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.
Clone this repository to your computer,
open the directory and start the compilation
with make:
# clone repository:
git clone https://github.com/Seba-birds/dsf.git
# change to project root directory:
cd dsf
# compile sources:
make
# see results:
ls
After compilation, you will find two new binary
files whose name depends on your operating
system. On MacOS those files are
dsf.pd_darwin and dsffm.pd_darwin.
Mind that those names are missing the tilde that is prescribed by puredata naming conventions. So we need to rename the binaries to meet the naming convention:
# replace file extension (".pd_darwin")
# according to your OS
mv dsf.pd_darwin dsf~.pd_darwin
mv dsffm.pd_darwin dsffm~.pd_darwin
Now we need to copy the binaries and the help files to the correct folder on your system, so that they are available in puredata. Refer to this site for more detailed information. On a standard installation on MacOS, you can do:
for i in dsf~.pd_darwin dsffm~.pd_darwin dsf~-help.pd dsffm~-help.pd ; \
do cp $i /Applications/Pd.app/Contents/Resources/extra/$i ; \
done;
After restarting puredata, you should now be
able to create the objects dsf~ and dsffm~
on the canvas and access the helper patches via
the right-click menu.
dsf~ is a puredata implementation of the discrete summation formula.
This module is controlled by messages and thus more transparent for
user interaction, yet not convenient to use in a context where parameters
are to be varied at signal speed. Refer to the doxygen-documentation
for more detailed information about the implementation and to the
dsf~-help.pd-file for more information about usage.
dsffm~ provides signal-rate inlets for fm-style modulation of several
parameters of the DSF. The three inlets provide signal-rate control over
pitch, overtone ratio and overtone weight. Opposed to the dsf~-module,
pitch is controlled in MIDI-notes, not frequency, thus providing the same
aural characteristics of a given modulation over the whole frequency
spectrum. Refer to the doxygen-documentation
for more detailed information about the implementation and to the
dsffm~-help.pd-file for more information about usage.
For detailed description of the code, generate the
documentation via doxygen like so:
doxygen Doxyfile
The documentation is created in a new
folder ./documentation/.
The following files where used and altered for this project:
- Makefile: https://github.com/pure-data/pd-lib-builder/
- *_pd.c-files: https://github.com/pure-data/externals-howto/blob/master/example4/pan%7E.c
- m_pd.h: https://github.com/pure-data/externals-howto#the-interface-to-pd
The following sources where used to learn about DSF synthesis: