This module refers to LabVIEW, a software development environment that features a graphical programming language. Please see the LabVIEW QuickStart Guide module for tutorials and documentation that will help you: • Apply LabVIEW to Audio Signal Processing • Get started with LabVIEW • Obtain a fully-functional evaluation edition of LabVIEW

Overview Additive synthesis creates complex sounds by adding together individual sinusoidal signals called partials. A partial's frequency and amplitude are each time-varying functions, so a partial is a more flexible version of the harmonic associated with a Fourier series decomposition of a periodic waveform. In this module you will learn about partials, how to model the timbre of natural instruments, various sources of control information for partials, and how to make a sinusoidal oscillator with an instantaneous frequency that varies with time.

Partials A partial is a generalization of the harmonic associated with a Fourier series representation of a periodic waveform. The screencast video of introduces important concepts associated with partials.

[video] Important concepts associated with partials

Modeling Timbre of Natural Instruments Perception of an instrument's timbre relies heavily on the attack transient of a note. Since partials can effectively enter and leave the signal at any time, additive synthesis is a good way to model physical instruments. The screencast video of discusses three important design requirements for partials necessary to successfully model a physical instrument.

[video] Three design requirements for partials to model physical instruments

Sources of Control Information The time-varying frequency of a partial is called its frequency trajectory, and is best visualized as a track or path on a spectrogram display. Similarly, the time-varying amplitude of a partial is called its amplitude trajectory. Control information for these trajectories can be derived from a number of sources. Perhaps the most obvious source is a spectral analysis of a physical instrument to be modeled. The screencast video of discusses this concept and demonstrates how a trumpet can be well-modeled by adding suitable partials. The code for the LabVIEW VI demonstrated within the video is available here: trumpet.zip. This VI requires installation of the TripleDisplay front-panel indicator.

[video] Modeling a trumpet tone by adding together increasing numbers of partials Control information can also be derived from other domains not necessarily related to music. The screencast video of provides some examples of non-music control information, and illustrates how an edge boundary from an image can be "auralized" by translating the edge into a partial's frequency trajectory.

[video] Skyline of Houston translated into a frequency trajectory

Instantaneous Frequency The frequency trajectory of a partial is defined as a time-varying frequency f(t) . Since a constant-frequency and constant-amplitude sinusoid is mathematically described as y(t)=Asin⁡(2π f 0 t) , intuition perhaps suggests that the partial should be expressed as y(t)=a(t)sin⁡(2πf(t)t) , where a(t) is the amplitude trajectory. However, as shown in the screencast video of this intuitive result is incorrect; the video derives the correct equation to describe a partial in terms of its trajectories f(t) and a(t) .

[video] Derivation of the equation of a partial given its frequency and amplitude trajectories