Vesa Välimäki

Splitting the unit delay [FIR/all pass filters design]

A fractional delay filter is a device for bandlimited interpolation between samples. It finds applications in numerous fields of signal processing, including communications, array processing, speech processing, and music technology. We present a comprehensive review of FIR and allpass filter design techniques for bandlimited approximation of a fractional digital delay. Emphasis is on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value. Various new approaches are proposed and several examples are provided to illustrate the performance of the methods. We also discuss the implementation complexity of the algorithms. We focus on four applications where fractional delay filters are needed: synchronization of digital modems, incommensurate sampling rate conversion, high-resolution pitch prediction, and sound synthesis of musical instruments.

Discrete-time modelling of musical instruments

This article describes physical modelling techniques that can be used for simulating musical instruments. The methods are closely related to digital signal processing. They discretize the system with respect to time, because the aim is to run the simulation using a computer. The physics-based modelling methods can be classified as mass–spring, modal, wave digital, finite difference, digital waveguide and source–filter models. We present the basic theory and a discussion on possible extensions for each modelling technique. For some methods, a simple model example is chosen from the existing literature demonstrating a typical use of the method. For instance, in the case of the digital waveguide modelling technique a vibrating string model is discussed, and in the case of the wave digital filter technique we present a classical piano hammer model. We tackle some nonlinear and time-varying models and include new results on the digital waveguide modelling of a nonlinear string. Current trends and future directions in physical modelling of musical instruments are discussed.

Principles of fractional delay filters

In numerous applications, such as communications, audio and music technology, speech coding and synthesis, antenna and transducer arrays, and time delay estimation, not only the sampling frequency but the actual sampling instants are of crucial importance. Digital fractional delay (FD) filters provide a useful building block that can be used for fine-tuning the sampling instants, i.e., implement the required bandlimited interpolation. In this paper an overview of design techniques and applications is given.

Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques

The digital waveguide mesh is an extension of the one-dimensional (1-D) digital waveguide technique. The mesh can be used for simulation of two- and three-dimensional (3-D) wave propagation in musical instruments and acoustic spaces. The original rectangular digital waveguide mesh algorithm suffers from direction-dependent dispersion. Alternative geometries, such as the triangular mesh, have been proposed previously to improve the performance of the mesh. In this paper, we show that the dispersion problem may be reduced using various other techniques. These methods include multidimensional interpolation, optimization of the point-spreading function, and frequency warping. We compare the accuracy and computational complexity of these techniques in the two-dimensional (2-D) case and conduct numerical simulations of a membrane. A rectangular mesh using second-order Lagrange interpolation can be implemented without multiplications, but its accuracy is worse than that of other enhanced structures. The most accurate technique in terms of the relative frequency error is the warped triangular mesh whose maximum error is 0.6%. The warped rectangular mesh with optimized weighting coefficients is not as exact, but still offers a 1.2% accuracy.

Modeling of tension modulation nonlinearity in plucked strings

A nonlinear discrete-time model that simulates a vibrating string exhibiting tension modulation nonlinearity is developed. The tension modulation phenomenon is caused by string elongation during transversal vibration. Fundamental frequency variation and coupling of harmonic modes are among the perceptually most important effects of this nonlinearity. The proposed model extends the linear bidirectional digital waveguide model of a string. It is also formulated as a computationally more efficient single-delay-loop structure. A method of reducing the computational load of the string elongation approximation is described, and a technique of obtaining the tension modulation parameter from recorded plucked string instrument tones is presented. The performance of the model is demonstrated with analysis/synthesis experiments and with examples of synthetic tones.

Musical aptitude and second language pronunciation skills in school-aged children: neural and behavioral evidence

The main focus of this study was to examine the relationship between musical aptitude and second language pronunciation skills. We investigated whether children with superior performance in foreign language production represent musical sound features more readily in the preattentive level of neural processing compared with children with less-advanced production skills. Sound processing accuracy was examined in elementary school children by means of event-related potential (ERP) recordings and behavioral measures. Children with good linguistic skills had better musical skills as measured by the Seashore musicality test than children with less accurate linguistic skills. The ERP data accompany the results of the behavioral tests: children with good linguistic skills showed more pronounced sound-change evoked activation with the music stimuli than children with less accurate linguistic skills. Taken together, the results imply that musical and linguistic skills could partly be based on shared neural mechanisms.

Fifty Years of Artificial Reverberation

The first artificial reverberation algorithms were proposed in the early 1960s, and new, improved algorithms are published regularly. These algorithms have been widely used in music production since the 1970s, and now find applications in new fields, such as game audio. This overview article provides a unified review of the various approaches to digital artificial reverberation. The three main categories have been delay networks, convolution-based algorithms, and physical room models. Delay-network and convolution techniques have been competing in popularity in the music technology field, and are often employed to produce a desired perceptual or artistic effect. In applications including virtual reality, predictive acoustic modeling, and computer-aided design of acoustic spaces, accuracy is desired, and physical models have been mainly used, although, due to their computational complexity, they are currently mainly used for simplified geometries or to generate reverberation impulse responses for use with a convolution method. With the increase of computing power, all these approaches will be available in real time. A recent trend in audio technology is the emulation of analog artificial reverberation units, such as spring reverberators, using signal processing algorithms. As a case study we present an improved parametric model for a spring reverberation unit.

Low-order modeling of head-related transfer functions using balanced model truncation

We propose a novel technique for the design of low-order infinite impulse response (IIR) filter models of head-related transfer functions (HRTFs) that uses balanced model truncation. We design tenth-order IIR filters, suitable for efficient real-time implementation, from preprocessed HRTF impulse responses that are of significantly superior quality to current IIR models derived with the Prony and Yule-Walker methods.

Interpolated rectangular 3-D digital waveguide mesh algorithms with frequency warping

Various interpolated three-dimensional (3-D) digital waveguide mesh algorithms are elaborated. We introduce an optimized technique that improves a formerly proposed trilinearly interpolated 3-D mesh and renders the mesh more homogeneous in different directions. Furthermore, various sparse versions of the interpolated mesh algorithm are investigated, which reduce the computational complexity at the expense of accuracy. Frequency-warping techniques are used to shift the frequencies of the output signal of the mesh in order to cancel the effect of dispersion error. The extensions improve the accuracy of 3-D digital waveguide mesh simulations enough so that in the future it can be used for acoustical simulations needed in the design of listening rooms, for example.

Methods for Modeling Realistic Playing in Acoustic Guitar Synthesis

Computer Music Journal Computer Music Journal, 25:3, pp. 38–49, Fall 2001