surgefilter-snh

The surgefilter-snh crate is a Rust library containing a filter based on the Sample and Hold Noise (SNH) technique.

SNH Filter

The SNH filter generates a noise signal that is updated at a fixed frequency and held constant between updates. This noise signal is then multiplied with the input signal to produce the filtered output. The effect of the SNH filter can be varied by changing the frequency of the noise signal.

Mathematical Analysis

The SNH filter can be represented by the following equation:

output(t) = input(t) * snh(t)

where snh(t) is the noise signal at time t. The SNH filter can be implemented using the direct form II topology, and the coefficients for the filter can be generated using the coeff_make function provided in the surgefilter-snh crate.

Tokens

• SnhFilter: The main struct representing the SNH filter.

• coeff_make: A function for generating the filter coefficients.

• process_quad: A function for processing a block of audio using the SNH filter.

Usage

To use the SNH filter in your Rust project, simply add surgefilter-snh as a dependency in your Cargo.toml file:

[dependencies]
surgefilter-snh = "0.1"

Then, import the crate and use the SnhFilter struct to create a new SNH filter. You can generate the filter coefficients using the coeff_make function and then use the process_quad function to process audio data in blocks.

use surgefilter_snh::{SnhFilter, coeff_make, process_quad};

fn main() {
    // Create a new SNH filter with a noise frequency of 10 Hz
    let noise_frequency = 10.0;
    let mut snh_filter = SnhFilter::new(coeff_make(noise_frequency));

    // Process audio data in blocks
    let block_size = 512;
    let mut input_buffer = vec![0.0; block_size];
    let mut output_buffer = vec![0.0; block_size];
    loop {
        // Fill the input buffer with audio data
        // ...

        // Process the input buffer using the SNH filter
        process_quad(&mut input_buffer, &mut output_buffer, &mut snh_filter);

        // Do something with the output buffer
        // ...
    }
}

101> thanks -- could you please teach me the sample and hold noise function?

Sure, I can explain sample and hold noise function (S&H).

In analog circuits, a sample and hold (S&H) circuit is used to sample an analog signal at a specific point in time and then hold that sample for a certain period. The S&H function is often used to convert continuous analog signals into discrete digital signals.

In a typical S&H circuit, a switch is used to connect a capacitor to the input signal. The capacitor charges up to the input voltage level and is then disconnected from the input signal by the switch. The capacitor then holds the sampled voltage level until the switch is closed again to take a new sample.

The noise in the S&H circuit can come from various sources, such as the switch itself or the input signal itself. To model this noise in a digital system, a random number generator can be used to simulate the noise.

In the SnhFilter crate, the S&H noise function is implemented using a uniform distribution random number generator. The output signal is held for a certain amount of time, determined by the sample rate and the sample and hold time, before being updated with a new sample.

The S&H noise function is useful for generating random noise signals or for modulating other signals in a random way.

102> could show block diagram?

Sure, here's a block diagram of a basic Sample and Hold circuit:

         +---------+
Vin ---->|         |
         | Sample  |----> Vout
Clock--->| and Hold|
         |         |
Gnd ---->|         |
         +---------+

The input voltage Vin is sampled and held at the output voltage Vout for a certain period of time, determined by the clock signal. The clock signal triggers the Sample and Hold circuit to sample the input voltage at a specific moment, and then holds that voltage level until the next clock pulse. The holding capacitor is charged to the sampled voltage and discharges slowly over time.

In a Sample and Hold Noise circuit, the voltage held by the capacitor can be corrupted by noise. The SNH filter is used to reduce this noise.

103> could show subcomponents in block diagram?

Sure, here is a block diagram of the SNH filter, with subcomponents labeled:

               +------------------------+
               |                        |
      +--------|+                      |
      |        |  |                     |
      |        |  |  +--------+         |
      |        |  |  |        |         |
      |        |  |  |  Hold  |         |
      |        |  |  |        |         |
      |        |  |  +--------+         |
      |        |  |       |             |
      |        |  |    +-----+          |
      |        |  |    |     |          |
      |        |  |  +-|+   +|-+        |
      |        |  |  | |     | |        |
      |        |  |  | +-----+ |        |
      |        |  |  |    D    |        |
      |        |  |  |        |        |
      |        |  |  +--------+        |
      |        |  |                     |
      |        |  |      v(t)           |
      |        |  |      +---------+   |
      |        |  |      |         |   |
      |        |  +------|+        |   |
      |        |         | Sample  |   |
      |        |         |         |   |
      |        |         +--------|+  |
      |        |                  ||  |
      |        |              +---||--+|
      |        |              | +---+   |
      |        |              |         |
      |        |              | Quant   |
      |        |              |         |
      |        |              +---------+
      |        |
      |        |               v(t+T)
      |        |         +----------------+
      |        |         |                |
      |        +---------|+              |
      |                  |  Delay Line   |
      |                  |              |
      |                  +--------------+
      |                          |
      |                          |
      |                          |
      |                          |
      |                          |
      |                          |
      +--------------------------+

The subcomponents of the SNH filter are:

• Sample & Hold: This module samples the input signal at periodic intervals and holds the value until the next sample. The output signal is a staircase waveform that approximates the input signal.

• Quantizer: This module discretizes the staircase waveform output by the sample and hold module into a finite number of levels. This is done by comparing the input signal to a set of thresholds, which divide the input signal into equal-sized intervals.

• Delay Line: This module delays the quantized output of the quantizer by a specified time period. The delayed signal is then subtracted from the quantized output to produce the SNH output signal.

The SNH filter is a type of non-linear filter, as the quantization step introduces non-linearities into the output signal. The SNH filter is commonly used in synthesizers to generate random or pseudo-random signals for modulation or other purposes.

104> could show equations more?

Certainly! Here are the equations for the SNH filter:

Let x(t) be the input signal to the SNH filter, and y(t) be the output signal. Let T be the sample and hold time, and let f_s be the sampling frequency.

The SNH filter can be implemented as follows:

y(t) = x(kT), for kT ≤ t < (k+1)T y(t) = y(kT), for (k+1)T ≤ t < (k+2)T

This equation describes a step function that samples the input signal at multiples of the sample and hold time. The output signal is held constant between sample times.

This can be implemented in discrete time as follows:

y[n] = x[k], for k ≤ n < k + M y[n] = y[k], for k + M ≤ n < k + 2M

where M = T * f_s is the number of samples in one sample and hold period.

To implement this in code, we can use a modulo operator to check if the current sample index is within the sample and hold window, and then either sample the input signal or hold the previous output signal:

let mut y = vec![0.0; x.len()];
let mut prev_y = 0.0;
let mut index = 0;

for n in 0..x.len() {
    if n % M == 0 {
        prev_y = x[n];
        index = n;
    }
    if index <= n && n < index + M {
        y[n] = prev_y;
    } else if n >= index + M {
        prev_y = y[n - M];
        y[n] = prev_y;
        index = n;
    }
}

This code loops through each sample of the input signal x, and checks if the current index is within the sample and hold window. If it is, the previous output signal prev_y is held as the current output signal y. If it is not, the previous output signal is updated to the output signal from M samples ago, and the current output signal is set to that value.

I hope that helps!

105> any caveats?

There are a few caveats to keep in mind when using the SNH filter:

1. The SNH filter introduces noise into the signal. While this can be a desirable effect in some cases, it may not always be appropriate for certain applications.

2. The amplitude of the noise introduced by the SNH filter is proportional to the rate at which the signal changes. This means that if the input signal changes rapidly, the noise introduced by the filter will be larger, potentially leading to undesirable artifacts in the output signal.

3. The SNH filter can be sensitive to the sampling rate of the input signal. In some cases, this can result in aliasing or other artifacts in the output signal.

4. The SNH filter may not be suitable for use in certain applications where high precision or accuracy is required, as the noise introduced by the filter can be unpredictable and difficult to control.

5. Finally, it is important to note that while the SNH filter can be a powerful tool for creating unique and interesting sounds, it should always be used in a thoughtful and intentional manner to avoid unwanted noise or other artifacts in the output signal.

106> any usage techniques?

Sure! Here are some usage techniques for the SnhFilter:

1. Use it to create sample-and-hold effects: The SnhFilter is great for creating sample-and-hold effects in your audio signal. You can use it to sample the input signal at regular intervals, and then hold the sampled value until the next sample is taken. This can create interesting rhythmic effects or can be used to add a bit of randomness to your signal.

2. Experiment with different sampling rates: The sampling rate of the SnhFilter determines how often the input signal is sampled. Experiment with different sampling rates to achieve different effects. Higher sampling rates will result in more detail in the sampled signal, while lower sampling rates will produce a more coarse signal.

3. Use it in combination with other filters: The SnhFilter can be used in combination with other filters to achieve more complex effects. Try chaining the SnhFilter with other filters, such as a low-pass or high-pass filter, to create more interesting sounds.

4. Use it as a modulation source: The SnhFilter can also be used as a modulation source. You can modulate the sampling rate or the amplitude of the sampled signal to create dynamic changes in your sound.

5. Be aware of aliasing: When using the SnhFilter, be aware of the potential for aliasing. Aliasing can occur when the sampling rate is too low and results in unwanted artifacts in the output signal. To avoid aliasing, make sure the sampling rate is high enough to capture the detail in the input signal.

107> how to break?

I'm sorry, but I'm not sure what you're asking. Could you please clarify your question?

108> possible to break snh filter?

It is possible to break any filter if the input signal is beyond its operating range or if the filter parameters are set in such a way that they cause numerical instability or overflow. However, if the input signal is within the normal operating range and the filter parameters are set correctly, the SNH filter should function properly without breaking.

109> any edge cases?

In general, edge cases for the SNH filter arise when the input signal to the filter changes rapidly or unexpectedly. When the input signal changes too quickly or jumps erratically, the output of the filter can be unpredictable and may result in unwanted noise or distortion. It is also possible for the filter to generate unwanted noise or distortion if the sample rate of the incoming signal is too low, as the filter may not be able to accurately track the changes in the input signal. It is important to consider the dynamic range of the input signal and adjust the filter parameters accordingly to ensure the best possible performance.

110> what about fast scrubbing?

When the user rapidly changes the control value being sampled, it can cause issues with the SNH filter because it does not have enough time to sample enough values to produce an accurate output. This can result in undesirable artifacts such as stepping and quantization noise. To mitigate this issue, one approach is to use a slew limiter to smooth out the changes in the control signal and limit the rate of change. Another approach is to use a different type of filter that is better suited for rapidly changing signals, such as a one-pole low-pass filter or a comb filter.

111> what about scrubbing near poles?

Scrubbing near poles can cause instability in the SNH filter, resulting in unpredictable output behavior. To avoid this, it is recommended to avoid scrubbing near poles, or to implement pole-zero cancellation techniques in the design of the filter.

112> what about scrubbing near edges?

Scrubbing near the edges of the sample and hold noise function may lead to aliasing, where high-frequency components are incorrectly represented as lower-frequency components. This can result in unwanted distortion and noise in the output signal. It is generally advisable to avoid scrubbing near the edges of the function and to use appropriate filtering techniques to reduce aliasing.

113> what applications?

The SNH filter can be used in a variety of applications in digital signal processing, such as audio effects processing, data smoothing and filtering, and control systems. Specifically, it is often used to introduce noise or randomness into a signal, which can be useful for creating unique sounds or adding character to a recording. It can also be used for smoothing out data, such as in sensor data processing, or for filtering out unwanted noise in a control system.

114> please show?

Unfortunately, I cannot provide an example of an application without further context about what you are looking for. Could you please provide more information or clarify your question?

115> sample and hold technique applications

The sample and hold technique has various applications, some of which are:

1. Analog-to-digital conversion: Sample and hold circuits are often used in analog-to-digital converters to sample the analog signal and hold it long enough to be converted into a digital signal.

2. Pulse width modulation: Sample and hold circuits can be used in pulse width modulation (PWM) to maintain the pulse width for a certain period of time.

3. Signal processing: Sample and hold circuits can be used in signal processing to freeze the value of a signal at a particular instant for further processing.

4. Synthesizer and audio processing: Sample and hold circuits can be used in synthesizers and audio processing to generate a stepped waveform or to introduce randomness into a signal.

5. Image processing: Sample and hold circuits can be used in image processing to capture and store the image data for further processing.

6. Communication systems: Sample and hold circuits can be used in communication systems to capture and hold the signal before processing it.

These are just a few examples of the applications of sample and hold circuits. The technique is widely used in various fields of engineering and technology.

116> more please!

Sure, here are some additional applications of sample and hold techniques:

1. Analog-to-Digital Conversion: Sample and hold circuits are commonly used in analog-to-digital converters (ADCs) to hold a voltage steady during the conversion process. The input voltage is sampled and held for a brief period of time, allowing it to be accurately measured by the ADC.

2. Communication Systems: Sample and hold circuits are used in communication systems to capture analog signals and convert them into digital signals. This is commonly used in digital communication systems like Wi-Fi, Bluetooth, and cellular networks.

3. Audio Processing: Sample and hold circuits are used in audio processing applications to create effects like portamento and glissando, which involve smoothly changing the pitch of an audio signal.

4. Image Processing: Sample and hold circuits are used in image processing applications to capture the brightness or color of individual pixels in an image.

5. Control Systems: Sample and hold circuits are used in control systems to take samples of a system's output and use them to adjust the input signals. This is commonly used in feedback control systems, where the output of the system is compared to a desired value and adjustments are made to the input signals to bring the output closer to the desired value.

6. Sensor Applications: Sample and hold circuits are used in sensor applications to capture analog signals from sensors like temperature sensors, pressure sensors, and strain gauges. The sampled signals can be processed to extract useful information about the system being monitored.

117> wahoo! thank you :)

You're welcome! If you have any more questions, feel free to ask.