Balázs Bank

Generation of longitudinal vibrations in piano strings: From physics to sound synthesis

Longitudinal vibration of piano strings greatly contributes to the distinctive character of low piano notes. In this paper a simplified modal model is developed, which describes the generation of phantom partials and longitudinal free modes jointly. The model is based on the simplification that the coupling from the transverse vibration to the longitudinal polarization is unidirectional. The modal formulation makes it possible to predict the prominent components of longitudinal vibration as a function of transverse modal frequencies. This provides a qualitative insight into the generation of longitudinal vibration, while the model is still capable of explaining the empirical results of earlier works. The semi-quantitative agreement with measurement results implies that the main source of phantom partials is the transverse to longitudinal coupling, while the string termination and the longitudinal to transverse coupling have only small influence. The results suggest that the longitudinal component of the tone can be treated as a quasi-harmonic spectrum with formantlike peaks at the longitudinal modal frequencies. The model is further simplified and applied for the real-time synthesis of piano sound with convincing sonic results.

Physically informed signal processing methods for piano sound synthesis: a research overview

This paper reviews recent developments in physics-based synthesis of piano. The paper considers the main components of the instrument, that is, the hammer, the string, and the soundboard. Modeling techniques are discussed for each of these elements, together with implementation strategies. Attention is focused on numerical issues, and each implementation technique is described in light of its efficiency and accuracy properties. As the structured audio coding approach is gaining popularity, the authors argue that the physical modeling approach will have relevant applications in the field of multimedia communication.

Robust loss filter design for digital waveguide synthesis of string tones

A robust loss filter design method is presented for digital waveguide string models, which can be used with high filter orders. The method aims at minimizing the decay time error in partials of the synthetic tone. This is achieved by a new weighting function based on the first-order Taylor series approximation of the decay time errors. Smoothing of decay time data and requiring the design to be minimum-phase are also proposed to facilitate the stability of the design. The new method is applicable to analysis-based sound synthesis of piano and guitar tones, for example.

A Modal-Based Real-Time Piano Synthesizer

This paper presents a real-time piano synthesizer where both the transverse and longitudinal motion of the string is modeled by modal synthesis, resulting in a coherent and highly parallel model structure. The paper applies recent developments in piano modeling and focuses on the issues related to practical implementation (e.g., numerical stability, aliasing, and efficiency). A strong emphasis is given to modeling nonlinear string vibrations, and a new variation of earlier synthesis techniques is proposed which is particularly well suited for modal synthesis. For soundboard modeling, the possibilities of using fast Fourier transform-based fast convolution and parallel second-order filters are discussed. Additionally, the paper describes the details of the software implementation and discusses the computational complexity of each model block. The piano model runs on current computer hardware with full polyphony in real time.

Perceptually Motivated Audio Equalization Using Fixed-Pole Parallel Second-Order Filters

In audio, equalizer design should take into account the frequency resolution of the auditory system. In this paper, this is accomplished by the fixed-pole design of parallel second-order filters. The design process has two steps: first, the poles of the filter are set according to the desired frequency resolution. Then, the feedforward coefficients of the second-order filters are determined by a linear least squares solution. The proposed parallel filter achieves effectively the same equalization results as the Kautz filter, but it requires 33% fewer multiplications and additions.

High-precision parallel graphic equalizer

This paper proposes a high-precision graphic equalizer based on second-order parallel filters. Previous graphic equalizers suffer from interaction between adjacent band filters, especially at high gain values, which can lead to substantial errors in the magnitude response. The fixed-pole design of the proposed parallel graphic equalizer avoids this problem, since the parallel second-order filters are optimized jointly. When the number of pole frequencies is twice the number of command points of the graphic equalizer, the proposed non-iterative design matches the target curve with high precision. In the three example cases presented in this paper, the proposed parallel equalizer clearly outperforms other non-iterative graphic equalizer designs, and its maximum global error is as low as 0.00-0.75 dB when compared to the target curve. While the proposed design has superior accuracy, the number of operations in the filter structure is increased only by 23% when compared to the second-order Regalia-Mitra structure. The parallel structure also enables the utilization of parallel computing hardware, which can nowadays easily outperform the traditional serial processing. The proposed graphic equalizer can be widely used in audio signal processing applications.

Multi-channel IIR filtering of audio signals using a GPU

In the audio signal processing field, multiple IIR filters are required in many applications. As an example, equalizing a Wave Field Synthesis system requires massive filter processing in real time. Graphics Processing Units (GPUs) are well known for their potential in highly parallel data processing. Up to now, the use of the GPUs for implementing IIR filters has not been clearly tackled in audio processing because of its feedback loop that prevents its total parallelization. However, using the Parallel form of IIR filters, this feedback is reduced, since every single sample is computed in a parallel way. This paper analyzes the performance of multiple IIR filters using GPUs and compares it with a powerful multi-core computer. The proposed GPU implementation can run up to 1256 concurrent IIR filters of order 256th in real time, which means 321,536 total filter order, with a latency time of 0.72 ms (sampling frequency of 44.1 kHz). This demonstrates that GPUs are well suited for computing massive IIR filtering.

Logarithmic Frequency Scale Parallel Filter Design With Complex and Magnitude-Only Specifications

Recently, the fixed-pole design of second-order parallel filters has been introduced to accomplish arbitrary (e.g., logarithmic) frequency resolution for transfer function modeling and equalization. The frequency resolution is set by the pole frequencies, and the resulting filter response corresponds to the smoothed (moving-average filtered) version of the target frequency response. This letter presents the frequency-domain version of the design algorithm for complex and real filter coefficients. The proposed frequency-domain design, besides its computational benefits, allows the use of frequency weighting. In addition, a magnitude-only variation of the algorithm is proposed. Examples of loudspeaker-room modeling and equalization are presented.

Improved Pole Positioning for Parallel Filters Based on Spectral Smoothing and Multiband Warping

The use of second-order parallel filters with pre-defined pole locations has been recently proposed for equalization and transfer function modeling. This letter presents an improved method for obtaining the pole positions of the parallel filter. The steps of the new method are the following: first, the target frequency response is smoothed to the required resolution. Then, multiple warped IIR filters with different warping parameters are designed to the smoothed target divided into frequency bands. Finally, the united pole set of the warped IIR designs is used for parallel filter design. The method leads to increased accuracy compared to earlier pole positioning techniques, and can also be used for Kautz filter designs. Examples of loudspeaker-room response modeling and equalization are presented.

Efficient synthesis of tension modulation in strings and membranes based on energy estimation

String and membrane vibrations cannot be considered as linear above a certain amplitude due to the variation in string or membrane tension. A relevant special case is when the tension is spatially constant and varies in time only in dependence of the overall string length or membrane surface. The most apparent perceptual effect of this tension modulation phenomenon is the exponential decay of pitch in time. Pitch glides due to tension modulation are an important timbral characteristic of several musical instruments, including the electric guitar and tom-tom drum, and many ethnic instruments. This paper presents a unified formulation to the tension modulation problem for one-dimensional (1-D) (string) and two-dimensional (2-D) (membrane) cases. In addition, it shows that the short-time average of the tension variation, which is responsible for pitch glides, is approximately proportional to the system energy. This proportionality allows the efficient physics-based sound synthesis of pitch glides. The proposed models require only slightly more computational resources than linear models as opposed to earlier tension-modulated models of higher complexity.