55,642 research outputs found
Sequential Complexity as a Descriptor for Musical Similarity
We propose string compressibility as a descriptor of temporal structure in
audio, for the purpose of determining musical similarity. Our descriptors are
based on computing track-wise compression rates of quantised audio features,
using multiple temporal resolutions and quantisation granularities. To verify
that our descriptors capture musically relevant information, we incorporate our
descriptors into similarity rating prediction and song year prediction tasks.
We base our evaluation on a dataset of 15500 track excerpts of Western popular
music, for which we obtain 7800 web-sourced pairwise similarity ratings. To
assess the agreement among similarity ratings, we perform an evaluation under
controlled conditions, obtaining a rank correlation of 0.33 between intersected
sets of ratings. Combined with bag-of-features descriptors, we obtain
performance gains of 31.1% and 10.9% for similarity rating prediction and song
year prediction. For both tasks, analysis of selected descriptors reveals that
representing features at multiple time scales benefits prediction accuracy.Comment: 13 pages, 9 figures, 8 tables. Accepted versio
Proof of a Conjectured Three-Valued Family of Weil Sums of Binomials
We consider Weil sums of binomials of the form , where is a finite field, is
the canonical additive character, , and .
If we fix and and examine the values of as runs
through , we always obtain at least three distinct values unless
is degenerate (a power of the characteristic of modulo ).
Choices of and for which we obtain only three values are quite rare and
desirable in a wide variety of applications. We show that if is a field of
order with odd, and with , then
assumes only the three values and . This
proves the 2001 conjecture of Dobbertin, Helleseth, Kumar, and Martinsen. The
proof employs diverse methods involving trilinear forms, counting points on
curves via multiplicative character sums, divisibility properties of Gauss
sums, and graph theory.Comment: 19 page
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A sub-Nyquist co-prime sampling music spectral approach for natural frequency identification of white-noise excited structures
Motivated by practical needs to reduce data transmission payloads in wireless sensors for vibration-based monitoring of civil engineering structures, this paper proposes a novel approach for identifying resonant frequencies of white-noise excited structures using acceleration measurements acquired at rates significantly below the Nyquist rate. The approach adopts the deterministic co-prime sub-Nyquist sampling scheme, originally developed to facilitate telecommunication applications, to estimate the autocorrelation function of response acceleration time-histories of low-amplitude white-noise excited structures treated as realizations of a stationary stochastic process. This is achieved without posing any sparsity conditions to the signals. Next, the standard MUSIC algorithm is applied to the estimated autocorrelation function to derive a denoised super-resolution pseudo-spectrum in which natural frequencies are marked by prominent spikes. The accuracy and applicability of the proposed approach is numerically assessed using computer-generated noise-corrupted acceleration time-history data obtained by a simulation-based framework pertaining to a white-noise excited structural system with two closely-spaced modes of vibration carrying the same amount of energy, and a third isolated weakly excited vibrating mode. All three natural frequencies are accurately identified by sampling at as low as 78% below Nyquist rate for signal to noise ratio as low as 0dB (i.e., energy of additive white noise equal to the signal energy), suggesting that the proposed approach is robust and noise-immune while it can reduce data transmission requirements in acceleration wireless sensors for natural frequency identification of engineering structures
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