The Kalman filter is a well-known tool used extensively in robotics, navigation, speech enhancement and finance. In this paper, we propose a novel pitch follower based on the Extended Complex Kalman Filter (ECKF). An advantage of this pitch follower is that it operates on a sample-by-sample basis, unlike other block-based algorithms that are most commonly used in pitch estimation. Thus, it estimates sample-synchronous fundamental frequency (assumed to be the perceived pitch), which makes it ideal for real-time implementation. Simultaneously, the ECKF also tracks the amplitude envelope of the input audio signal. Finally, we test our ECKF pitch detector on a number of cello and double bass recordings played with various ornaments, such as vibrato, portamento and trill, and compare its result with the well-known YIN estimator, to conclude the effectiveness of our algorithm.

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Noise subspace methods are popular for estimating the parameters of complex sinusoids in the presence of uncorrelated noise and have applications in musical instrument modeling and microphone array processing. One such algorithm, MUSIC (Multiple Signal Classification) has been popular for its ability to resolve closely spaced sinusoids. However, the computational efficiency of MUSIC is relatively low, since it requires an explicit eigenvalue decomposition of an autocorrelation matrix, followed by a linear search over a large space. In this paper, we discuss methods for and the benefits of converting the Toeplitz structure of the autocorrelation matrix to circulant form, so that eigenvalue decomposition can be replaced by a Fast Fourier Transform (FFT) of one row of the matrix. This transformation requires modeling the signal as at least approximately periodic over some duration. For these periodic signals, the pseudospectrum calculation becomes trivial and the accuracy of the frequency estimates only depends on how well periodicity detection works. We derive a closed-form expression for the pseudospectrum, yielding large savings in computation time. We test our algorithm to resolve closely spaced piano partials.

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An improved and expanded method for carillon bell synthesis is proposed. Measurements of a carillon bell and its clapper were made to serve as the basis for an efficient synthesis framework. Mode frequencies, damping, and amplitudes are used to form a modal model fit to measurements. A parameterized clapper interaction model is proposed to drive the bell model, reproducing variation of timbre as the bell is played in different dynamic ranges. Reverberation of the belfry was measured from several listener perspectives and an efficient modal reverberation architecture is shown to model the sound of the bell from locations inside and outside the belfry.

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Feedback delay network reverberators have decay filters associated with each delay line to model the frequency dependent reverberation time (T60) of a space. The decay filters are typically designed such that all delay lines independently produce the same T60 frequency response. However, in real rooms, there are multiple, concurrent T60 responses that depend on the geometry and physical properties of the materials present in the rooms. In this paper, we propose the Grouped Feedback Delay Network (GFDN), where groups of delay lines share different target T60s. We use the GFDN to simulate coupled rooms, where one room is significantly larger than the other. We also simulate rooms with different materials, with unique decay filters associated with each delay line group, designed to represent the T60 characteristics of a particular material. The T60 filters are designed to emulate the materials’ absorption characteristics with minimal computation. We discuss the design of the mixing matrix to control inter- and intra-group mixing, and show how the amount of mixing affects behavior of the room modes. Finally, we discuss the inclusion of air absorption filters on each delay line and physically motivated room resizing techniques with the GFDN.

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Computer simulations of room acoustics suffer from an efficiency vs accuracy trade-off, with highly accurate wave-based models being highly computationally expensive, and delay-network-based models lacking in physical accuracy. The Scattering Delay Network (SDN) is a highly efficient recursive structure that renders first order reflections exactly while approximating higher order ones. With the purpose of improving the accuracy of SDNs, in this paper, several variations on SDNs are investigated, including appropriate node placement for exact modeling of higher order reflections, redesigned scattering matrices for physically-motivated scattering, and pruned network connections for reduced computational complexity. The results of these variations are compared to state-of-the-art geometric acoustic models for different shoebox room simulations. Objective measures (Normalized Echo Densities (NEDs) and Energy Decay Curves (EDCs)) showed a close match between the proposed methods and the references. A formal listening test was carried out to evaluate differences in perceived naturalness of the synthesized Room Impulse Responses. Results show that increasing SDNs’ order and adding directional scattering in a fully-connected network improves perceived naturalness, and higher-order pruned networks give similar performance at a much lower computational cost.

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