Abstract
From the emissions of massive quasars scattered across the universe, to the fluctuations in the stock market and the melodies of music, several real world signals have a power spectral density (PSD) that follows an inverse relationship with their frequency. Specifically, this type of random process is referred to as a \(1/f\) signal, and has been of much interest in research, as sequences that have this property better mimic natural signals. In the context of constraint programming, a recent work has defined a constraint that enforces sequences to exhibit a \(1/f\) PSD, as well as a corresponding constraint propagator. In this paper we show that the set of valid solutions associated with this propagator misses an exponential number of \(1/f\) solutions and accepts solutions that do not have a \(1/f\) PSD. Additionally, we address these two issues by proposing two non-exclusive algorithms for this constraint. The first one can find a larger set of valid solutions, while the second prevents most non-\(1/f\) solutions. We demonstrate in our experimental section that using the hybrid of these two methods results in a more robust propagator for this constraint.
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References
Herriman, A., McCartney, J., Burk, P., Downey, A., Whittle, R., Kellet, P.: Generation of pink (1/f) noise. http://www.firstpr.com.au/dsp/pink-noise/
Arafailova, E., et al.: Global constraint catalog, vol. II, time-series constraints. arXiv preprint arXiv:1609.08925 (2016)
Chemillier, M., Truchet, C.: Computation of words satisfying the rhythmic oddity property (after simha arom’s works). Inf. Process. Lett. 86(5), 255–261 (2003)
Gardner, M.: White and brown music, fractal curves and one-over-f fluctuations. Sci. Am. 238(4), 16–32 (1978)
Hennig, H., et al.: The nature and perception of fluctuations in human musical rhythms. PLoS ONE 6(10), e26457 (2011)
Kasdin, N.J.: Discrete simulation of colored noise and stochastic processes and 1/f/sup/spl alpha//power law noise generation. Proc. IEEE 83(5), 802–827 (1995)
Keshner, M.S.: 1/f noise. Proc. IEEE 70(3), 212–218 (1982)
Morin, M., Quimper, C.-G.: The markov transition constraint. In: Simonis, H. (ed.) CPAIOR 2014. LNCS, vol. 8451, pp. 405–421. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07046-9_29
Pachet, F., Roy, P., Papadopoulos, A., Sakellariou, J.: Generating 1/f noise sequences as constraint satisfaction: the voss constraint. In: IJCAI, pp. 2482–2488 (2015)
Papadopoulos, A., Pachet, F., Roy, P., Sakellariou, J.: Exact sampling for regular and markov constraints with belief propagation. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 341–350. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_24
Perez, G., Régin, J.-C.: Efficient operations on MDDs for building constraint programming models. In: IJCAI, pp. 374–380 (2015)
Perez, G., Régin, J.-C.: MDDs are efficient modeling tools: an application to some statistical constraints. In: Salvagnin, D., Lombardi, M. (eds.) CPAIOR 2017. LNCS, vol. 10335, pp. 30–40. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59776-8_3
Perez, G., Régin, J.-C.: MDDs: sampling and probability constraints. In: Beck, J.C. (ed.) CP 2017. LNCS, vol. 10416, pp. 226–242. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66158-2_15
Perlin, K.: An image synthesizer. ACM Siggraph Comput. Graph. 19(3), 287–296 (1985)
Perron, L.: Or-tools. In: Workshop CP Solvers: Modeling, Applications, Integration, and Standardization (2013)
Pesant, G.: Achieving domain consistency and counting solutions for dispersion constraints. INFORMS J. Comput. 27(4), 690–703 (2015)
Rossi, R., Prestwich, S., Tarim, S.A.: Statistical constraints. arXiv preprint arXiv:1402.5161 (2014)
Roy, P., Pachet, F.: Enforcing meter in finite-length markov sequences. In: AAAI (2013)
Schaus, P., Deville, Y., Dupont, P., Régin, J.-C.: The deviation constraint. In: Van Hentenryck, P., Wolsey, L. (eds.) CPAIOR 2007. LNCS, vol. 4510, pp. 260–274. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72397-4_19
Schaus, P., Régin, J.-C.: Bound-consistent spread constraint. EURO J. Comput. Optim. (2013)
Truchet, C., Assayag, G.: Constraint Programming in Music. ISTE-Wiley, Hoboken (2011)
Truchet, C., Codognet, P.: Musical constraint satisfaction problems solved with adaptive search. Soft. Comput. 8(9), 633–640 (2004)
Voss, R.F., Clarke, J.: 1/f noise in music and speech. Nature 258(5533), 317–318 (1975)
Voss, R.F., Clarke, J.: 1/f noisein music: Music from 1/f noise. J. Acous. Soc. Am. 63(1), 258–263 (1978)
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Perez, G., Rappazzo, B., Gomes, C. (2018). Extending the Capacity of 1 / f Noise Generation. In: Hooker, J. (eds) Principles and Practice of Constraint Programming. CP 2018. Lecture Notes in Computer Science(), vol 11008. Springer, Cham. https://doi.org/10.1007/978-3-319-98334-9_39
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DOI: https://doi.org/10.1007/978-3-319-98334-9_39
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