juan pablo bello el9173 selected topics in signal ...juan pablo bello el9173 selected topics in...
TRANSCRIPT
![Page 1: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/1.jpg)
Periodicity detection
Juan Pablo BelloEL9173 Selected Topics in Signal Processing: Audio Content AnalysisNYU Poly
![Page 2: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/2.jpg)
Periodicity detection
• Formally, a periodic signal is defined as:
• Detect the fundamental period/frequency (and phase)
x(t) = x(t+ T0), 8t
![Page 3: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/3.jpg)
Applications
• At short (pitch) and long (rhythm) time scales:
• pitch-synchronous analysis• voice/sound identification• prosodic analysis• bioacoustics• melodic analysis• note transcription• beat tracking, segmentation
![Page 4: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/4.jpg)
Difficulties
• Quasi-periodicities, temporal variations
• Multiple periodicities associated with f0
• transients and noise
• Polyphonies: information overlap
![Page 5: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/5.jpg)
Difficulties
• Quasi-periodicities, temporal variations
• Multiple periodicities associated with f0
• transients and noise
• Polyphonies: information overlap
![Page 6: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/6.jpg)
Difficulties
• Quasi-periodicities, temporal variations
• Multiple periodicities associated with f0
• transients and noise
• Polyphonies: information overlap
![Page 7: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/7.jpg)
Difficulties
• Quasi-periodicities, temporal variations
• Multiple periodicities associated with f0
• transients and noise
• Polyphonies: information overlap
![Page 8: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/8.jpg)
Difficulties
• Quasi-periodicities, temporal variations
• Multiple periodicities associated with f0
• transients and noise
• Polyphonies: information overlap
![Page 9: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/9.jpg)
Overlap
![Page 10: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/10.jpg)
Architecture
Audio
time
f0 smoo
thing
Break into blocks
Detection function + peak-picking
Integration over time
![Page 11: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/11.jpg)
Overview of Methods
• DFT
• Autocorrelation
• Spectral Pattern Matching
• Cepstrum
• Spectral Autocorrelation
• YIN
• Auditory model
![Page 12: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/12.jpg)
DFTT0
f0
![Page 13: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/13.jpg)
DFTT0
f0
![Page 14: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/14.jpg)
DFTT0
f0
![Page 15: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/15.jpg)
DFTT0
f0
![Page 16: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/16.jpg)
• Cross-product measures similarity across time
• Cross-correlation of two real-valued signals x and y:
• Unbiased (short-term) Autocorrelation Function (ACF):
Autocorrelation
r
xy
(l) =1
N
N�1X
n=0
x(n)y(n+ l)
l = 0, 1, 2, · · · , N � 1
modulo N
r
x
(l) =1
N � l
N�1�lX
n=0
x(n)x(n+ l)
l = 0, 1, 2, · · · , L� 1
![Page 17: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/17.jpg)
Autocorrelation
![Page 18: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/18.jpg)
Autocorrelation
• The short-term ACF can also be computed as:
r
x
(l) =
⇣1
N�l
⌘real(IFFT (|X|2))
X ! FFT (x)
x zero-padded to next power of 2
after (N + L)� 1
![Page 19: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/19.jpg)
Autocorrelation
• This is equivalent to the following correlation:
r
x
(l) =1
K � l
K�1X
k=0
cos(2⇡lk/K)|X(k)|2
![Page 20: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/20.jpg)
Pattern Matching
• Comb filtering is a common strategy
• Any other template that realistically fits the magnitude spectrum
• Templates can be specific to sound sources
• Matching strategies vary: correlation, likelihood, distance, etc.
![Page 21: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/21.jpg)
Pattern Matching
![Page 22: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/22.jpg)
• Treat the log magnitude spectrum as if it were a signal -> take its (I)DFT
• Measures rate of change across frequency bands (Bogert et al., 1963)
• Cepstrum -> Anagram of Spectrum (same for quefrency, liftering, etc)
• For a real-valued signal is defined as:
Cepstrum
c
x
(l) = real(IFFT (log(|FFT (x)|)))
![Page 23: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/23.jpg)
Cepstrum
![Page 24: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/24.jpg)
Spectral ACF
• Spectral location -> sensitive to quasi-periodicities
• (Quasi-)Periodic Spectrum, Spectral ACF.
• Exploits intervalic information (more stable than locations of partials), while adding shift-invariance.
rX(lf ) =1
N � lf
N�1�lfX
k=0
|X(k)||X(k + lf )|
lf = 0, 1, 2, · · · , L� 1
![Page 25: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/25.jpg)
Spectral ACF
![Page 26: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/26.jpg)
YIN
• Alternative to the ACF that uses the squared difference function (deCheveigne, 02):
• For (quasi-)periodic signals, this functions cancel itself at l = 0, l0 and its multiples. Zero-lag bias is avoided by normalizing as:
d(l) =N�1�lX
n=0
(x(n)� x(n+ l))2
ˆd(l) =
⇢1 l = 0
d(l)/[(1/l)Pl
u=1 d(u)] otherwise
![Page 27: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/27.jpg)
YIN
![Page 28: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/28.jpg)
Auditory model
Auditory filterbank
Inner hair-cell model
Periodicity
Summarization
Inner hair-cell model
Periodicity
x(n)
xc(n)
zc(n)
rc(n)
Summary periodicity function
![Page 29: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/29.jpg)
Auditory model
• Auditory filterbank: gammatone filters (Slaney, 93; Klapuri, 06):
![Page 30: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/30.jpg)
Auditory model
The Equivalent Rectangular Bandwidths (ERB)
of the filters:
bc
= 0.108fc
+ 24.7
fc
= 229⇥�10
/21.4 � 1
�
= min
: ( max
� min
)/F : max
min/max
= 21.4⇥ log10(0.00437fmin/max
+ 1)
F = number of filters.
![Page 31: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/31.jpg)
Auditory model
• Beating: interference between sounds of frequencies f1 and f2
• Fluctuation of amplitude envelope of frequency |f2 - f1|
• The magnitude of the beating is determined by the smaller of the two amplitudes
![Page 32: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/32.jpg)
• Inner hair-cell (IHC) model:
Auditory model
![Page 33: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/33.jpg)
Auditory model
• Sub-band periodicity analysis using ACF
• Summing across channels (Summary ACF)
• Weighting of the channels changes the topology of the SACF
![Page 34: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/34.jpg)
Auditory model
![Page 35: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/35.jpg)
Comparing detection functions
![Page 36: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/36.jpg)
Comparing detection functions
![Page 37: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/37.jpg)
Comparing detection functions
![Page 38: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/38.jpg)
Comparing detection functions
![Page 39: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/39.jpg)
Tempo
• Tempo refers to the pace of a piece of music and is usually given in beats per minutes (BPM).
• Global quality vs time-varying local characteristic.
• Thus, in computational terms we differentiate between tempo estimation and tempo (beat) tracking.
• In tracking, beats are described by both their rate and phase.
• Vast literature: see, e.g. Hainsworth, 06; or Goto, 06 for reviews.
![Page 40: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/40.jpg)
• Novelty function (NF): remove local mean + half-wave rectify
• Periodicity: dot multiply ACF of NF with a weighted comb filterbank
•
Tempo estimation and tracking (Davies, 05)
Rw(l) = (l/b2)e�l2
2b2
*From Davies and Plumbley, ICASSP 2005
![Page 41: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/41.jpg)
Tempo estimation and tracking (Davies, 05)
• Choose lag that maximizes the ACF
![Page 42: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/42.jpg)
Tempo estimation and tracking (Davies, 05)
• Choose filter that maximizes the dot product
![Page 43: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/43.jpg)
Tempo estimation and tracking (Davies, 05)
• Phase: dot multiply DF with shifted versions of selected comb filter
![Page 44: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/44.jpg)
Tempo estimation and tracking (Grosche, 09)
• DFT of novelty function γ(n) for frequencies:
• Choose frequency that maximizes the magnitude spectrum at each frame
• Construct a sinusoidal kernel:
• In Grosche, 09 phase is computed as:
• Alternatively, we can find the phase that maximizes the dot product of γ(n) with shifted versions of the kernel, as before.
(m) = w(m� n)cos(2⇡(!̂m� '̂))
! 2 [30 : 600]/(60⇥ fs�)
'̂ =
1
2⇡arccos
✓Re(F (!̂, n))
|F (!̂, n)|
◆
![Page 45: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/45.jpg)
Tempo estimation and tracking (Grosche, 09)
• tracking function: Overlap-add of optimal local kernels + half-wave rectify
*From Grosche and Mueller, WASPAA 2009
![Page 46: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/46.jpg)
Tempo estimation and tracking (Davies, 05)
![Page 47: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/47.jpg)
Tempo estimation and tracking (Grosche, 09)
![Page 48: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/48.jpg)
Tempo estimation and tracking (Davies, 05)
![Page 49: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/49.jpg)
Tempo estimation and tracking (Grosche, 09)
![Page 50: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/50.jpg)
Tempo estimation and tracking (Davies, 05)
![Page 51: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/51.jpg)
Tempo estimation and tracking (Grosche, 09)
![Page 52: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/52.jpg)
Tempo estimation and tracking (Davies, 05)
![Page 53: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/53.jpg)
Tempo estimation and tracking (Grosche, 09)
![Page 54: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/54.jpg)
References
• Wang, D. and Brown, G. (Eds) “Computational Auditory Scene Analysis”. Wiley-Interscience (2006): chapter 2, de Cheveigné, A. “Multiple F0 Estimation”; and chapter 8, Goto, M. “Analysis of Musical Audio Signals”.
• Klapuri, A. and Davy, M. (Eds) “Signal Processing Methods for Music Transcription”. Springer (2006): chapter 1, Klapuri, A. “Introduction to Music Transcription”; chapter 4, Hainsworth, S. “Beat Tracking and Musical Metre Analysis”; and chapter 8, Klapuri, A. “Auditory Model-based methods for Multiple Fundamental Frequency Estimation”
• Slaney, M. “An efficient implementation of the Patterson Holdsworth auditory filter bank”. Technical Report 35, Perception Group, Advanced Technology Group, Apple Computer, 1993.
• Smith, J.O. “Mathematics of the Discrete Fourier Transform (DFT)”. 2nd Edition, W3K Publishing (2007): chapter 8, “DFT Applications”.
![Page 55: Juan Pablo Bello EL9173 Selected Topics in Signal ...Juan Pablo Bello EL9173 Selected Topics in Signal Processing: Audio Content Analysis NYU Poly. Periodicity detection • Formally,](https://reader033.vdocuments.site/reader033/viewer/2022041814/5e59a50e68a10d2ec33026bc/html5/thumbnails/55.jpg)
References
• Grosche, P. and Müller, M. “Computing Predominant Local Periodicity Information in Music Recordings”. Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), New Paltz, NY, 2009.
• Davies, M.E.P. and Plumbley, M.D. “Beat Tracking With A Two State Model”. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vol. 3, pp 241-244 Philadelphia, USA, March 19-23, 2005.
• This lecture borrows heavily from: Emmanuel Vincent’s lecture notes on pitch estimation (QMUL - Music Analysis and Synthesis); and from Anssi Klapuri’s lecture notes on F0 estimation and automatic music transcription (ISMIR 2004 Graduate School: http://ismir2004.ismir.net/graduate.html)