SurgeTables: Waveshaping and Envelope Utilities for the Surge Synthesizer System
SurgeTables is a Rust crate that provides a variety of waveshaping, envelope, and sinc tables for the Surge Synthesizer System. It includes utilities for generating and accessing tables, as well as mathematical functions to support synthesis operations.
SurgeTables is a collection of tables and utilities used in the Surge Synthesizer System, supporting various waveshaping, envelope, and sinc operations. The crate is divided into several subcomponents, each focusing on a specific aspect of sound synthesis.
SineTables contains precomputed sine wave values
for efficient lookup during synthesis. These sine
wave values are stored in different formats, such
as f32, f64, and i16.
WaveshapeTables provides tables and utilities for
waveshaping synthesis. Waveshaping is a nonlinear
distortion technique used to modify the harmonic
content of a signal. It supports functions such as
lookup_waveshape and lookup_waveshape_warp for
accessing these tables and applying the desired
transformations.
GainTables provides utilities for converting
between decibel (dB) and linear scales, as well as
functions for applying clipping and scaling to
audio signals. The db_to_linear function, for
example, converts a decibel value to its
corresponding linear gain value:
linear_gain = 10^(dB/20)
EnvelopeTables provides tables and functions for
handling the linear and low-pass filtered (LPF)
envelope rates in the synthesizer. The
envelope_rate_linear and envelope_rate_lpf
functions provide utilities for controlling these
rates.
SincTables contains tables and utilities for
windowed sinc functions, which are used for
resampling and other signal processing tasks. The
windowed_sinc function generates a sinc function
windowed by a specified window function:
windowed_sinc(x) = sinc(x) * window_function(x)
where sinc(x) = sin(πx) / (πx) for x ≠ 0 and
sinc(0) = 1.
These types provide a convenient way to handle and manage the lifetime of the tables created by the various subcomponents in the crate.
With SurgeTables, users can efficiently access and manipulate a variety of tables and mathematical functions to support the waveshaping, envelope, and sinc operations in the Surge Synthesizer System.
2> /file surge-rs/surge-tables/src/envelope.rs
EnvelopeTables
What is this table used for?
The EnvelopeTables struct contains two
tables: table_envrate_lpf and
table_envrate_linear. These tables are used
for efficient lookup of envelope rates in the
Surge Synthesizer System. The envelope rates
determine how quickly an envelope progresses
through its stages (attack, decay, sustain,
release) and are crucial for shaping the
amplitude and timbre of a synthesized sound.
Which calculations are involved in the precomputation?
The precomputation involves the calculation of two tables:
table_envrate_lpf: This table contains
values related to the low-pass filtered (LPF)
envelope rates. The precomputation involves
an exponential decay calculation with a time
constant based on the sample rate and
a power-of-two mapping.
table_envrate_linear: This table contains
values related to the linear envelope
rates. The precomputation involves a simple
division by the time constant based on the
sample rate and a power-of-two mapping.
How much performance are we saving?
By precomputing these envelope rate values and storing them in tables, we save performance by avoiding the need to recalculate these values in real-time during the synthesis process. This can lead to significant performance improvements, especially when dealing with complex synthesizer patches and polyphony.
How can we improve this table?
Some possible improvements to the
EnvelopeTables include:
Interpolation: The current implementation uses linear interpolation to access the table values. Other interpolation methods, such as cubic or spline interpolation, could provide more accurate results at the cost of additional complexity.
Adaptive table size: The current implementation uses a fixed table size of
Alternative precomputation methods: Exploring different methods for generating the envelope rate values in the precomputation step could lead to more accurate or faster results. This may involve using different mathematical approximations or algorithms for the exponential decay and linear rate calculations.
3> /file surge-rs/surge-tables/src/gain.rs
GainTables
What is this table used for?
The GainTables struct contains a table called
table_db, which is used for efficient
conversion between decibel (dB) and linear
scales. This is useful for operations involving
gain, attenuation, or other processes where
logarithmic scales are involved. The table also
provides a clipscale function to calculate
the scaling factor depending on the filter
subtype (Rough or Smooth).
Which calculations are involved in the precomputation?
The precomputation involves the calculation of a single table:
table_db: This table contains values for
converting decibel values to linear gain
values. The precomputation involves
calculating the linear gain for a given dB
value using the formula: linear_gain
= 10^(0.05 * (dB - 384)).How much performance are we saving?
By precomputing these decibel-to-linear gain values and storing them in a table, we save performance by avoiding the need to recalculate these values in real-time during the synthesis process. This can lead to noticeable performance improvements, especially when processing audio signals that require frequent conversions between decibel and linear scales.
How can we improve this table?
Some possible improvements to the GainTables
include:
Interpolation: The current implementation uses linear interpolation to access the table values. Other interpolation methods, such as cubic or spline interpolation, could provide more accurate results at the cost of additional complexity.
Adaptive table size: The current implementation uses a fixed table size of
Additional gain-related functions: Expanding
the GainTables struct to include other
gain-related functions, such as
linear-to-decibel conversions or different
types of gain scaling, could make the table
more versatile and useful for a wider range
of audio processing tasks.
4> /file surge-rs/surge-tables/src/sinc.rs
SincTables
What is this table used for?
The SincTables struct contains three tables:
table, table_1x, and table_i16. These
tables store precomputed windowed sinc function
values, which are commonly used in digital
signal processing, particularly in
interpolation and resampling tasks. By
precomputing these values, the SincTables can
be used to perform efficient interpolation in
real-time audio processing.
Which calculations are involved in the precomputation?
The precomputation involves the calculation of three tables:
table: This table stores windowed sinc
function values for a specific cutoff
frequency cutoff.
table_1x: This table stores windowed sinc
function values for a different cutoff
frequency cutoff1x.
table_i16: This table stores windowed sinc
function values for another cutoff frequency
cutoff_i16, but in 16-bit integer format.
The precomputation calculates the windowed sinc function values using the following steps:
Calculate the time t for each table entry
using the get_table_t function.
Calculate the windowed sinc function value
using the windowed_sinc function, which
involves the product of a symmetric Blackman
window and the sinc function with the given
cutoff frequency.
Store the calculated values in the respective tables.
How much performance are we saving?
By precomputing the windowed sinc function values and storing them in tables, the performance of real-time audio processing tasks, such as interpolation and resampling, can be significantly improved. This is because the computationally expensive sinc and Blackman window calculations are avoided during real-time processing, and the precomputed values can be quickly accessed from the tables.
How can we improve this table?
Some possible improvements to the SincTables
include:
Adaptive table sizes: Allowing for user-defined table sizes could enable users to balance memory usage and lookup accuracy based on their specific needs.
Additional interpolation methods: Expanding
the SincTables struct to include other
interpolation methods could make the table
more versatile and useful for a wider range
of audio processing tasks.
Optimizing sinc and window functions: The current implementation calculates the windowed sinc values using standard Blackman window and sinc functions. Optimized versions of these functions, such as those found in specialized libraries, could potentially improve the accuracy or performance of the tables.
5> /file surge-rs/surge-tables/src/sine.rs
SineTables
What is this table used for?
The SineTables struct contains two tables:
table_sin and table_sin_offset. These
tables store precomputed sine function values
and their corresponding offsets. By
precomputing these values, the SineTables can
be used to perform efficient trigonometric
calculations, such as oscillations and
frequency modulation, in real-time audio
processing.
Which calculations are involved in the precomputation?
The precomputation involves the calculation of two tables:
table_sin: This table stores sine function
values for angles between 0 and 2π, uniformly
spaced with a step size of 2π
/ SIN_TABLE_SIZE_D.
table_sin_offset: This table stores the
difference between consecutive sine function
values in table_sin.
The precomputation calculates the sine function values and their offsets using the following steps:
Calculate the angle t for each table entry
as 2π * (i / SIN_TABLE_SIZE_D), where i is
the index of the entry.
Calculate the sine function value sin(t)
and store it in table_sin.
Calculate the sine function value `sin(t
and store the
difference between this value andsin(t)
intablesin_offset`.How much performance are we saving?
By precomputing the sine function values and their offsets and storing them in tables, the performance of real-time audio processing tasks that involve trigonometric calculations can be significantly improved. This is because the computationally expensive sine calculations are avoided during real-time processing, and the precomputed values can be quickly accessed from the tables.
How can we improve this table?
Some possible improvements to the SineTables
include:
Adaptive table sizes: Allowing for user-defined table sizes could enable users to balance memory usage and lookup accuracy based on their specific needs.
Additional trigonometric functions: Expanding
the SineTables struct to include other
trigonometric functions, such as cosine or
tangent, could make the table more versatile
and useful for a wider range of audio
processing tasks.
Optimizing sine function calculations: The current implementation calculates the sine values using the standard sine function. Optimized versions of these functions, such as those found in specialized libraries, could potentially improve the accuracy or performance of the tables.
6> /file surge-rs/surge-tables/src/waveshape.rs
WaveshapeTables
What is this table used for?
The WaveshapeTables struct contains a table
of precomputed waveshaping function values that
can be used to quickly modify the shape of
audio waveforms in real-time audio
processing. By using these precomputed values,
the performance of audio processing tasks
involving waveshaping can be significantly
improved.
Which waveshaping functions are included?
The WaveshapeTables struct includes
precomputed values for five different
waveshaping functions:
wst_tanh: Hyperbolic tangent function.
wst_hard: A hard clipping function, based
on the fifth power of the absolute value of
x, followed by a hyperbolic tangent and
a power of 0.2.
wst_asym: An asymmetric waveshaping
function using the "shafted_tanh" function,
which is shifted by 0.5.
wst_sine: Sine function.
wst_digi: A digital-style waveshaping
function using the hyperbolic tangent
function with a different scaling factor.
How much performance are we saving?
By precomputing the waveshaping function values and storing them in tables, the performance of real-time audio processing tasks involving waveshaping can be significantly improved. This is because the computationally expensive waveshaping function calculations are avoided during real-time processing, and the precomputed values can be quickly accessed from the tables.
How can we improve this table?
Some possible improvements to the
WaveshapeTables include:
Adaptive table sizes: Allowing for user-defined table sizes could enable users to balance memory usage and lookup accuracy based on their specific needs.
Additional waveshaping functions: Expanding
the WaveshapeTables struct to include more
waveshaping functions could make the table
more versatile and useful for a wider range
of audio processing tasks.
Optimizing waveshaping function calculations: The current implementation calculates the waveshaping function values using standard functions. Optimized versions of these functions, such as those found in specialized libraries, could potentially improve the accuracy or performance of the tables.
Interpolation: Implementing interpolation between table entries could improve the accuracy of the waveshaping functions when using the lookup methods.