Özetçe -Bu çalışmada, monofonik Türk makam müzigi kayıtları içerisindeki temel titreşim frekanslarının, Degişken Kip Ayrışım (DKA) yöntemi kullanılarak kestirimi önerilmektedir. Degişken Kip Ayrışımının amacı, reel degerli bir sinyali sonlu sayıda alt sinyallere (kiplere) ayrıştırmaktır. DKA sinyal içerisindeki temel bandların yinelemesiz ve adaptif olarak belirlenmesi ve eş zamanlı olarak uygun kiplerin kestirilmesini saglar. Bu yöntemde sinyali en iyi temsil edebilecek kipler, Görgül Kip Ayrışım (GKA) yönteminde kullanılan özgül kip fonksiyonları (ÖKF) gibi dar bantlı olma özelligine sahiptir. Yapılan benzetim çalışmalarında, müzik sinyalinde ayrıştırma aracı olarak sıkça kullanılan GKA, YIN, MELODIA ve spektrogram tabanlı yöntemler ile karşılaştırıldıgında, sentetik ve gerçek test sinyalleri ile elde edilen temel titreşim frekansı kestirim sonuçları daha başarılıdır.Anahtar Kelimeler-Degişken kip ayrışımı, monofonik müzik, Türk makam müzigi, temel titreşim frekansı.Abstract-In this study, a new method is presented for the fundamental frequency estimation of Turkish makam music recordings by using Variational Mode Decomposition (VMD). VMD is a method to decompose an input signal into an ensemble of sub-signals (modes) which is entirely non-recursive and determines the relevant bands adaptively and estimates the corresponding modes concurrently. In order to decompose a given signal optimally, actuated by the narrow-band properties corresponding to the Intrinsic Mode Function (IMF) definition used in Emprical Mode Decomposition (EMD), and we seek an ensemble of modes. Simulation results on fundamental frequency estimation of real music and synthetic test data show better performance compared to other common decomposition methods for music signals such as spectrogram, YIN, MELODIA and EMD based methods.
Abstract-In this paper, a new Variational Mode Decomposition (VMD) is introduced, and applied to the fundamental frequency estimation of monophonical Turkish maqam music. VMD is a method to decompose an input signal into an ensemble of sub-signals (modes) which is entirely non-recursive. It determines the relevant bands adaptively, and estimates the corresponding modes concurrently. In order to optimally decompose a given signal, VMD seeks an ensemble of modes with narrow-band properties corresponding to the Intrinsic Mode Function (IMF) definition used in Empirical Mode Decomposition (EMD). In our proposed modified VMD approach, in order to obtain the bandwidth of a mode, each mode is shifted to baseband by mixing an exponential that is adjusted to the respective center frequency. The bandwidth is estimated through elastic net method that linearly combines penalties of the Lasso and Ridge Regression methods. Simulation results on fundamental frequency estimation of real music and synthetic test data show better performance compared to classical VMD based approach, and other common methods used for music signals, such as YIN and MELODIA based methods.
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