Publication Type:

Conference Paper


SMC Conference 2005 (2005)




One of the most widely employed technique for the sound synthesis is based on the Fourier theorem that states that any signal can be obtained as a sum of sinusoids. Unfortunately this algorithm, when applied to synthesizers, requires some peculiar operations, as the addressing of a Look Up Table, that are not easily built-in in standard processors, thus requiring specially designed architectures. The aim of this paper is to show that, when using a new method for the analysis and polar coordinates, a much broader class of functions can be employed as a basis, and it turns out that the square wave is one of such functions. When the synthesis of signals is carried out by summing square waves, the additive synthesizer architecture results much more simplified, allowing for example to synthesize complex sounds simply in software, using general purpose microprocessors, even in real-time. Firstly it will be proven that the L2 function space admits a broad class of functions as a basis, and the requirements for a function, in order to be a basis, will be defined. A straightforward and computationally simple algorithm for the analysis of any function on such generic basis will be proposed. Finally the architecture for the square wave based synthesizer will be sketched and examples of synthesized waveforms will be given.