Dieudonné determinant: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>TakuyaMurata
en>Quondum
no, it es equal – Undid revision 611526761 by 128.176.12.200 (talk)
 
Line 1: Line 1:
{{No footnotes|date=May 2011}}
Spyderco Gayle Bradley Folder Knife - That is a powerful, but easy folding knife. The rationale it is dear is just because of the material it’s made with. The blade is a hollow-floor satin finished Crucible Steel CPM-M4. For those who’re not sure what that means, it refers to the metal type, m4 may be very powerful against any type of impression – making it one robust knife. The Crucible version of the blade is a process that works alongside the m4 in creating a superfine, metal grain construction making a beyond impressive affect resistance even more impressive. $152.46.<br><br><br><br>Ka-Bar Mule Field Folder Knife - Wow, we merely can't imagine this knife is underneath $50.00. This positively deserves to be thought of one of the best folding knives for the value. You can put this knife up to any check, and it will move your expectations by far. This knife weighs rather less than half of of a pound – which is an [http://Sito-web.org/top-pocket-knives-0 efficient factor] as a result of this knife will last you awhile! The KA-BAR mule knife is perfect for any labor task, and great for being within the wilderness. The opening and closing methodology of this knife will ensure you don’t have any unintended closures in your finger.<br><br>The Blur features the patented SpeedSafe opening and shutting system, as effectively. It isn't a switchblade, however the user can open the knife one-handed. It's not push-button operated , however a torsion bar is pushed with the thumb, releasing the blade, which the consumer can then snap into place with a flick of the wrist. The blade of the Aegis is treated with SOG’s cryogenic heat [http://www.thebestpocketknifereviews.com/ http://Www.thebestpocketknifereviews.com] course of. That is meant to increase toughness, and make the blade more sturdy. During this course of, the blade is frozen cryogenically, then gradually brought up to room temperature. This atomically re-aligns the molecules, producing a hard metallic that can hold its edge.<br><br>Researching knife locks is like wading into shark infested waters carrying a cow carcass. There's so much advertising and marketing and hype and fanboyism that simply taking a look at “locks” yields little information. Being more specific and monitoring traits on the Web from reliable sources and/or multiple sources can yield significantly better information. Breaking the evaluation down like I did could be very helpful for me. It may help you. The first 500 run of Bushcrafters had spines that have been unsharpened (together with the one initially sent for this overview), which made them unsuitable for placing a firesteel. This prompted a bit of controversy in boards like Bushcraft USA<br><br>Everyone knows what a “buck knife” is — it’s develop into a generic term for searching knife. But it surely may not be very apparent to everybody that the Publish Falls, Idaho, brand wasn’t at all times a shorthand term. Nor is it instantly obvious that Buck Knives is just a knife maker. It doesn’t make multitools because multitools make lousy knives — a philosophy that tells you numerous about Buck and the [http://www.myfreeyoga.com/members/profile/350612/JiDiggles fourth technology] of family members who preserve Buck private and need to do so eternally. Right here is an outline of the preferred knife locking mechanisms you'll encounter with today’[http://Mobiletycoon.org/index.php?title=Top_Brand_Pocket_Knives s pocket] knives. Liner Lock (Locking Liner)<br><br>While the Tenacious is just not as simple to deploy as the other folding knives that rely on springs and buttons, it is more reliable because it doesn't rely on a set of moving elements that can erode over time. It also has one of many widest blades on this listing making it perfect for varied uses in the kitchen and the workshop. Of all of the knives on this listing, the Benchmade Mini Griptilian is the greatest folding knife in our opinion. It has the right mix of fine design and a sturdy blade that makes it straightforward to make use of and comfy at the similar time.<br><br>The controversy on that are the perfect survival knives are each ongoing and extremely heated. When trying to find the best survival knives there are just so many selections on the market that it's mind-boggling. I have searched long and hard, read a whole bunch of evaluations and examined survival knives time and again and have provide you with my elite checklist of the best 5 survival knives on the planet. Why 5? The truth is just as every knife is different, every particular person is completely different and what survival knife is the very best for you may not be one of the best for another person.
 
'''Time–frequency analysis for music signals''' is one of the applications of [[time–frequency analysis]]. Musical sound can be more complicated than human vocal sound, occupying a wider band of frequency. Music signals are time-varying signals; while the classic Fourier transform is not sufficient to analyze them, time–frequency analysis is an efficient tool for such use.  Time–frequency analysis is extended from the classic Fourier approach. [[Short-time Fourier transform]] (STFT), [[Gabor transform]] (GT) and [[Wigner distribution function]] (WDF) are famous time–frequency methods, useful for analyzing music signals such as notes played on a piano, a flute or a guitar.
 
==Knowledge about music signal==
 
Music is a type of sound that has some stable frequencies in a time period. Music can be produced by several methods. For example, the sound of a piano is produced by striking [[Strings (music)|strings]], and the sound of a violin is produced by [[Bow (music)|bowing]]. All musical sounds have their [[fundamental frequency]] and overtones. Fundamental frequency is the lowest frequency in harmonic series. In a periodic signal, the fundamental frequency is the inverse of the period length. Overtones are integer multiples of the fundamental frequency.
 
:{| class="wikitable" border="1"
|+Table. 1 the fundamental frequency and overtone
|-
!Frequency
!Order
!
!
|-
|''f'' = 440&nbsp;Hz
|''N'' = 1
|Fundamental frequency
|1st harmonic
|-
|f = 880&nbsp;Hz
|''N'' = 2
|1st overtone
|2nd harmonic
|-
|''f'' = 1320&nbsp;Hz
|''N'' = 3
|2nd overtone
|3rd harmonic
|-
|''f'' = 1760&nbsp;Hz
|''N'' = 4
|3rd overtone
|4th harmonic
|}
 
In [[musical theory]], pitch represents the perceived fundamental frequency of a sound. However the actual fundamental frequency may differ from the perceived fundamental frequency because of overtones.
 
==Short-time Fourier transform==
 
[[File:Chord.jpg|thumb|Fig.1 Waveform of the audio file "Chord.wav"{{where|date=October 2012}}]]
 
[[File:Garbor of Chord.png|thumb|Fig.2 Gabor transform of "Chord.wav"]]
 
[[File:Spectrogram of Chord.jpg|thumb|Fig. 3 Spectrogram of "Chord.wav"]]
 
===Continuous STFT===
 
Short-time Fourier transform is a basic type of time–frequency analysis. If there is a continue signal ''x''(''t''), we can compute the short-time Fourier transform by
:<math> \mathbf{STFT} \left \{ x(t) \right \} \equiv X(t, f) = \int_{-\infty}^{\infty} x(\tau) w(t-\tau) e^{-j 2 \pi f \tau} \, d \tau </math>
where ''w''(''t'') is a [[window function]]. When the ''w''(''t'') is a rectangular function, the transform is called Rec-STFT. When the ''w''(''t'') is a Gaussian function, the transform is called [[Gabor transform]].
 
===Discrete STFT===
 
However, normally the musical signal we have is not a continuous signal. It is sampled in a sampling frequency. Therefore, we can’t use the formula to compute the Rec-short-time Fourier transform. We change the original form to
:<math> X(n \, \Delta t,m \, \Delta f) = \sum_{p=n-Q}^{n+Q} x(p \, \Delta t) e^{-j 2 \pi p m \, \Delta t \, \Delta f} \, \Delta t</math>
Let <math> t = n \, \Delta t </math>, <math>f = m \, \Delta f</math>, <math>\tau = p \, \Delta t </math> and <math> B = Q \, \Delta t</math>. There are some constraints of discrete short-time Fourier transform:
*<math>\Delta t \, \Delta f = \frac{1}{N},</math> where ''N'' is an integer.
*<math>N \ge 2Q+1</math>
*<math>\Delta < \frac{1}{2f_\max}</math> , where <math>f_\max</math> is the highest frequency in the signal.
 
==STFT example==
 
Fig.1 shows the waveform of a piano music audio file with 44100&nbsp;Hz sampling frequency. And Fig.2 shows the result of short-time Fourier transform (we use Gabor transform here) of the audio file. We can see from the time–frequency plot, from ''t''&nbsp;=&nbsp;0 to 0.5 second, there is a chord with three notes, and the chord changed at ''t''&nbsp;=&nbsp;0.5, and then changed again at&nbsp;''t''&nbsp;=&nbsp;1. The fundamental frequency of each note in each chord is show in the time–frequency plot.
 
==Spectrogram==
 
Figure 3 shows the [[spectrogram]] of the audio file shows in Figure 1. Spectrogram is the square of STFT, time-varying spectral representation. The spectrogram of a signal ''s''(''t'') can be estimated by computing the squared [[magnitude (mathematics)|magnitude]] of the STFT of the signal ''s''(''t''), as shown below:
 
: <math> \mathbf {spectrogram} (t,f) = \left| \mathbf{STFT} (t,f) \right|^2 </math>
 
Although the spectrogram is profoundly useful, it still has one drawback. It displays frequencies on a uniform scale. However, musical scales are based on a logarithmic scale for frequencies. Therefore, we should describe the frequency in logarithmic scale related to human hearing.
 
==Wigner distribution function==
 
The [[Wigner distribution function]] can also be used to analyze music signal.  The advantage of Wigner distribution function is the high clarity. However, it needs high calculation and has cross-term problem, so it's more suitable to analyze signal without more than one frequency at the same time.
 
===Formula===
 
The Wigner distribution function <math>W_x(t,f)</math> is:
 
:<math> \mathbf W_x(t,f) = \int_ {-\infty}^\infty x(t+\tau/2)x^*(t-\tau/2) e^{-j2\pi\tau\,f} \,d \tau, </math>
 
where ''x''(''t'') is the signal, and ''x''*(''t'') is the conjugate of the signal.
 
==See also==
 
*[[Musical acoustics]]
*[[Harmonic pitch class profiles]] (HPCP)
 
==Sources==
 
* Joan Serra, Emilia Gomez, Perfecto Herrera, and [[Xavier Serra]], "Chroma Binary Similarity and Local Alignment Applied to Cover Song Identification," August, 2008
* William J. Pielemeier, Gregory H. Wakefield, and Mary H. Simoni, "Time–frequency Analysis of Musical Signals," September,1996
* Jeremy F. Alm and James S. Walker, "Time–Frequency Analysis of Musical Instruments," 2002
* Monika Dorfler, "What Time–Frequency Analysis Can Do To Music Signals," April,2004
* EnShuo Tsau, Namgook Cho and C.-C. Jay Kuo, "Fundamental Frequency Estimation For Music Signals with Modified [[Hilbert–Huang transform]]" IEEE International Conference on Multimedia and Expo, 2009.
 
{{DEFAULTSORT:Time-frequency analysis for music signals}}
[[Category:Musical analysis]]
[[Category:Time–frequency analysis|Musical signal]]

Latest revision as of 21:59, 4 June 2014

Spyderco Gayle Bradley Folder Knife - That is a powerful, but easy folding knife. The rationale it is dear is just because of the material it’s made with. The blade is a hollow-floor satin finished Crucible Steel CPM-M4. For those who’re not sure what that means, it refers to the metal type, m4 may be very powerful against any type of impression – making it one robust knife. The Crucible version of the blade is a process that works alongside the m4 in creating a superfine, metal grain construction making a beyond impressive affect resistance even more impressive. $152.46.



Ka-Bar Mule Field Folder Knife - Wow, we merely can't imagine this knife is underneath $50.00. This positively deserves to be thought of one of the best folding knives for the value. You can put this knife up to any check, and it will move your expectations by far. This knife weighs rather less than half of of a pound – which is an efficient factor as a result of this knife will last you awhile! The KA-BAR mule knife is perfect for any labor task, and great for being within the wilderness. The opening and closing methodology of this knife will ensure you don’t have any unintended closures in your finger.

The Blur features the patented SpeedSafe opening and shutting system, as effectively. It isn't a switchblade, however the user can open the knife one-handed. It's not push-button operated , however a torsion bar is pushed with the thumb, releasing the blade, which the consumer can then snap into place with a flick of the wrist. The blade of the Aegis is treated with SOG’s cryogenic heat http://Www.thebestpocketknifereviews.com course of. That is meant to increase toughness, and make the blade more sturdy. During this course of, the blade is frozen cryogenically, then gradually brought up to room temperature. This atomically re-aligns the molecules, producing a hard metallic that can hold its edge.

Researching knife locks is like wading into shark infested waters carrying a cow carcass. There's so much advertising and marketing and hype and fanboyism that simply taking a look at “locks” yields little information. Being more specific and monitoring traits on the Web from reliable sources and/or multiple sources can yield significantly better information. Breaking the evaluation down like I did could be very helpful for me. It may help you. The first 500 run of Bushcrafters had spines that have been unsharpened (together with the one initially sent for this overview), which made them unsuitable for placing a firesteel. This prompted a bit of controversy in boards like Bushcraft USA

Everyone knows what a “buck knife” is — it’s develop into a generic term for searching knife. But it surely may not be very apparent to everybody that the Publish Falls, Idaho, brand wasn’t at all times a shorthand term. Nor is it instantly obvious that Buck Knives is just a knife maker. It doesn’t make multitools because multitools make lousy knives — a philosophy that tells you numerous about Buck and the fourth technology of family members who preserve Buck private and need to do so eternally. Right here is an outline of the preferred knife locking mechanisms you'll encounter with today’s pocket knives. Liner Lock (Locking Liner)

While the Tenacious is just not as simple to deploy as the other folding knives that rely on springs and buttons, it is more reliable because it doesn't rely on a set of moving elements that can erode over time. It also has one of many widest blades on this listing making it perfect for varied uses in the kitchen and the workshop. Of all of the knives on this listing, the Benchmade Mini Griptilian is the greatest folding knife in our opinion. It has the right mix of fine design and a sturdy blade that makes it straightforward to make use of and comfy at the similar time.

The controversy on that are the perfect survival knives are each ongoing and extremely heated. When trying to find the best survival knives there are just so many selections on the market that it's mind-boggling. I have searched long and hard, read a whole bunch of evaluations and examined survival knives time and again and have provide you with my elite checklist of the best 5 survival knives on the planet. Why 5? The truth is just as every knife is different, every particular person is completely different and what survival knife is the very best for you may not be one of the best for another person.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Dieudonné_determinant&oldid=267795"