<< Chapter < Page Chapter >> Page >

Preparation

Before filtering, we take the lists of spectral peaks that is the output of the landmarks generator algorithm and generate matrices that are the same size as the spectrograms, with the peaks replaced by 1’s in their respective positions and all other points replaced by 0’s. At some point during our project we had the idea of convolving this matrix with a Gaussian curve, in order to allow peaks to match somewhat if they were shifted only slightly. However, we later determined that even a very small Gaussian would worsen our noise resistance, so this idea was dropped. So basically now we have one map for each song that shows the position in time and frequency bins of all peaks. Next we normalize these matrices using their Frobenius norm. This ensures that the final score is normalized. Then we apply the matched filter which basically consists of flipping one of the matrices and convolving them, which is done by zero padding them both to the proper size and multiplying their 2D FFT’s, for speed. The result is a cross correlation matrix, but we still need to extract a single number from it to be our match score.

Extracting information from the cross correlation matrix

Through much testing, we determined that the most accurate and noise-resistant measure of the match was simply taking the global maximum of the result. Other approaches that we tried, such as taking the trace of the X T X or the sum of the global maxima for each row or column, had much more frequent mismatches. Taking just the global maximum of the whole matrix was simple and extremely effective.

When looking at test results, however, we saw that the score still had a certain dependency on the size of the segments being compared. Through more testing, we determined that this dependency looked approximately like a dependency on the square root of the ratio of the lower number of peaks by the higher number of peaks, when testing with a noiseless fragment of a larger song. This can be seen in this plot:

A plot showing the score of a song fragment that should perfectly match the song it was taken from, seen without correcting the square root dependency mentioned above

In the plot above, the original segment has 6915 peaks and the fragment was tested with between 100 and 5000 peaks, in intervals of 100. Since smaller sample sizes usually lead to having fewer peaks, we had to get rid of this dependency. To prevent the square root growth of the scores, the final score is multiplied by the inverse of this square root, yielding a match score that is approximately independent of sample size. This can be seen in the next stem plot, made with the same segments as the first:

The same plot shown before, but with the square root dependency on number of peaks removed

So clearly this allows us to get better match scores with small song segments. After this process, we had a score that was approximately independent of segment size, normalized and could tell apart matches and mismatches, even with lots of noise. All that was left was to test it against different sets of data and set a threshold for distinguishing between matches and non-matches.

Setting a threshold

The filter’s behavior proved to be very consistent. Perfect matches (trying to match a segment with itself) always got scores of 1. Matching noiseless segments to the whole song usually yielded scores in the upper .8’s or in the .9’s, with a few rare exceptions that could have been caused by a bad choice of segment, such as a segment with a long period of silence, for example. Noisy segments usually gave us low scores such as in the .1’s, but more importantly mismatches were even lower, in the .05’s to .07’s or so. This allowed us to set a threshold for determining when we have a match or not.

During our testing, we considered using a statistical approach to set the threshold. For example, if we wanted a 95% certainty that a song matched, we could require the highest match score to be greater than 1.66*[σ/sqrt(n)] + µ, where σ is the standard deviation, n is the sample size and µ is the mean. However, with our very small sample size, this threshold seemed to yield inaccurate results, so the simple threshold criterion of the highest match having to be at least 1.5 times the second highest in order to be considered a match was used.

Similarities and differences from shazam’s approach

Even though we followed the ideas in the paper by Wang, we still had some significant differences from the approach used by Shazam. We followed the ideas they had for fingerprint creation, to a certain extent, however the company uses hash tables instead of matched filters to perform the comparison. While evidently faster than using a matched filter, hash tables are not covered in ELEC 301. Furthermore, when making a hash, Wang says they combine several points in an area with an anchor point and pair them up combinatorially. This allows the identification of a time offset to be used with the hash tables and makes the algorithm even faster and more robust. Perhaps investigating this would be an interesting extension of the project, if we had more time.

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Digital song analysis using frequency analysis. OpenStax CNX. Dec 19, 2009 Download for free at http://cnx.org/content/col11148/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital song analysis using frequency analysis' conversation and receive update notifications?

Ask