A Highly Robust Audio Fingerprinting System
`
`A Highly Robust Audio Fingerprinting System
`Ton Kalker
`Jaap Haitsma
`Philips Research
`Philips Research
`Prof. Holstlaan 4, 5616 BA,
`Prof. Holstlaan 4, 5616 BA,
`Eindhoven, The Netherlands
`Eindhoven, The Netherlands
`++31-40-2742648
`++31-40-2743839
`Jaap.Haitsma@philips.com
`Ton.Kalker@ieee.org
`
`ABSTRACT
`Imagine the following situation. You’re in your car, listening to
`the radio and suddenly you hear a song that catches your attention.
`It’s the best new song you have heard for a long time, but you
`missed the announcement and don’t recognize the artist. Still, you
`would like to know more about this music. What should you do?
`You could call the radio station, but that’s too cumbersome.
`Wouldn’t it be nice if you could push a few buttons on your
`mobile phone and a few seconds later the phone would respond
`with the name of the artist and the title of the music you’re
`listening to? Perhaps even sending an email to your default email
`address with some supplemental information. In this paper we
`present an audio fingerprinting system, which makes the above
`scenario possible. By using the fingerprint of an unknown audio
`clip as a query on a fingerprint database, which contains the
`fingerprints of a large library of songs, the audio clip can be
`identified. At the core of the presented system are a highly robust
`fingerprint extraction method and a very efficient fingerprint
`search strategy, which enables searching a large fingerprint
`database with only limited computing resources.
`1. INTRODUCTION
`Fingerprint systems are over one hundred years old. In 1893 Sir
`Francis Galton was the first to “prove” that no two fingerprints of
`human beings were alike. Approximately 10 years later Scotland
`Yard accepted a system designed by Sir Edward Henry for
`identifying fingerprints of people. This system relies on the pattern
`of dermal ridges on the fingertips and still forms the basis of all
`“human” fingerprinting techniques of today. This type of forensic
`“human” fingerprinting system has however existed for longer
`than a century, as 2000 years ago Chinese emperors were already
`using thumbprints to sign important documents. The implication is
`that already those emperors (or at least their administrative
`servants) realized that every fingerprint was unique. Conceptually
`a fingerprint can be seen as a “human” summary or signature that
`is unique for every human being. It is important to note that a
`human fingerprint differs from a textual summary in that it does
`not allow the reconstruction of other aspects of the original. For
`example, a human fingerprint does not convey any information
`about the color of the person’s hair or eyes.
`Recent years have seen a growing scientific and industrial interest
`in computing fingerprints of multimedia objects [1][2][3][4]
`[5][6]. The growing industrial interest is shown among others by a
`large number of (startup) companies [7][8][9][10][11][12][13]
`and the recent request for information on audio fingerprinting
`technologies by the International Federation of the Phonographic
`Industry (IFPI) and the Recording Industry Association of
`America (RIAA) [14].
`
`Permission to make digital or hard copies of all or part of this
`work for personal or classroom use is granted without fee
`provided that copies are not made or distributed for profit or
`commercial advantage and that copies bear this notice and the
`full citation on the first page.
`© 2002 IRCAM – Centre Pompidou
`
`3.
`
`2.
`
`The prime objective of multimedia fingerprinting is an efficient
`mechanism to establish the perceptual equality of two multimedia
`objects: not by comparing the (typically large) objects themselves,
`but by comparing the associated fingerprints (small by design). In
`most systems using fingerprinting technology, the fingerprints of a
`large number of multimedia objects, along with their associated
`meta-data (e.g. name of artist, title and album) are stored in a
`database. The fingerprints serve as an index to the meta-data. The
`meta-data of unidentified multimedia content are then retrieved by
`computing a fingerprint and using this as a query in the
`fingerprint/meta-data database. The
`advantage of using
`fingerprints instead of the multimedia content itself is three-fold:
`1. Reduced memory/storage requirements as fingerprints
`are relatively small;
`Efficient comparison as perceptual irrelevancies have
`already been removed from fingerprints;
`Efficient searching as the dataset to be searched is
`smaller.
`As can be concluded from above, a fingerprint system generally
`consists of two components: a method to extract fingerprints and a
`method to efficiently search for matching fingerprints in a
`fingerprint database.
`This paper describes an audio fingerprinting system that is suitable
`for a large number of applications. After defining the concept of
`an audio fingerprint in Section 2 and elaborating on possible
`applications in Section 3, we focus on the technical aspects of the
`proposed audio fingerprinting system. Fingerprint extraction is
`described in Section 4 and fingerprint searching in Section 5.
`2. AUDIO FINGERPRINTING CONCEPTS
`2.1 Audio Fingerprint Definition
`Recall that an audio fingerprint can be seen as a short summary of
`an audio object. Therefore a fingerprint function F should map an
`audio object X, consisting of a large number of bits, to a
`fingerprint of only a limited number of bits.
`Here we can draw an analogy with so-called hash functions1,
`which are well known in cryptography. A cryptographic hash
`function H maps an (usually large) object X to a (usually small)
`hash value (a.k.a. message digest). A cryptographic hash function
`allows comparison of two large objects X and Y, by just
`comparing their respective hash values H(X) and H(Y). Strict
`mathematical equality of the latter pair implies equality of the
`former, with only a very low probability of error. For a properly
`designed cryptographic hash function this probability is 2-n, where
`n equals the number of bits of the hash value. Using cryptographic
`hash functions, an efficient method exists to check whether or not
`a particular data item X is contained in a given and large data set
`Y={Yi}. Instead of storing and comparing with all of the data in Y,
`
`1 In the literature fingerprinting is sometimes also referred to as
`robust or perceptual hashing[5].
`
`0001
`
`EX1029
`Roku V. Media Chain
`U.S. Patent No. 10,489,560
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`

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`A Highly Robust Audio Fingerprinting System
`
`it is sufficient to store the set of hash values {hi = H(Yi)}, and to
`compare H(X) with this set of hash values.
`At first one might think that cryptographic hash functions are a
`good candidate for fingerprint functions. However recall from the
`introduction that, instead of strict mathematical equality, we are
`interested in perceptual similarity. For example, an original CD
`quality version of ‘Rolling Stones – Angie’ and an MP3 version at
`128Kb/s sound the same to the human auditory system, but their
`waveforms can be quite different. Although the two versions are
`perceptually similar they are mathematically quite different.
`Therefore cryptographic hash functions cannot decide upon
`perceptual equality of
`these
`two versions. Even worse,
`cryptographic hash functions are typically bit-sensitive: a single
`bit of difference in the original object results in a completely
`different hash value.
`Another valid question the reader might ask is: “Is it not possible
`to design a fingerprint function that produces mathematically
`equal fingerprints for perceptually similar objects?” The question
`is valid, but the answer is that such a modeling of perceptual
`similarity is fundamentally not possible. To be more precise: it is a
`known fact that perceptual similarity is not transitive. Perceptual
`similarity of a pair of objects X and Y and of another pair of
`objects Y and Z does not necessarily imply the perceptual
`similarity of objects X and Z. However modeling perceptual
`similarity by mathematical equality of fingerprints would lead to
`such a relationship.
`Given the above arguments, we propose to construct a fingerprint
`function in such a way that perceptual similar audio objects result
`in similar fingerprints. Furthermore,
`in order
`to be able
`discriminate between different audio objects, there must be a very
`high probability that dissimilar audio objects result in dissimilar
`fingerprints. More mathematically, for a properly designed
`fingerprint function F, there should be a threshold T such that
`with very high probability ||F(X)-F(Y)||T if objects X and Y are
`similar and ||F(X)-F(Y)||>T when they are dissimilar.
`2.2 Audio Fingerprint System Parameters
`Having a proper definition of an audio fingerprint we now focus
`on the different parameters of an audio fingerprint system. The
`main parameters are:
` Robustness: can an audio clip still be identified after
`severe signal degradation? In order to achieve high
`robustness the fingerprint should be based on perceptual
`features that are invariant (at least to a certain degree)
`with respect to signal degradations. Preferably, severely
`degraded audio still leads to very similar fingerprints.
`The false negative rate is generally used to express the
`robustness. A
`false negative occurs when
`the
`fingerprints of perceptually similar audio clips are too
`different to lead to a positive match.
` Reliability: how often is a song incorrectly identified?
`E.g. “Rolling Stones – Angie” being identified as
`“Beatles – Yesterday”. The rate at which this occurs is
`usually referred to as the false positive rate.
`Fingerprint size: how much storage is needed for a
`fingerprint? To enable fast searching, fingerprints are
`usually stored
`in RAM memory. Therefore
`the
`fingerprint size, usually expressed in bits per second or
`bits per song, determines to a large degree the memory
`resources that are needed for a fingerprint database
`server.
` Granularity: how many seconds of audio is needed to
`identify an audio clip? Granularity is a parameter that
`
`
`
`
`
`can depend on the application. In some applications the
`whole song can be used for identification, in others one
`prefers to identify a song with only a short excerpt of
`audio.
`Search speed and scalability: how long does it take to
`find a fingerprint in a fingerprint database? What if the
`database contains thousands and thousands of songs?
`For the commercial deployment of audio fingerprint
`systems, search speed and scalability are a key
`parameter. Search speed should be in the order of
`milliseconds for a database containing over 100,000
`songs using only limited computing resources (e.g. a
`few high-end PC’s).
`These five basic parameters have a large impact on each other. For
`instance, if one wants a lower granularity, one needs to extract a
`larger fingerprint to obtain the same reliability. This is due to the
`fact that the false positive rate is inversely related to the
`fingerprint size. Another example: search speed generally
`increases when one designs a more robust fingerprint. This is due
`to the fact that a fingerprint search is a proximity search. I.e. a
`similar (or the most similar) fingerprint has to be found. If the
`features are more robust the proximity is smaller. Therefore the
`search speed can increase.
`3. APPLICATIONS
`In this section we elaborate on a number of applications for audio
`fingerprinting.
`3.1 Broadcast Monitoring
`Broadcast monitoring is probably the most well known application
`for audio fingerprinting[2][3][4][5][12][13]. It refers to the
`automatic playlist generation of radio,
`television or web
`broadcasts for, among others, purposes of royalty collection,
`program verification, advertisement verification and people
`metering. Currently broadcast monitoring is still a manual process:
`i.e. organizations interested in playlists, such as performance
`rights organizations, currently have “real” people listening to
`broadcasts and filling out scorecards.
`A large-scale broadcast monitoring system based on fingerprinting
`consists of several monitoring sites and a central site where the
`fingerprint server is located. At the monitoring sites fingerprints
`are extracted from all the (local) broadcast channels. The central
`site
`collects
`the
`fingerprints
`from
`the monitoring sites.
`Subsequently, the fingerprint server, containing a huge fingerprint
`database, produces the playlists of all the broadcast channels.
`3.2 Connected Audio
`Connected audio is a general term for consumer applications
`where music is somehow connected to additional and supporting
`information. The example given in the abstract, using a mobile
`phone to identify a song is one of these examples. This business is
`actually pursued by a number of companies [10][13]. The audio
`signal in this application is severely degraded due to processing
`applied by radio stations, FM/AM transmission, the acoustical
`path between the loudspeaker and the microphone of the mobile
`phone, speech coding and finally the transmission over the mobile
`network. Therefore, from a technical point of view, this is a very
`challenging application.
`Other examples of connected audio are (car) radios with an
`identification button or fingerprint applications “listening” to the
`audio streams leaving or entering a soundcard on a PC. By
`pushing an “info” button in the fingerprint application, the user
`could be directed to a page on the Internet containing information
`about the artist. Or by pushing a “buy” button the user would be
`
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`

`

`A Highly Robust Audio Fingerprinting System
`
`able to buy the album on the Internet. In other words, audio
`fingerprinting can provide a universal linking system for audio
`content.
`3.3 Filtering Technology for File Sharing
`Filtering refers to active intervention in content distribution. The
`prime example for filtering technology for file sharing was
`Napster [15]. Starting in June 1999, users who downloaded the
`Napster client could share and download a large collection of
`music for free. Later, due to a court case by the music industry,
`Napster users were forbidden to download copyrighted songs.
`Therefore in March 2001 Napster installed an audio filter based
`on file names, to block downloads of copyrighted songs. The filter
`was not very effective, because users started to intentionally
`misspell filenames. In May 2001 Napster introduced an audio
`fingerprinting system by Relatable [8], which aimed at filtering
`out copyrighted material even if it was misspelled. Owing to
`Napster’s closure only two months later, the effectiveness of that
`specific fingerprint system is, to the best of the author’s
`knowledge, not publicly known.
`In a legal file sharing service one could apply a more refined
`scheme than just filtering out copyrighted material. One could
`think of a scheme with free music, different kinds of premium
`music (accessible to those with a proper subscription) and
`forbidden music.
`Although from a consumer standpoint, audio filtering could be
`viewed as a negative technology, there are also a number of
`potential benefits to the consumer. Firstly it can organize music
`song titles in search results in a consistent way by using the
`reliable meta-data of
`the
`fingerprint database. Secondly,
`fingerprinting can guarantee that what is downloaded is actually
`what it says it is.
`3.4 Automatic Music Library Organization
`Nowadays many PC users have a music library containing several
`hundred, sometimes even thousands, of songs. The music is
`generally stored in compressed format (usually MP3) on their
`hard-drives. When these songs are obtained from different
`sources, such as ripping from a CD or downloading from file
`sharing networks, these libraries are often not well organized.
`Meta-data is often inconsistent, incomplete and sometimes even
`incorrect. Assuming that the fingerprint database contains correct
`meta-data, audio fingerprinting can make the meta-data of the
`songs in the library consistent, allowing easy organization based
`on, for example, album or artist. For example, ID3Man [16], a
`tool powered by Auditude [7] fingerprinting technology is already
`available for tagging unlabeled or mislabeled MP3 files. A similar
`tool from Moodlogic [11] is available as a Winamp plug-in [17].
`4. AUDIO FINGERPRINT EXTRACTION
`4.1 Guiding Principles
`Audio fingerprints intend to capture the relevant perceptual
`features of audio. At the same time extracting and searching
`fingerprints should be fast and easy, preferably with a small
`granularity to allow usage in highly demanding applications (e.g.
`mobile phone recognition). A few fundamental questions have to
`be addressed before starting the design and implementation of
`such an audio fingerprinting scheme. The most prominent
`question to be addressed is: what kind of features are the most
`suitable. A scan of the existing literature shows that the set of
`relevant features can be broadly divided into two classes: the class
`of semantic features and the class of non-semantic features.
`Typical elements in the former class are genre, beats-per-minute,
`and mood. These types of features usually have a direct
`
`2.
`
`3.
`
`interpretation, and are actually used to classify music, generate
`play-lists and more. The latter class consists of features that have a
`more mathematical nature and are difficult for humans to ‘read’
`directly from music. A
`typical element
`in
`this class
`is
`AudioFlatness that is proposed in MPEG-7 as an audio descriptor
`tool [2]. For the work described in this paper we have for a
`number of reasons explicitly chosen to work with non-semantic
`features:
`1.
`
`Semantic features don’t always have a clear and
`unambiguous meaning. I.e. personal opinions differ over
`such classifications. Moreover, semantics may actually
`change over
`time. For example, music
`that was
`classified as hard rock 25 years ago may be viewed as
`soft listening today. This makes mathematical analysis
`difficult.
`Semantic features are in general more difficult to
`compute than non-semantic features.
`Semantic features are not universally applicable. For
`example, beats-per-minute does not typically apply to
`classical music.
`A second question to be addressed is the representation of
`fingerprints. One obvious candidate is the representation as a
`vector of real numbers, where each component expresses the
`weight of a certain basic perceptual feature. A second option is to
`stay closer in spirit to cryptographic hash functions and represent
`digital fingerprints as bit-strings. For reasons of reduced search
`complexity we have decided in this work for the latter option. The
`first option would imply a similarity measure involving real
`additions/subtractions and depending on the similarity measure
`maybe even real multiplications. Fingerprints that are based on bit
`representations can be compared by simply counting bits. Given
`the expected application scenarios, we do not expect a high
`robustness for each and every bit in such a binary fingerprint.
`Therefore, in contrast to cryptographic hashes that typically have a
`few hundred bits at the most, we will allow fingerprints that have
`a few thousand bits. Fingerprints containing a large number bits
`allow reliable identification even if the percentage of non-
`matching bits is relatively high.
`A final question involves the granularity of fingerprints. In the
`applications that we envisage there is no guarantee that the audio
`files that need to be identified are complete. For example, in
`broadcast monitoring, any interval of 5 seconds is a unit of music
`that has commercial value, and therefore may need to be identified
`and recognized. Also, in security applications such as file filtering
`on a peer-to-peer network, one would not wish that deletion of the
`first few seconds of an audio file would prevent identification. In
`this work we therefore adopt the policy of fingerprints streams by
`assigning sub-fingerprints to sufficiently small atomic intervals
`(referred to as frames). These sub-fingerprints might not be large
`enough to identify the frames themselves, but a longer interval,
`containing sufficiently many frames, will allow robust and reliable
`identification.
`4.2 Extraction Algorithm
`Most fingerprint extraction algorithms are based on the following
`approach. First the audio signal is segmented into frames. For
`every frame a set of features is computed. Preferably the features
`are chosen such that they are invariant (at least to a certain degree)
`to signal degradations. Features that have been proposed are well
`known audio features such as Fourier coefficients [4], Mel
`Frequency Cepstral Coefficients (MFFC) [18], spectral flatness
`[2], sharpness [2], Linear Predictive Coding (LPC) coefficients
`[2] and others. Also derived quantities such as derivatives, means
`and variances of audio features are used. Generally the extracted
`
`0003
`
`

`

`Original
`Original
`
`
`
`MP3@128KbpsMP3@128Kbps
`
`
`
`Bit ErrorsBit Errors
`
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`
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`
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`
`
`
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`Time (Frames)
`Time (Frames)
`
`
`
`256256
`
`
`(a)(a)
`
`(b)(b)
`
`(c)(c)
`Figure 2. (a) Fingerprint block of original music clip,
`(b) fingerprint block of a compressed version, (c) the
`difference between a and b showing the bit errors in
`black (BER=0.078).
`Figure 1, where T is a delay element):
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`Figure 2 shows an example of 256 subsequent 32-bit sub-
`fingerprints (i.e. a fingerprint block), extracted with the above
`scheme from a short excerpt of “O Fortuna” by Carl Orff. A ‘1’
`bit corresponds to a white pixel and a ‘0’ bit to a black pixel.
`Figure 2a and Figure 2b show a fingerprint block from an original
`CD and the MP3 compressed (32Kbps) version of the same
`excerpt, respectively. Ideally these two figures should be identical,
`but due to the compression some of the bits are retrieved
`incorrectly. These bit errors, which are used as the similarity
`measure for our fingerprint scheme, are shown in black in Figure
`2c.
`The computing resources needed for the proposed algorithm are
`limited. Since the algorithm only takes into account frequencies
`below 2kHz the received audio is first down sampled to a mono
`audio stream with a sampling rate of 5kHz. The sub-fingerprints
`are designed such that they are robust against signal degradations.
`Therefore very simple down sample filters can be used without
`introducing any performance degradation. Currently 16 tap FIR
`filters are used. The most computationally demanding operation is
`the Fourier transform of every audio frame. In the down sampled
`audio signal a frame has a length of 2048 samples. If the Fourier
`transform is implemented as a fixed point real-valued FFT the
`fingerprinting algorithm has been shown to run efficiently on
`portable devices such as a PDA or a mobile phone.
`4.3 False Positive Analysis
`Two 3-second audio signals are declared similar if the Hamming
`distance (i.e. the number of bit errors) between the two derived
`fingerprint blocks is below a certain threshold T. This threshold
`value T directly determines the false positive rate Pf, i.e. the rate at
`which audio signals are incorrectly declared equal: the smaller T,
`the smaller the probability Pf will be. On the other hand, a small
`value of T will negatively effect the false negative probability Pn,
`
`A Highly Robust Audio Fingerprinting System
`
`
`
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`
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`
`Figure 1. Overview fingerprint extraction scheme.
`
`features are mapped into a more compact representation by using
`classification algorithms, such as Hidden Markov Models [3], or
`quantization [5]. The compact representation of a single frame
`will be referred to as a sub-fingerprint. The global fingerprint
`procedure converts a stream of audio into a stream of sub-
`fingerprints. One sub-fingerprint usually does not contain
`sufficient data to identify an audio clip. The basic unit that
`contains sufficient data to identify an audio clip (and therefore
`determining the granularity) will be referred to as a fingerprint-
`block.
`The proposed fingerprint extraction scheme is based on this
`general streaming approach. It extracts 32-bit sub-fingerprints for
`every interval of 11.6 milliseconds. A fingerprint block consists of
`256 subsequent sub-fingerprints, corresponding to a granularity of
`only 3 seconds. An overview of the scheme is shown in Figure 1.
`The audio signal is first segmented into overlapping frames. The
`overlapping frames have a length of 0.37 seconds and are
`weighted by a Hanning window with an overlap factor of 31/32.
`This strategy results in the extraction of one sub-fingerprint for
`every 11.6 milliseconds. In the worst-case scenario the frame
`boundaries used during identification are 5.8 milliseconds off with
`respect to the boundaries used in the database of pre-computed
`fingerprints. The large overlap assures that even in this worst-case
`scenario the sub-fingerprints of the audio clip to be identified are
`still very similar to the sub-fingerprints of the same clip in the
`database. Due to the large overlap subsequent sub-fingerprints
`have a large similarity and are slowly varying in time. Figure 2a
`shows an example of an extracted fingerprint block and the slowly
`varying character along the time axis.
`The most important perceptual audio features live in the frequency
`domain. Therefore a spectral representation is computed by
`performing a Fourier transform on every frame. Due to the
`sensitivity of the phase of the Fourier transform to different frame
`boundaries and the fact that the Human Auditory System (HAS) is
`relatively insensitive to phase, only the absolute value of the
`spectrum, i.e. the power spectral density, is retained.
`In order to extract a 32-bit sub-fingerprint value for every frame,
`33 non-overlapping frequency bands are selected. These bands lie
`in the range from 300Hz to 2000Hz (the most relevant spectral
`range for the HAS) and have a logarithmic spacing. The
`logarithmic spacing is chosen, because it is known that the HAS
`operates on approximately logarithmic bands (the so-called Bark
`scale). Experimentally it was verified that the sign of energy
`differences (simultaneously along the time and frequency axes) is
`a property that is very robust to many kinds of processing. If we
`denote the energy of band m of frame n by E(n,m) and the m-th bit
`of the sub-fingerprint of frame n by F(n,m), the bits of the sub-
`fingerprint are formally defined as (see also the gray block in
`
`0004
`
`

`

`Translating the above back to the case of fingerprints bits, a
`correlation factor a between subsequent fingerprint bits implies an
`increase in standard deviation for the BER by a factor
`
`(6)
`
`.
`
`22
`aa
`
`11
`
`To determine the distribution of the BER with real fingerprint
`blocks a fingerprint database of 10,000 songs was generated.
`Thereafter the BER of 100,000 randomly selected pairs of
`fingerprint blocks were determined. The standard deviation of the
`resulting BER distribution was measured
`to be 0.0148,
`approximately 3 times higher than the 0.0055 one would expect
`from random i.i.d. bits.
`Figure 3 shows the log Probability Density Function (PDF) of the
`measured BER distribution and a normal distribution with mean
`of 0.5 and a standard deviation of 0.0148. The PDF of the BER is
`a close approximation to the normal distribution. For BERs below
`0.45 we observe some outliers, due to insufficient statistics. To
`incorporate the larger standard deviation of the BER distribution
`Formula (2) is modified by inclusion of a factor 3.
`α
`)21(
`
`23
`The threshold for the BER used during experiments was  = 0.35.
`This means that out of 8192 bits there must be less than 2867 bits
`in error in order to decide that the fingerprint blocks originate
`from the same song. Using formula (7) we arrive at a very low
`false positive rate of erfc(6.4)/2= 3.6·10-20.
`4.4 Experimental Robustness Results
`In this subsection we show the experimental robustness of the
`proposed audio fingerprinting scheme. That is, we try to answer
`the question of whether or not the BER between the fingerprint
`block of an original and a degraded version of an audio clip
`remains under the threshold α
`We selected four short audio excerpts (Stereo, 44.1kHz, 16bps)
`from songs that belong to different musical genres: “O Fortuna”
`by Carl Orff, “Success has made a failure of our home” by Sinead
`o’Connor, “Say what you want” by Texas and “A whole lot of
`Rosie” by AC/DC. All of the excerpts were subjected to the
`following signal degradations:
` MP3 Encoding/Decoding at 128 Kbps and 32 Kbps.
` Real Media Encoding/Decoding at 20 Kbps.
` GSM Encoding at Full Rate with an error-free channel and
`a channel with a carrier to interference (C/I) ratio of 4dB
`(comparable to GSM reception in a tunnel).
` All-pass Filtering using the system function: H(z)=(0.81z2-
`1.64z+1)/ (z2-1.64z+0.81).
` Amplitude Compression with the following compression
`ratios: 8.94:1 for |A|  -28.6 dB; 1.73:1 for -46.4 dB  |A|  -
`28.6 dB; 1:1.61 for |A|  -46.4 dB.
` Equalization A typical10-band equalizer with the following
`settings:
`8k 16k
`4k
`2k
`1k
`62 125 250 500
`31
`Freq.(Hz)
`-3
`+3
`+3
`-3
`+3
`+3
`-3
`+3
`-3
`-3
`Gain(dB)
` Band-pass Filtering using a second order Butterworth filter
`with cut-off frequencies of 100Hz and 6000Hz.
` Time Scale Modification of +4% and -4% . Only the tempo
`changes, the pitch remains unaffected.
`
`
`
`n
`
`
`
`erfc
`
`21
`
`Pf
`
`
`
`α
`
`
`
`(7)
`
`A Highly Robust Audio Fingerprinting System
`
`
`
`22
`
`
`
`11
`
`
`
`00
`
`
`
`-1-1
`
`
`
`-2-2
`
`
`
`-3-3
`
`log(pdf)
`log(pdf)
`
`
`
`0.440.44
`
`
`
`0.460.46
`
`
`
`0.480.48
`
`
`0.50.5
`
`Bit Error RateBit Error Rate
`Figure 3. Comparison of the probability density function of
`the BER plotted as ‘+’ and the normal distribution.
`
`
`
`0.520.52
`
`
`
`0.540.54
`
`
`
`0.560.56
`
`i.e. the probability that two signals are ‘equal’, but not identified
`as such.
`In order to analyze the choice of this threshold T, we assume that
`the
`fingerprint
`extraction process yields
`random
`i.i.d.
`(independent and identically distributed) bits. The number of bit
`errors will then have a binomial distribution (n,p), where n equals
`the number of bits extracted and p (= 0.5) is the probability that a
`‘0’ or ‘1’ bit is extracted. Since n (= 8192 = 32  256) is large in
`our application, the binomial distribution can be approximated by
`a normal distribution with a mean μ = np and standard deviation
`σ =√(np(1-p)). Given a fingerprint block F1, the probability that a
`randomly selected fingerprint block F2 has less than T = α n errors
`with respect to F1 is given by:
`
`
`
`α
`π
`
`
`α
`21
`n
`
`where α denotes the Bit Error Rate (BER).
`However, in practice the sub-fingerprints have high correlation
`along the time axis. This correlation is due not only to the inherent
`time correlation in audio, but also by the large overlap of the
`frames used in fingerprint extraction. Higher correlation implies a
`larger standard deviation, as shown by the following argument.
`Assume a symmetric binary source with alphabet {-1,1} such that
`the probability that symbol xi and symbol xi+1 are the same is
`equals to q. Then one may easily show that
`E[
`]
`,
`xx
`a
`|k
`|
`
`i
`ki
`where a = 2·q-1. If the source Z is the exclusive-or of two such
`sequences X and Y, then Z is symmetric and
`E[
`]
`.
`zz
`a
`|2 k
`|
`
`i
`ki
`
`(2)
`
`
`
`n
`
`α
`)21(
`
`2
`
`
`
`erfc
`
`21
`
`
`
`x
`
`22
`
`e
`
`dx
`
`
`
`21
`
`P
`f
`
`
`
`(3)
`
`(4)
`NZ over N
`For N large, the standard deviation of the average
`consecutive samples of Z can be approximately described by a
`normal distribution with mean 0 and standard deviation equal to
`1
`a
`
`1(
`N
`
`
`(5)
`
`.
`
`2
`
`)
`
`2 a
`
`0005
`
`

`

`
`
`1010
`
`0123456789
`0123456789
`
`Bit errors per sub-fingerprint ( )
`Bit errors per sub-fingerprint ( )
`
`
`5050
`
`100100
`
`150150
`
`200200
`
`Frame numberFrame number
`Figure 4. Bit errors per sub-fingerprint for the “MP3@
`128Kbps version” of excerpt of ‘O Fortuna’ by Carl Orff.
`
`
`
`250250
`
`Most reliable erroneous bit ( )
`Most reliable erroneous bit ( )
`
`
`
`3030
`
`
`
`2525
`
`
`
`2020
`
`
`
`1515
`
`
`
`1010
`
`
`
`55
`
`
`
`00
`
`
`
`5050
`
`
`
`100100
`
`
`150150
`
`Frame numberFrame number
`
`
`
`200200
`
`
`
`250250
`
`
`
`3030
`
`
`
`2525
`
`
`
`2020
`
`
`
`1515
`
`
`
`1010
`
`
`
`55
`
`
`
`00
`
`Bit errors per sub-fingerprint ( )
`Bit errors per sub-fingerprint ( )
`
`Figure 5. Bit errors per sub-fingerprint (gray line) and the
`reliability of the most reliable erroneous bit (black line) for
`the “M