\mainpage Puredata DSF external
\section intro Discrete summation formula
When synthesizing sounds digitally, classic waveforms with rich spectra inevitably create unwanted alias-frequencies. This results from the fact that the overtone series goes to infinity while a digital system can only realize a limited bandwith. The surplus energy is being reflected back into the created frequency spectrum as alias-frequencies.
One way around this problem is to create the overtones piece by piece up to the maximal frequency (which is the Nyquist frequency or half the sample rate at which the digital system operates). Especially with low frequencies, this is not feasible, because the number of sine waves to keep track of can grow up to 1000 for low bass notes.
DSF synthesis creates sine and cosine waves by rotating phasors. Instead of generating sine waves up to the Nyquist frequency, the complex numbers which represent the position of the phasors are being put into a geometric series for which a closed formula exists. This formula can be computed in near-linear time, so that computational costs stay low.
One main factor in this is the efficient calculation of a complex power function as implemented here: power_complex(). Using a "divide-and-conquer" approach, the number of calculations are reduced to the 2-logarithm of the number of calculations in the naive implementation power_complex_naiv(). When creating an 8Hz wave with 1400 overtones, the difference between those two implementations resulted in a cpu-usage of 5% vs 50%, which is a ten-fold speedup.
\section imp Implementation
The core functionality is implemented in dsflib.c. When compiling, two externals dsf~ and dsffm~ are produced, based on the code in dsf.c and dsffm.c. While dsf~ provides a userfriendly message-based interface to access the functionality of the dsflib, dsffm~ is optimized for signal-rate shaping of the dsf-parameters. Please refer to the pd-helper patches in this repository for a demonstration of the functionality.
The connection to the puredata interface is implemented via dsf_pd.c and dsffm_pd.c, both of which are based on an example by Johannes Zmoelnig (see here) and include the m_pd.h header with essential definitions of the puredata interface.