Merge old algo description from LAC20-old file into the article ad make adjustments.

1 files changed, 33 insertions, 23 deletions

diff --git a/sampling_alg_lac2020/LAC-20.tex b/sampling_alg_lac2020/LAC-20.tex
index 3eaa57a..12c7d69 100644
--- a/sampling_alg_lac2020/LAC-20.tex
+++ b/sampling_alg_lac2020/LAC-20.tex
@@ -284,14 +284,15 @@
 
 \todobent{Discuss DGs old sampling algorithm briefly.}
 
-The evolution of the DrumGizmo sample selection engine:
-
- * Velocity groups with probabilities for randomization.
-
-The early versions of drumgizmo used a sample selection algorithm
-based on grouping of samples, each with a corresponding velocity
-range, with a number of audio files, each with a probability of being
-played in the group:
+The engine gets a value $l \in [0,1]$ which must then be used by the
+engine for deciding how the output should be produced.
+Some engines use this value as a gain factor but in the case of
+DrumGizmo it is used for sample selection only.
+The early versions used a sample selection algorithm based on velocity
+groups, akin to the one used by sfz \todo{add bib reference}, in which
+each group spans a specfied velocity range and the sample selection is
+made by uniformly randomly selecting one of the samples contained in
+the group corresponding to the input velocity:
 {\tiny\begin{verbatim}
                    ________________                _________________
                   /                \              / uniformly random \
@@ -299,32 +300,41 @@ played in the group:
      [0; 1]       \________________/              \__________________/
 \end{verbatim}}
 
-\todobent{Write this algorithm in psudocode syntax.}
-
- * StdDev/Mean based using measured power values of each sample
+This algorithm did not give good results in small samplesets so later
+an improved algorithm was introduced which was instead on normal
+distributed random numbers and with power values for each sample in
+the set.
+
+The power values of a drum kit are floating point numbers without any
+restrictions but assumed to be positive. Then the input value
+$l$ is mapped using the canonical bijections between $[0,1]$ and
+$[p_{\min}, p_{max}]$ and afterwards shifted\todo{by which
+amount?}. We call this new value $p$.
+
+Now the real sample selection algorithm starts. We select a value $p'$
+drawn normal distributed at random from $\mathcal{N}(p', \sigma^2)$,
+where the mean value, $\mu$, set to the input value $l$ and
+and the stddev, $\sigma$, is a parameter controlled by the user
+expressed in fractions of the size and span of the sampleset.
+Now we simply find the sample $s$ with the power $q$ which is closest
+to $p'$ -- ties are broken such that the first minimal value is chosen
+(which is problematic as explained below). In case $s$ is equal to the
+last sample that we played we repeat this process, otherwise we return
+$s$. If we did not find another sample than the last played after $4$
+iterations, we just return the last played sample.
 
-Later a new algorithm was created using a normal distributed random
-number for the sample selection with the mean controlled by the input
-velocity and the stddev calculated on the number of samples in the
-instrument as well as their power span.
 {\tiny\begin{verbatim}
            stddev
                  \ ________                _________________
                   /        \              /  nearest power  \
 -- input note --> | random | -- power --> | sample selector | -- sample -->
      [0; 1]       \________/              \_________________/
+                 /
+             mean
 \end{verbatim}}
 In order to make this new algorithm the power of each sample must be
 present along with the sample data.
 
-\todobent{Again, write this algorithm in psudocode syntax.}
-
-
-In both algorithms, to prevent the same sample to be selected twice in a row, a
-re-selection is being performed whenever the selected sample is the
-same as the last one selected up to a maximum number of times.
-This is being stored per instrument.
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%