
 
where ''f'' is in kHz. The VOICEBOX speech processing toolbox for [[MATLAB]] implements the conversion and its [[Inverse function|inverse]] as:
 
:<math>
\mathrm{ERBS}(f) = 11.17268 \cdot \ln\left(1 + \frac{46.06538 \cdot f}{f + 14678.49}\right)
</math> <ref>{{cite web |url=http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/doc/voicebox/frq2erb.html |title=frq2erb |last1=Brookes |first1=Mike |date=22 December 2012  |work=VOICEBOX: Speech Processing Toolbox for MATLAB |publisher=Department of Electrical & Electronic Engineering, Imperial College, UK |accessdate=20 January 2013}}</ref>
:<math>
f = \frac{676170.4}{47.06538 - e^{0.08950404 \cdot \mathrm{ERBS}(f)}} - 14678.49
</math> <ref>{{cite web |url=http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/doc/voicebox/erb2frq.html |title=erb2frq |last1=Brookes |first1=Mike |date=22 December 2012  |work=VOICEBOX: Speech Processing Toolbox for MATLAB |publisher=Department of Electrical & Electronic Engineering, Imperial College, UK |accessdate=20 January 2013}}</ref>
 
where ''f'' is in Hz.
 
Using the linear approximation ({{EquationNote|Eq.2}}) for ERB(''f'') yields:
 
:<math>
\mathrm{ERBS}(f) = 21.4 \cdot log_{10}(1 + 0.00437 \cdot f)
</math> <ref name=josabel99>{{cite web |url=https://ccrma.stanford.edu/~jos/bbt/Equivalent_Rectangular_Bandwidth.html |title=Equivalent Rectangular Bandwidth |last1=Smith |first1=Julius O. |last2=Abel |first2=Jonathan S. |date=10 May 2007 |work=Bark and ERB Bilinear Transforms |publisher=Center for Computer Research in Music and Acoustics (CCRMA), Stanford University, USA |accessdate=20 January 2013}}</ref>
 
where ''f'' is in Hz.
 
==See also==
 
* [[Critical bands]]
* [[Bark scale]]
 
==References==
 
{{Reflist}}
 
== External links ==
* http://www2.ling.su.se/staff/hartmut/bark.htm
 
[[Category:Acoustics]]
[[Category:Hearing]]
[[Category:Signal processing]]

Revision as of 03:49, 21 January 2014

The equivalent rectangular bandwidth or ERB is a measure used in psychoacoustics, which gives an approximation to the bandwidths of the filters in human hearing, using the unrealistic but convenient simplification of modeling the filters as rectangular band-pass filters.

Approximations

For moderate sound levels and young listeners, the bandwidth of human auditory filters can be approximated by the polynomial equation:

Template:NumBlk

where f is the center frequency of the filter in kHz and ERB(f) is the bandwidth of the filter in Hz. The approximation is based on the results of a number of published simultaneous masking experiments and is valid from 0.1 to 6.5 kHz.[1]

The above approximation was given in 1983 by Moore and Glasberg,[1] who in 1990 published another approximation:[2]

Template:NumBlk

where f is in kHz and ERB(f) is in Hz. The approximation is applicable at moderate sound levels and for values of f between 0.1 and 10 kHz.[2]

ERB-rate scale

The ERB-rate scale, or simply ERB scale, can be defined as a function ERBS(f) which returns the number of equivalent rectangular bandwidths below the given frequency f. It can be constructed by solving the following differential system of equations:

The solution for ERBS(f) is the integral of the reciprocal of ERB(f) with the constant of integration set in such a way that ERBS(0) = 0.[1]

Using the second order polynomial approximation (Template:EquationNote) for ERB(f) yields:

[1]

where f is in kHz. The VOICEBOX speech processing toolbox for MATLAB implements the conversion and its inverse as:

[3]
[4]

where f is in Hz.

Using the linear approximation (Template:EquationNote) for ERB(f) yields:

[5]

where f is in Hz.

See also

References

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External links

  1. ↑ 1.0 1.1 1.2 1.3 B.C.J. Moore and B.R. Glasberg, "Suggested formulae for calculating auditory-filter bandwidths and excitation patterns" Journal of the Acoustical Society of America 74: 750-753, 1983.
  2. ↑ 2.0 2.1 B.R. Glasberg and B.C.J. Moore, "Derivation of auditory filter shapes from notched-noise data", Hearing Research, Vol. 47, Issues 1-2, p. 103-138, 1990.
  3. ↑ Template:Cite web
  4. ↑ Template:Cite web
  5. ↑ Template:Cite web
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