Download Rounding Corners with BLAMP The use of the bandlimited ramp (BLAMP) function as an antialiasing tool for audio signals with sharp corners is presented. Discontinuities in the waveform of a signal or its derivatives require infinite bandwidth and are major sources of aliasing in the digital domain. A polynomial correction function is modeled after the ideal BLAMP function. This correction function can be used to treat aliasing caused by sharp edges or corners which translate into discontinuities in the first derivative of a signal. Four examples of cases where these discontinuities appear are discussed: synthesis of triangular waveforms, hard clipping, and half-wave and fullwave rectification. Results obtained show that the BLAMP function is a more efficient tool for alias reduction than oversampling. The polynomial BLAMP can reduce the level of aliasing components by up to 50 dB and improve the overall signal-to-noise ratio by about 20 dB. The proposed method can be incorporated into virtual analog models of musical systems.
Download A Modal Approach to the Numerical Simulation of a String Vibrating Against an Obstacle: Applications to Sound Synthesis A number of musical instruments (electric basses, tanpuras, sitars...) have a particular timbre due to the contact between a vibrating string and an obstacle. In order to simulate the motion of such a string with the purpose of sound synthesis, various technical issues have to be resolved. First, the contact phenomenon, inherently nonlinear and producing high frequency components, must be described in a numerical manner that ensures stability. Second, as a key ingredient for sound perception, a fine-grained frequencydependent description of losses is necessary. In this study, a new conservative scheme based on a modal representation of the displacement is presented, allowing the simulation of a stiff, damped string vibrating against an obstacle with an arbitrary geometry. In this context, damping parameters together with eigenfrequencies of the system can be adjusted individually, allowing for complete control over loss characteristics. Two cases are then numerically investigated: a point obstacle located in the vicinity of the boundary, mimicking the sound of the tanpura, and then a parabolic obstacle for the sound synthesis of the sitar.