Computational Models of Music Similarity and their ... - OFAI

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20 2 Audio-based Similarity Measures The power spectrum is transformed to the Mel-scale using a filter bank consisting of triangular filters. Each triangular filter defines the response of one frequency band and is normalized such that the sum of weights for each triangle is the same. In particular, the height of each triangle is 2/d where d is the width of the frequency band. The triangles overlap each other such that the center frequency of one triangle is the starting point for the next triangle, and the end point of the previous triangle (see Figure 2.5). The triangular filters can be computed in Matlab as follows. 10 First, the variables are initialized and memory allocated. 01 num_filt = 36; %% number of Mel frequency bands (2.4) 02 03 f = linspace(0,fs/2,seg_size/2+1); %% frequency bins of P 04 mel = log(1+f/700)*1127.01048; 05 mel_idx = linspace(0,mel(end),num_filt+2); 06 mel_filter = zeros(num_filt,seg_size/2+1); 07 08 f_idx = zeros(num_filt+2,1); 09 for i=1:num_filt+2, 10 [tmp f_idx(i)] = min(abs(mel - mel_idx(i))); 11 end 12 freqs = f(f_idx); 13 14 %% height of triangles 15 h = 2./(freqs(3:num_filt+2)-freqs(1:num_filt)); Second, in the main loop for each triangular filter the weights are computed. 16 for i=1:num_filt, (2.5) 17 mel_filter(i,:) = ... 18 (f > freqs(i) & f freqs(i+1) & f < freqs(i+2)).* ... 21 h(i).*(freqs(i+2)-f)/(freqs(i+2)-freqs(i+1)); 22 end 10 This code is based on Malcolm Slaney’s Auditory Toolbox.
2.2 Techniques 21 Triangular Filter Matrix 1 mel_filter 10 20 30 36 1 128 257 Mel Power Spectrum [dB] 80 10*log10(M(:,i)) 60 40 20 0 1 10 20 30 36 Figure 2.6: Mel filter matrix as computed in Algorithm 2.4 (high values are visualized black), and Mel power spectrum of the audio signal in Figure 2.3. The dimensions of the filter matrix are Mel frequency bands on the y-axis and FFT frequency bins (Hz) on the x-axis. The dimensions of the Mel power spectrum are dB on the y-axis and Mel on the x-axis. In lines 18–21 the variable freqs(i) is the lower bound of the frequency band, freqs(i+1) is the center frequency, and freqs(i+2) is the upper bound. The mel_filter matrix and its effect on the power spectrum is visualized in Figure 2.6. As can be seen, the spectrum is smoothed. Specifically, details in the higher frequencies are lost. The mel_filter is applied by adding the following two lines to Algorithm 2.1 and 2.2. 04b M = zeros(num_filt,num_segments); (2.6) 12b M(:,i) = mel_filter * P(:,i); 2.2.2.3 Decibel Similarly to the non-linear perception of frequency, the human auditory system does not perceive loudness linearly (with respect to the physical properties of the audio signal). In particular, the just noticeable difference in loudness for sounds with a low intensity (Watts/m 2 ) is much smaller than for sounds with a high intensity. A useful approximation of the loudness perception is to use a logarithmic ratio scale known as Decibel (dB). The important part of this scale is the reference to which the ratio is computed. In the examples used in this thesis the reference is 1, and the audio signals are rescaled with respect to this reference as described in Section 1.2. This reference is the threshold of hearing. Decibels values are computed as follows. (First, all values smaller than the reference are set to the reference.) M(M
Page 1: DISSERTATION Computational Models o
Page 5: Abstract This thesis aims at develo
Page 8 and 9: evaluate similarity measures for dr
Page 10 and 11: 2.2.7.3 Always Dissimilar . . . . .
Page 13 and 14: Chapter 1 Introduction This chapter
Page 15 and 16: 1.1 Outline of this Thesis 3 measur
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2.5 Alternative: Web-based Similari
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2.6 Conclusions 91 2.5.3 Limitation
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Chapter 3 Applications This chapter
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3.2 Islands of Music 95 Figure 3.1:
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3.2 Islands of Music 97 they use to
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3.2 Islands of Music 99 a b c d Fig
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3.2 Islands of Music 101 AMBIENT CL
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3.2 Islands of Music 103 Figure 3.6
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3.2 Islands of Music 105 scribing a
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3.3 Fuzzy Hierarchical Organization
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3.4 Dynamic Playlist Generation 125
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3.5 Conclusions 137 + Punk / Bad Re
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Chapter 4 Conclusions In this thesi
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Bibliography [AHH + 03] Eric Allama
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[CKGB02] Pedro Cano, Martin Kaltenb
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[Got03] Masataka Goto, A Chorus-Sec
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[Lüb05] Dominik Lübbers, SoniXplo
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[PFW05b] , Improvements of Audio-Ba
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[SKW05a] Markus Schedl, Peter Knees
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Elias Pampalk I was born in 1978 in
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