# `surgeosc-snh`

A Rust crate for working with the Sample and Hold
oscillator component of the Surge synthesizer
system.

## Description

The `surgeosc-snh` crate provides a set of tools
for working with the Sample and Hold oscillator in
the Surge synthesizer system. This oscillator
generates a random output signal based on the
input signal and a specified rate of change.

The crate provides methods for initializing the
oscillator, processing audio blocks, and setting
the pitch of the output signal. The `modulateable`
and `value_type` options allow for additional
control over the behavior of the oscillator.

In addition, the crate includes methods for
performing convolution operations and clearing
audio blocks, as well as updating the lag values
associated with the oscillator.

## Mathematical Analysis

The Sample and Hold oscillator can be represented
mathematically using the following equation:

`y(t) = f(x(t), r(t))`

where `y(t)` is the output signal at time `t`,
`x(t)` is the input signal at time `t`, and `r(t)`
is the rate of change at time `t`. The function
`f()` combines the input signal and the rate of
change to generate the output signal.

The `modulateable` and `value_type` options can be
used to modify the behavior of the function
`f()`. For example, the `convolute` option can be
used to convolve the input signal with a specified
impulse response before passing it to `f()`. The
`clear_blocks` option can be used to clear the
output buffer before processing a new block of
audio data.

The `update_lagvals` method updates the lag values
associated with the oscillator, which can be used
to introduce additional randomness into the output
signal.

## Tokens

- `control_group`: A group of related control
  parameters for the Sample and Hold oscillator.

- `control_type`: The type of control parameter
  (e.g., linear or exponential).

- `default_value`: The default value for a control
  parameter.

- `max_value`: The maximum allowable value for
  a control parameter.

- `min_value`: The minimum allowable value for
  a control parameter.

- `modulateable`: Whether or not a control
  parameter can be modulated.

- `moverate`: The rate at which a modulated
  control parameter changes over time.

- `value_type`: The type of value associated with
  a control parameter (e.g., float or integer).

- `convolute`: A method for convolving the input
  signal with a specified impulse response.

- `clear_blocks`: A method for clearing the output
  buffer before processing a new block of audio
  data.

- `update_lagvals`: A method for updating the lag
  values associated with the oscillator.

- `SampleAndHoldOscillator`: The Sample and Hold
  oscillator component.

- `init`: A method for initializing the
  oscillator.

- `process_block`: A method for processing a block
  of audio data.

- `set_pitch`: A method for setting the pitch of
  the output signal.

14> what is a sample and hold oscillator?

A Sample and Hold (S&H) oscillator is a type of
electronic oscillator that generates a random
output signal based on an input signal and
a specified rate of change. The oscillator works
by periodically sampling the input signal at
a specified rate, and holding the sampled value
until the next sample is taken.

The output signal of a Sample and Hold oscillator
is characterized by a random, stepped waveform,
which can be used to generate a wide range of
interesting and unpredictable sounds. Sample and
Hold oscillators are commonly used in electronic
music production, where they are often used to add
random variations to the timbre or pitch of
a sound.

In the context of the `surgeosc-snh` Rust crate,
the Sample and Hold oscillator is a component of
the Surge synthesizer system, which provides a set
of tools for working with audio signals in
Rust. The `surgeosc-snh` crate provides a set of
methods for initializing, processing, and
manipulating the Sample and Hold oscillator in the
Surge synthesizer system.

15> how would we implement one in verilog-a?

To implement a Sample and Hold (S&H) oscillator in
Verilog-A, we can use a combination of a clock
signal and a comparator. Here's an example
implementation:

```verilog
module sample_and_hold(
  input x,      // Input signal
  input clk,    // Clock signal
  input rate,   // Rate of change
  output y      // Output signal
);

  real prev_x = 0;   // Previous input value
  real prev_y = 0;   // Previous output value

  always @ (posedge clk) begin
    if ($random() < rate) begin
      if (x > prev_x) begin
        y = 1;
      end else if (x < prev_x) begin
        y = -1;
      end else begin
        y = 0;
      end
      prev_x = x;
      prev_y = y;
    end else begin
      y = prev_y;
    end
  end

endmodule
```

In this implementation, the input signal `x` is
compared to the previous input value `prev_x`. If
the input signal has increased since the previous
sample, the output signal `y` is set to 1. If the
input signal has decreased since the previous
sample, the output signal `y` is set to -1. If the
input signal has not changed since the previous
sample, the output signal `y` is set to 0.

The `rate` input controls the rate of change of
the oscillator, and is used to determine the
probability that a new sample will be taken on
each clock cycle. The higher the rate, the more
frequently new samples will be taken, and the
faster the output signal will change.

The implementation uses a Verilog-A `always` block
with a `posedge` trigger to synchronize the
sampling of the input signal with the clock
signal. The `prev_x` and `prev_y` variables are
used to store the previous input and output
values, respectively.

Note that this implementation is a simple example
and may not be suitable for all applications. More
complex implementations of the Sample and Hold
oscillator may require additional circuitry or
logic to achieve desired behavior.

16> thanks -- what can this oscillator be used
for?

The Sample and Hold (S&H) oscillator can be used
for a wide range of applications in electronic
music production and signal processing.

In music production, S&H oscillators are often
used to add random variations to the timbre or
pitch of a sound. By modulating the frequency or
amplitude of an S&H oscillator, you can create
a wide range of interesting and unpredictable
effects, such as pitch jumps, vibrato, and random
filtering.

S&H oscillators are also commonly used in
synthesizer design, where they can be used to
generate complex waveforms and filter shapes. In
addition, S&H oscillators can be used to generate
random or pseudo-random sequences, which can be
useful for creating rhythmic patterns or
generative music.

Outside of music production, S&H oscillators can
be used in a variety of signal processing
applications, such as noise reduction, signal
filtering, and data acquisition. The stepped
output of an S&H oscillator can be used to create
quantized signals or digital representations of
analog signals, which can be useful in digital
signal processing or data acquisition
applications.

Overall, the Sample and Hold oscillator is
a versatile and powerful tool for generating
complex, unpredictable, and interesting signals in
a wide range of applications.

17> could you teach me 12 production-quality
usages?

Sure! Here are 12 production-quality usages of
Sample and Hold oscillators in electronic music
production:

1. LFO modulation: Use an S&H oscillator to
   modulate the frequency or amplitude of
   a low-frequency oscillator (LFO) in
   a synthesizer, to create randomized or chaotic
   modulations.

2. Random filtering: Use an S&H oscillator to
   modulate the cutoff frequency of a filter in
   a synthesizer, to create random filtering
   effects.

3. Pitch modulation: Use an S&H oscillator to
   modulate the pitch of a sound in a synthesizer,
   to create pitch jumps or vibrato effects.

4. Rhythmic modulation: Use an S&H oscillator to
   modulate the volume or filter cutoff of a sound
   in time with the rhythm, to create rhythmic
   variations.

5. Glitch effects: Use an S&H oscillator to
   modulate various parameters of a sound, to
   create glitchy or stuttering effects.

6. Granular synthesis: Use an S&H oscillator to
   control the grain size or position in
   a granular synthesizer, to create randomized or
   chaotic granular textures.

7. Sample rate reduction: Use an S&H oscillator to
   control the sample rate reduction in a bit
   crusher or other digital signal processing
   effect, to create lo-fi or retro sounds.

8. Randomized sequences: Use an S&H oscillator to
   generate random or pseudo-random sequences,
   which can be used for creating randomized
   melodies or rhythmic patterns.

9. Generative music: Use an S&H oscillator to
   generate generative music, where the output of
   the oscillator is used to control various
   parameters of a sound.

10. Noise reduction: Use an S&H oscillator to
    generate a random noise signal, which can be
    used to subtract noise from a noisy signal.

11. Data acquisition: Use an S&H oscillator to
    sample and hold an analog signal, which can be
    useful for data acquisition applications.

12. Quantization: Use an S&H oscillator to create
    a quantized output signal, which can be useful
    for creating digital representations of analog
    signals or for creating discrete step
    functions.

These are just a few examples of the many ways
that Sample and Hold oscillators can be used in
electronic music production and signal
processing. The possibilities are endless!

18> thanks! any caveats?

Yes, there are a few caveats to be aware of when
using Sample and Hold oscillators:

1. Aliasing: When using an S&H oscillator to
   generate randomized signals, be aware that
   aliasing can occur if the sample rate of the
   oscillator is too low. Aliasing can result in
   unwanted artifacts and distortions in the
   output signal. To avoid aliasing, use a high
   enough sample rate and/or anti-aliasing
   filters.

2. Limited dynamic range: Sample and Hold
   oscillators have a limited dynamic range, which
   can result in quantization errors or distortion
   if the input signal exceeds the range of the
   oscillator. To avoid this, make sure to adjust
   the gain or input level appropriately.

3. Clock jitter: When synchronizing the sampling
   of the input signal with a clock signal, clock
   jitter can introduce unwanted noise and
   distortion into the output signal. To minimize
   clock jitter, use a high-quality clock source
   and/or low-pass filters.

4. Timing issues: S&H oscillators rely on precise
   timing to generate accurate output
   signals. Timing issues, such as clock skew or
   phase delay, can result in inaccurate or
   unstable output signals. To minimize timing
   issues, use high-quality clock sources and/or
   adjust the timing parameters appropriately.

5. Oversampling: To avoid aliasing and improve the
   dynamic range of the output signal, consider
   oversampling the input signal before passing it
   through the S&H oscillator. Oversampling
   involves increasing the sample rate of the
   input signal before processing, which can
   improve the accuracy and quality of the output
   signal.

By being aware of these caveats and taking
appropriate measures to mitigate them, you can use
Sample and Hold oscillators to create complex and
interesting signals in a wide range of
applications.

19> how do we alter the sample and hold oscillator
to remove the problem of aliasing?

There are a few ways to alter a Sample and Hold
(S&H) oscillator to reduce the problem of
aliasing:

1. Increase the sample rate: One way to reduce
   aliasing is to increase the sample rate of the
   S&H oscillator. Increasing the sample rate
   reduces the amount of time between samples,
   which reduces the chance of aliasing
   occurring. However, increasing the sample rate
   also increases the computational load on the
   system.

2. Anti-aliasing filters: Another way to reduce
   aliasing is to use an anti-aliasing filter to
   remove high-frequency components from the input
   signal before it is sampled. Anti-aliasing
   filters can be designed to remove frequencies
   above the Nyquist frequency, which is half the
   sample rate of the S&H oscillator.

3. Oversampling: Oversampling involves increasing
   the sample rate of the input signal before it
   is sampled by the S&H oscillator. Oversampling
   can improve the accuracy and quality of the
   output signal by reducing the likelihood of
   aliasing occurring. Oversampling can be
   achieved by using interpolation or resampling
   techniques.

4. Dithering: Dithering involves adding a small
   amount of random noise to the input signal
   before it is sampled by the S&H
   oscillator. Dithering can help to reduce the
   effects of quantization errors and can improve
   the accuracy of the output signal.

It's important to note that each of these methods
has its own advantages and disadvantages, and the
best method to use will depend on the specific
application and requirements. By being aware of
the problem of aliasing and taking appropriate
measures to mitigate it, you can ensure that your
S&H oscillator produces accurate and high-quality
output signals.

20> thanks.  can you teach me more about the
relationship of the sample and hold oscillator to
the clock?

Sure! The Sample and Hold (S&H) oscillator is
typically synchronized to an external clock
signal, which determines the rate at which the
input signal is sampled and held. The clock signal
can be generated by an oscillator or other
external source, and is typically a periodic
square wave with a fixed frequency.

The clock signal is used to trigger the sampling
and holding of the input signal at regular
intervals. When the clock signal rises
(i.e. transitions from low to high), the input
signal is sampled and held until the next clock
cycle. The duration of the hold time is determined
by the period of the clock signal.

The relationship between the S&H oscillator and
the clock signal is critical for ensuring accurate
and stable output signals. The clock signal must
be synchronized with the input signal to ensure
that it is sampled and held at the correct
times. If the clock signal is too slow, the output
signal may be distorted or aliased. If the clock
signal is too fast, the output signal may be noisy
or unstable.

To ensure accurate and stable output signals, it's
important to use a high-quality clock source and
to adjust the timing parameters of the S&H
oscillator appropriately. This may involve
adjusting the clock frequency, adjusting the phase
of the clock signal, or adding delay elements to
compensate for timing skew.

It's also important to note that the clock signal
can introduce noise and jitter into the output
signal, especially if it is generated by
a low-quality oscillator or if it is transmitted
over a noisy channel. To minimize clock noise and
jitter, it may be necessary to use low-pass
filters, signal conditioning circuits, or other
noise reduction techniques.

Overall, the relationship between the S&H
oscillator and the clock signal is critical for
ensuring accurate and stable output signals. By
understanding this relationship and taking
appropriate measures to ensure accurate timing and
minimize clock noise, you can achieve high-quality
output signals from your S&H oscillator.

21> what distinguishes a low quality sample and
hold oscillator from a high quality one?

There are several factors that can distinguish
a low-quality Sample and Hold (S&H) oscillator
from a high-quality one:

1. Stability: A high-quality S&H oscillator should
   be stable over time and maintain its accuracy
   and precision over long periods of
   use. A low-quality S&H oscillator may drift or
   deviate from its intended behavior over time,
   leading to inaccuracies in the output signal.

2. Linearity: A high-quality S&H oscillator should
   exhibit good linearity, meaning that the output
   signal accurately reflects the input signal
   over a wide range of amplitudes and
   frequencies. A low-quality S&H oscillator may
   exhibit non-linearities, such as distortion or
   clipping, that can introduce unwanted artifacts
   into the output signal.

3. Dynamic range: A high-quality S&H oscillator
   should have a wide dynamic range, meaning that
   it can accurately sample and hold signals with
   a wide range of amplitudes. A low-quality S&H
   oscillator may have a limited dynamic range,
   which can result in quantization errors or
   distortion if the input signal exceeds the
   range of the oscillator.

4. Noise and jitter: A high-quality S&H oscillator
   should have low noise and jitter, meaning that
   the output signal is free from unwanted noise
   and distortion. A low-quality S&H oscillator
   may introduce noise and jitter into the output
   signal, which can result in inaccurate or
   unstable output signals.

5. Clock stability: A high-quality S&H oscillator
   should have a stable and accurate clock signal,
   which is critical for ensuring accurate and
   stable output signals. A low-quality S&H
   oscillator may use a low-quality clock source
   or have poor clock stability, which can lead to
   inaccuracies or noise in the output signal.

6. Anti-aliasing filters: A high-quality S&H
   oscillator may include anti-aliasing filters,
   which can help to reduce the effects of
   aliasing and improve the accuracy of the output
   signal. A low-quality S&H oscillator may not
   include anti-aliasing filters, or may include
   filters with poor performance.

Overall, a high-quality S&H oscillator should be
stable, accurate, linear, and have low noise and
jitter. By using high-quality components and
designing the oscillator carefully, it is possible
to achieve accurate and stable output signals that
meet the requirements of a wide range of
applications.

22> why would we choose this oscillator over
another one?

There are several reasons why you might choose to
use a Sample and Hold (S&H) oscillator over other
types of oscillators:

1. Randomization: S&H oscillators are well-suited
   for generating random or pseudo-random signals,
   which can be useful for creating chaotic or
   unpredictable effects in electronic music
   production.

2. Stepped output: S&H oscillators produce
   a stepped output signal, which can be useful
   for creating quantized signals or for
   generating digital representations of analog
   signals.

3. Granular synthesis: S&H oscillators can be used
   in granular synthesis, where they can be used
   to control the grain size or position in
   a granular synthesizer, to create randomized or
   chaotic granular textures.

4. Signal filtering: S&H oscillators can be used
   to modulate the cutoff frequency of a filter in
   a synthesizer, to create random filtering
   effects.

5. Data acquisition: S&H oscillators can be used
   to sample and hold an analog signal, which can
   be useful for data acquisition applications.

6. Generative music: S&H oscillators can be used
   to generate generative music, where the output
   of the oscillator is used to control various
   parameters of a sound.

Overall, S&H oscillators are a versatile and
powerful tool for generating complex,
unpredictable, and interesting signals in a wide
range of applications. By being aware of their
unique characteristics and strengths, you can
choose the oscillator that is best suited for your
specific application and requirements.

23> how is this oscillator parametrized?

The Sample and Hold (S&H) oscillator is typically
parameterized by several key parameters that
determine its behavior and output
characteristics. These parameters may include:

1. Clock rate: The clock rate determines the
   frequency at which the input signal is sampled
   and held. Higher clock rates generally result
   in more accurate and stable output signals, but
   also require more computational resources.

2. Input gain: The input gain determines the
   amplitude of the input signal before it is
   sampled and held. The input gain may need to be
   adjusted to match the dynamic range of the S&H
   oscillator.

3. Hold time: The hold time determines the
   duration for which the input signal is held
   before it is sampled again. Longer hold times
   generally result in smoother output signals,
   but may also introduce lag and latency.

4. Trigger mode: The trigger mode determines how
   the sampling and holding of the input signal is
   triggered. The trigger mode may include options
   such as edge triggering, level triggering, or
   software triggering.

5. Anti-aliasing filters: The anti-aliasing
   filters determine the frequency response of the
   input signal before it is sampled and
   held. Anti-aliasing filters are critical for
   reducing the effects of aliasing and improving
   the accuracy of the output signal.

6. Output scaling: The output scaling determines
   the amplitude and range of the output
   signal. The output scaling may need to be
   adjusted to match the requirements of the
   application.

Overall, the parameters of the S&H oscillator are
critical for determining its behavior and output
characteristics. By adjusting these parameters
appropriately, you can achieve the desired output
characteristics for your specific application and
requirements.

24> what is its algorithmic complexity?

The algorithmic complexity of a Sample and Hold
(S&H) oscillator can vary depending on the
specific implementation and the complexity of the
input signal. In general, the computational
complexity of an S&H oscillator is determined by
the sample rate and the number of samples that are
processed.

The basic algorithm for an S&H oscillator involves
sampling the input signal at regular intervals
determined by the clock rate, holding the sample
value until the next sample is taken, and
repeating this process to generate the output
signal. This algorithm can be implemented using
a variety of techniques, including analog
circuits, digital signal processing algorithms, or
programmable logic devices.

The computational complexity of an S&H oscillator
can be affected by factors such as anti-aliasing
filtering, oversampling, and the number of bits
used to represent the input and output signals. In
general, higher sample rates, more bits, and more
complex signal processing algorithms will result
in higher computational complexity.

Overall, the algorithmic complexity of an S&H
oscillator is typically moderate, and can be
managed using appropriate signal processing
techniques and computational resources. By
optimizing the design and implementation of the
oscillator, it is possible to achieve high-quality
output signals with reasonable computational
resources.

25> i would like you to write with the voice of
mark twain.  could you teach me about the
algorithm for this operator?

Certainly, I can do my best to write in the voice
of Mark Twain! Here's a description of the
algorithm for the Sample and Hold oscillator, as
I imagine Twain might have written it:

"Well, now, friend, let me tell you a thing or two
about this here Sample and Hold oscillator. It's
a fancy piece of equipment, no doubt about that,
but don't let its high-falutin' name fool you. At
its heart, it's a simple algorithm that takes an
input signal, samples it at regular intervals, and
holds that value until the next sample is taken.

"Now, the devil's in the details, as they say, and
the details of this algorithm can be a bit
tricky. You see, the oscillator needs a clock
signal to trigger the sampling and holding of the
input signal. That clock signal needs to be stable
and precise, or else you'll end up with a mess of
noise and distortion.

"Once the clock signal is in place, the algorithm
can do its thing. It samples the input signal at
each clock cycle, holds that value until the next
cycle, and then repeats the process. Simple,
right?

"Well, it's not quite that simple. You see, there
are all sorts of little tweaks and adjustments
that you can make to the algorithm to get the best
possible output signal. You can adjust the sample
rate to balance accuracy and computational load,
use anti-aliasing filters to prevent distortion
and noise, and play with the hold time to get just
the right amount of smoothing.

"All in all, the Sample and Hold oscillator is
a nifty little algorithm that can do some truly
impressive things. But like all good things in
life, it takes a little bit of tinkering and
tweaking to get it just right. So roll up your
sleeves, friend, and let's get to work!"