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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Impulse Response01:17

Impulse Response

The impulse response is the system's reaction to an input impulse. In an RC circuit, the voltage source is the input, and the capacitor's voltage is the output. The system's state and output response before and after input excitation are distinctly defined.
Kirchhoff's law forms an input signal equation, with the capacitor's current and voltage providing the output. Substituting the current and dividing by RC yields a differential equation. The output for an impulse input is the impulse...
Sound as Pressure Waves01:17

Sound as Pressure Waves

Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
The pressure fluctuation depends on the difference in displacements between the successive points in the...
Beats01:09

Beats

The study of music provides many examples of the superposition of waves and the constructive and destructive interference that occurs. Very few examples of music being performed consist of a single source playing a single frequency for an extended period of time. A single frequency of sound for an extended period might be monotonous to the point of irritation, similar to the unwanted drone of an aircraft engine or a loud fan. Music is pleasant and exciting due to mixing the changing frequencies...
Bandpass Sampling01:17

Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2. The spectrum...

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Time domain simulation and sound synthesis for the snare drum.

Stefan Bilbao1

  • 1Acoustics and Fluid Dynamics Group/Music, University of Edinburgh, Room 7306B, James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom. sbilbao@staffmail.ed.ac.uk

The Journal of the Acoustical Society of America
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Summary

This study applies finite difference time domain techniques to model the complex snare drum system. The research details membrane-snare interactions and numerical challenges for advanced sound synthesis.

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Area of Science:

  • Acoustics
  • Computational Physics
  • Musical Instrument Design

Background:

  • The snare drum is a complex acoustic system with interacting components like membranes and snares.
  • Traditional physical modeling synthesis methods struggle with the snare drum's multidimensionality and non-linear snare interactions.

Purpose of the Study:

  • To apply finite difference time domain (FDTD) techniques to a full 3D snare drum model.
  • To analyze key interactions, including membrane coupling and membrane-snare dynamics.
  • To discuss numerical considerations and computational complexity for FDTD modeling of percussion instruments.

Main Methods:

  • Finite Difference Time Domain (FDTD) applied to a 3D snare drum model.
  • Examination of multi-physics interactions within the snare drum system.
  • Analysis of numerical artifacts like mode splitting and bandwidth limitations.

Main Results:

  • Detailed examination of membrane-snare coupling and interactions.
  • Identification and discussion of numerical challenges inherent in FDTD modeling of complex systems.
  • Presentation of computational complexity estimates and sound examples.

Conclusions:

  • FDTD techniques offer a viable approach for modeling the complex snare drum system.
  • Understanding numerical features is crucial for accurate physical modeling synthesis of percussion.
  • The study provides insights into the acoustic behavior and computational aspects of snare drum simulation.