Lib.rs

Note

This contains an adaptation of the filter found at: https://ccrma.stanford.edu/~jatin/ComplexNonlinearities/NLFeedback.html

with coefficient calculation from: https://webaudio.github.io/Audio-EQ-Cookbook/audio-eq-cookbook.html

NonlinearFeedbackFilter

The NonlinearFeedbackFilter is an IIR filter that uses nonlinear feedback to create complex, interesting distortion effects. The filter is designed to be used in audio processing applications such as music synthesis, audio effects processing, and sound design.

The filter is implemented using a feedback loop that includes a nonlinear distortion element, which introduces harmonic distortion and other nonlinear effects into the audio signal. The exact nature of the distortion element can be controlled by adjusting the filter coefficients and other parameters.

The NonlinearFeedbackFilter is implemented as a Rust struct that exposes a set of methods for configuring and processing audio signals. The filter can be used in real-time audio processing applications or in offline audio processing workflows.

Mathematical Analysis

The NonlinearFeedbackFilter is an IIR filter, which means that it uses feedback to create a resonant response to certain frequencies in the audio signal. The filter is implemented as a set of difference equations that describe the relationship between the input signal, the output signal, and the internal state of the filter. The equations can be expressed mathematically as:

y[n] = a0 * x[n] + a1 * x[n-1] + a2 * x[n-2] - b1 * y[n-1] - b2 * y[n-2]

where x[n] and y[n] represent the input and output signals at time n, and a0, a1, a2, b1, and b2 represent the filter coefficients.

The specific values of the filter coefficients determine the frequency response and distortion characteristics of the filter. The coeff_make method can be used to generate filter coefficients for a given cutoff frequency and resonance value.

Token Descriptions

• C: This token represents the value of the feedback capacitance in the filter circuit. The value of C affects the resonance and frequency response of the filter.

• R: This token represents the value of the feedback resistor in the filter circuit. The value of R affects the resonance and frequency response of the filter.

• clamped_frequency: This token represents a frequency value that has been clamped to a specific range. Clamping the frequency value ensures that it remains within a valid range for the filter.

• fastsin_ps: This token represents a fast implementation of the sine function that uses a polynomial approximation. The fastsin_ps function can be used to generate nonlinear distortion effects in the filter.

• ojd_waveshaper: This token represents a waveshaping function that can be used to generate distortion effects in the filter.

• ojd_waveshaper_ps: This token represents a fast implementation of the ojd_waveshaper function that uses a polynomial approximation.

• coeff_make: This token represents a method that generates filter coefficients for a given cutoff frequency and resonance value. The coeff_make method takes these values as input parameters and returns a set of filter coefficients.

• process_quad: This token represents a method that processes a quad of samples using the filter. The process_quad method takes four input samples and returns four output samples.

END

44> thanks! what is a nonlinear feedback filter?

A nonlinear feedback filter is an IIR (infinite impulse response) filter that uses a nonlinear feedback loop to introduce nonlinear distortion and other interesting effects into an audio signal. Unlike traditional linear feedback filters, which rely solely on the principle of resonance to shape the frequency response of the signal, nonlinear feedback filters also use nonlinear effects to create complex harmonic and subharmonic content.

The exact nature of the nonlinear distortion introduced by the feedback loop can be controlled by adjusting the filter coefficients and other parameters. In some cases, the feedback loop may include a distortion element such as a waveshaper or a clipping circuit, which further modifies the signal.

Nonlinear feedback filters are often used in audio processing applications such as music synthesis, audio effects processing, and sound design. They can be used to create a wide range of interesting and unique sounds, from subtle harmonic enhancement to extreme distortion and saturation.

45> /file surge-rs/surgefilter-nlfeedback/src/process.rs

Certainly! This code implements the process_quad() function for the NonlinearFeedbackFilter struct. The purpose of this function is to apply the filter to an input signal, producing an output signal that has been shaped by the nonlinear feedback loop of the filter.

The function begins by initializing the input signal and extracting some parameters from the filter state. The stages variable determines the number of filter stages to apply, while the sat variable selects the type of saturator to use in the feedback loop.

The function then iterates through each filter stage, applying the filter coefficients and feedback loop at each stage. For each stage, the function calculates the filter output using the current filter state and input signal, and then applies the nonlinear feedback loop using the selected saturator function.

After applying the nonlinear feedback, the function updates the filter state for the current stage, storing the calculated values for the next iteration. The output signal is then scaled by a makeup coefficient, which is applied to each filter stage.

Finally, the function applies any changes to the filter coefficients that have been made since the last call to process_quad(), and returns the output signal.

Overall, the process_quad() function implements the core signal processing functionality of the NonlinearFeedbackFilter struct, applying a configurable number of filter stages and nonlinear feedback loops to the input signal to produce a shaped output signal.

46> /file surge-rs/surgefilter-nlfeedback/src/coeff.rs

Sure, let me explain the coeff_make function in more detail. This function takes in the frequency and resonance values and returns an array of coefficients used by the filter's process_quad function.

First, the resonance value is limited to the range of 0 to 1. Then, the function calculates the number of stages and selects the appropriate saturator function based on the comb write position.

Next, it calculates the quality factor (Q) based on the resonance value. Then, it calculates the normalized frequency and the cutoff frequency. It also calculates the sine and cosine of the cutoff frequency, which are used later in the function.

The function then calculates the alpha value, which is used to calculate the feedback coefficients. The reciprocal of a0 is calculated, as it is used to normalize the other coefficients.

Depending on the type of filter, the function calculates different coefficients. For example, for a low-pass filter, it calculates the b0, b1, and b2 coefficients based on the normalized frequency and cosine of the cutoff frequency. It also calculates a makeup gain based on the resonance value, the normalized frequency, and a normalization factor.

Once all the coefficients are calculated, they are stored in an array and returned. These coefficients are used in the process_quad function to process the audio signal.

I hope that helps!

47> /file surge-rs/surgefilter-nlfeedback/src/nlff.rs

This is the definition of the NonlinearFeedbackFilter struct.

It is a struct that contains an adaptation of the filter found at https://ccrma.stanford.edu/~jatin/ComplexNonlinearities/NLFeedback.html with coefficient calculation from https://webaudio.github.io/Audio-EQ-Cookbook/audio-eq-cookbook.html.

The struct has the following fields:

• tuner: a handle to a Tuner object used to calculate the frequency of the filter

• srunit: a handle to a SampleRate object used to calculate the sample rate

• ty: an NLFFType object representing the type of the filter (low-pass, high-pass, band-pass, notch, or all-pass)

• subty: a FilterSubType object representing the subtype of the filter (used to select the saturator)

The struct also has the following methods:

• clamped_frequency: a method that takes a pitch value and returns the clamped frequency of the filter within a certain range

• fastsin_ps: a method that applies a fast sine function to each element of a __m128 vector by breaking it into floats and reassembling

• ojd_waveshaper: a method that applies a custom waveshaper function to a single float value

• ojd_waveshaper_ps: a method that applies the custom waveshaper function to each element of a __m128 vector by breaking it into floats and reassembling

Overall, the NonlinearFeedbackFilter struct represents a complex filter that combines nonlinear feedback with various types of saturators to achieve a desired sound.

48> thanks! could you teach me more about the mathematical concepts involved in this crate?

Sure! The Nonlinear Feedback Filter crate implements a nonlinear digital filter with feedback. Let me explain the key mathematical concepts involved in this process:

1. Nonlinear filters: Nonlinear filters modify an input signal based on nonlinear functions, which can be much more complex than simple linear filters. Nonlinear filters are often used for creative sound synthesis and sound design, as they can create complex and interesting harmonic structures.

2. Feedback: Feedback is a process in which a portion of the output of a system is fed back into the input, to modify the system's behavior. Feedback can have both positive and negative effects, depending on the system and the feedback loop design.

3. Coefficient calculation: Coefficient calculation is the process of determining the filter coefficients, which determine the behavior of the filter. In the Nonlinear Feedback Filter crate, the coefficients are calculated based on the desired frequency and resonance of the filter, using the formulas from the Audio EQ Cookbook.

4. Saturators: A saturator is a type of nonlinear function that can be used to create distortion and other interesting effects. In the Nonlinear Feedback Filter crate, the filter uses different types of saturators to modify the feedback signal.

5. SIMD: SIMD (Single Instruction Multiple Data) is a technique for processing multiple data elements in parallel, using a single instruction. The Nonlinear Feedback Filter crate uses SIMD instructions to process multiple samples simultaneously, improving performance and efficiency.

These are just a few of the mathematical concepts involved in the Nonlinear Feedback Filter crate. Let me know if you have any further questions!

49> thanks! what are some others?

Here are some additional mathematical concepts that may be relevant to the surgefilter-nlfeedback crate:

• Biquad filters: NonlinearFeedbackFilter implements a biquad filter, which is a type of digital filter commonly used in audio signal processing. A biquad filter consists of two poles and two zeros, and can be used to implement various types of filters, such as low-pass, high-pass, band-pass, and notch filters. The coefficients of the biquad filter determine the frequency response of the filter, and can be calculated using various design methods.

• Saturators: NonlinearFeedbackFilter also implements several saturators, which are nonlinear functions that can be used to distort or clip an input signal. Saturators can be used to create various types of distortion effects in audio processing, such as overdrive, fuzz, and distortion. The nonlinear behavior of saturators can be described using various mathematical models, such as piecewise-linear models, exponential models, and polynomial models.

• Frequency response: The frequency response of a filter is the relationship between the input and output signals at different frequencies. The frequency response of a filter can be represented using various graphical and mathematical representations, such as magnitude response, phase response, frequency response curves, transfer functions, and pole-zero plots. The frequency response of a filter is determined by its design and coefficient values.

• Trigonometric functions: NonlinearFeedbackFilter uses various trigonometric functions, such as sine and cosine, to calculate the coefficients of the filter and to implement some of the saturators. Trigonometric functions are mathematical functions that relate the angles and sides of triangles, and are used in various areas of mathematics and science, such as geometry, calculus, physics, and engineering.

• Digital signal processing: NonlinearFeedbackFilter is a digital filter, which means that it operates on discrete-time signals. Digital signal processing is the branch of signal processing that deals with the analysis, manipulation, and synthesis of discrete-time signals using digital computers. Digital signal processing techniques are used in various areas of science and engineering, such as audio and video processing, telecommunications, control systems, and biomedical signal processing.

50> ok, great! thanks for your help!

You're welcome! Don't hesitate to ask if you have any more questions.