surgeosc-sine: A Sine Wave Oscillator for the Surge Synthesizer System

A simple and efficient sine wave oscillator for audio synthesis in the Surge synthesizer system.

Overview

The surgeosc-sine crate provides a sine wave oscillator as a subcomponent of the Surge synthesizer system. It generates a pure sine wave signal, which is a fundamental building block for audio synthesis and sound design. The oscillator can be modulated and combined with other audio components to create complex sounds and textures.

Mathematical Properties

The sine wave oscillator is based on the sine function, which is defined as:

y(t) = A * sin(2 * π * f * t + φ)

where:

• A is the amplitude
• f is the frequency
• t is time
• φ is the phase

The sine wave is a smooth, continuous waveform that oscillates between positive and negative values. It represents the simplest type of audio waveform and is the basis for many other waveforms and synthesis techniques.

Features and Implementation

The SineWaveOscillator struct contains various control parameters and methods for generating and processing sine wave audio signals.

Tokens and their associated mathematical ideas:

• process_block_legacy: Processes a block of audio samples using the sine wave oscillator, handling streaming mismatches if necessary.

• handle_streaming_mismatches: Ensures proper handling of streaming mismatches by adapting the internal state of the oscillator.

• value_from_sin_and_cos: Calculates the output value of the sine wave oscillator using the sine and cosine values at the current phase.

• do_sine_block: Processes a single sine wave audio sample.

• smoke: (No associated mathematical idea)

• init: Initializes the sine wave oscillator with default parameter values.

• process_block: Processes a block of audio samples using the sine wave oscillator.

Control parameters:

• control_group: Groups related control parameters for easier organization and management.

• control_type: Defines the type of control for a given parameter (e.g., continuous, discrete, etc.).

• default_value: Specifies the default value for a control parameter.

• max_value: Defines the maximum allowed value for a control parameter.

• min_value: Defines the minimum allowed value for a control parameter.

• modulateable: Indicates if a control parameter can be modulated by other audio components (e.g., LFOs, envelopes, etc.).

• moverate: Determines the rate at which a control parameter can be changed or modulated.

• value_type: Specifies the data type of a control parameter (e.g., integer, float, etc.).

The surgeosc-sine crate offers a lightweight and efficient sine wave oscillator, which can be used as a foundation for more complex audio synthesis and sound design in the Surge synthesizer system.

The SineWaveOscillator is an audio oscillator that generates a sine wave output based on the input parameters. Here's a step-by-step breakdown of how the oscillator works:

1. The process_block method is called with a configuration OscillatorProcessBlockCfg containing the required parameters such as pitch, drift, stereo, frequency modulation (fm), and fm_depth. If the oscillator is set to use the legacy processing method (FMBehavior parameter), it calls process_block_legacy and returns early.

2. The oscillator generates a drift noise (self.driftlfo1) using the drift_noise function and the self.driftlfo2 value.

3. The oscillator calculates the angular frequency (omega) based on the input pitch and drift, using the pitch2omega method of the self.tuner object. The value of omega is clamped to be no greater than PI.

4. The oscillator updates the fm_depth parameter using the provided fm_depth value, and sets the feedback value based on the SineWaveOscillatorParam::Feedback parameter.

5. For each sample in the block (BLOCK_SIZE_OS), the oscillator calls the do_sine_block method, which performs the following steps:

   a. The oscillator retrieves the master oscillator value for the current sample k.

   b. It computes the phase p by adding the current phase, the last output value, and, if frequency modulation is enabled, the product of fm_depth and the master oscillator value.

   c. The output value for the current sample is computed using the value_from_sin_and_cos function, which calculates the sine wave output based on the sine and cosine values of the phase p and the waveform shape mode (wf_mode).

   d. The oscillator updates the phase by adding omega and updates the last output value based on the current output value and the feedback value.

   e. The oscillator processes the fm_depth and feedback parameters for the next iteration.

6. If the cfg.stereo flag is set, the oscillator duplicates the output channel to create a stereo output.

The SineWaveOscillator generates a sine wave output that can be modulated and combined with other audio components to create more complex sounds and textures. The frequency modulation and feedback features allow for additional control over the oscillator's output, enabling a wide range of sonic possibilities.

19> thanks -- what else can you teach me about this oscillator? what about their mathematical properties?

The SineWaveOscillator relies on the fundamental properties of sine waves and their generation. Let's dive deeper into the mathematical properties of this oscillator.

1. Sine wave generation: The core of this oscillator is the generation of a sine wave. A sine wave is a continuous waveform that can be described by the mathematical function:

   y(t) = A * sin(2π * f * t + φ)

   where:

   • A is the amplitude
   • f is the frequency in Hz
   • t is time
   • φ is the phase

2. Angular frequency: The oscillator converts the frequency (pitch) into angular frequency (omega) using the following formula:

   ω = 2π * f

   The angular frequency represents the rate of change of the phase of the sine wave, measured in radians per second.

3. Phase: The phase of the sine wave determines the position of the waveform at any given time. The oscillator updates the phase based on the angular frequency and feedback to create the desired output. The phase is then used in conjunction with sine and cosine functions to compute the output value for each sample.

4. Frequency modulation: The oscillator supports frequency modulation (FM), a technique where the frequency of the sine wave is modulated by another signal (the master oscillator). In the SineWaveOscillator, the phase p is modified by adding the product of fm_depth and the master oscillator value. FM synthesis can create complex waveforms and timbres by altering the carrier frequency with a modulating signal.

5. Feedback: The feedback parameter allows the oscillator to incorporate its previous output value into the current output calculation. This can lead to the creation of more complex waveforms and introduces a form of recursion into the sine wave generation process.

These mathematical properties are the foundation of the SineWaveOscillator, allowing it to generate a wide range of sonic textures by controlling and modulating the sine wave. The oscillator can be further customized by adjusting parameters such as waveform shape mode, pitch, drift, stereo, and frequency modulation depth.

20> how does this algorithm compare to what we would find in a hardware function generator?

1. Signal generation: Hardware function generators, when generating sine waves, may use techniques such as Direct Digital Synthesis (DDS) or analog circuits like Wien Bridge or Phase Shift Oscillators. In contrast, software oscillators like the SineWaveOscillator generate signals using mathematical functions and algorithms that run on a digital processor.

2. Precision and stability: Hardware function generators can be affected by environmental factors such as temperature and component tolerances, leading to variations in frequency and amplitude stability. However, high-quality hardware function generators can offer good stability over a wide frequency range. Software oscillators are generally less susceptible to environmental factors and can provide more precise control over parameters like frequency, amplitude, and phase.

3. Flexibility: Software oscillators are more easily customizable and can offer a wide range of features and capabilities that may not be available or practical to implement in a hardware function generator. For example, software oscillators can support multiple waveform shapes, frequency modulation, and precise control over various parameters through software updates, while hardware function generators may require additional modules or options to achieve the same level of flexibility.

4. Signal processing: Hardware function generators generate signals directly in the analog domain or use digital-to-analog converters (DACs) if they rely on DDS techniques. Software oscillators generate signals in the digital domain, which then need to be converted to analog signals using a DAC. The conversion process can introduce quantization noise, aliasing, and other artifacts if not properly implemented. However, modern high-quality DACs can minimize these issues and provide high-fidelity output.

In summary, both hardware function generators and software oscillators are capable of generating sine waves, but they differ in the methods they use for signal generation, precision, flexibility, and signal processing. The choice between a hardware function generator and a software oscillator depends on factors such as the desired sound quality, flexibility, and the specific application in which the oscillator is used.

22> thanks -- could you teach me about direct digital synthesis? what about wien bridge or phase shift oscillators?

Certainly! Let's start with Direct Digital Synthesis (DDS) and then move on to Wien Bridge and Phase Shift Oscillators.

Direct Digital Synthesis (DDS):

DDS is a method of generating analog waveforms, such as sine waves, using digital techniques. A DDS system typically consists of a phase accumulator, a phase-to-amplitude converter (often a look-up table), and a digital-to-analog converter (DAC). The main idea behind DDS is to generate a digital representation of the desired waveform, which is then converted to an analog signal using a DAC. The key steps in the DDS process are:

1. A frequency control word (FCW) is added to the phase accumulator at a fixed clock rate. The FCW determines the output frequency of the waveform.

2. The output of the phase accumulator is used as an address to access the look-up table, which contains precomputed amplitude values for the desired waveform (e.g., a sine wave).

3. The amplitude value from the look-up table is sent to the DAC, which converts the digital amplitude value into an analog signal.

4. The analog signal is then filtered to remove high-frequency components introduced during the DAC conversion process.

DDS systems offer several advantages, such as high frequency resolution, rapid frequency switching, and precise control over phase and amplitude. However, they can be limited by the resolution and speed of the DAC and may introduce noise and distortion if not carefully designed.

Wien Bridge Oscillator:

A Wien Bridge Oscillator is a type of analog oscillator that generates sine waves using a combination of resistors, capacitors, and an operational amplifier (op-amp). The Wien Bridge Oscillator consists of a positive feedback loop and a negative feedback loop. The positive feedback loop provides the necessary phase shift for oscillation, while the negative feedback loop stabilizes the amplitude of the output signal.

The Wien Bridge Oscillator has the following characteristics:

1. It generates a low-distortion sine wave with good frequency stability.

2. The frequency of the output signal is determined by the values of the resistors and capacitors used in the circuit.

3. The amplitude of the output signal is stabilized using an automatic gain control (AGC) circuit, which is often implemented with a light-dependent resistor (LDR) or a field-effect transistor (FET).

Phase Shift Oscillator:

A Phase Shift Oscillator is another type of analog oscillator that generates sine waves using resistors, capacitors, and an amplifier (usually an op-amp or a transistor). The main idea behind a Phase Shift Oscillator is to create a phase shift of 180 degrees through a cascade of RC (resistor-capacitor) networks, which are connected to the inverting input of the amplifier. The amplifier itself provides an additional 180 degrees of phase shift, resulting in a total phase shift of 360 degrees, which is necessary for sustained oscillation.

The Phase Shift Oscillator has the following characteristics:

1. It generates a sine wave with relatively low distortion and good frequency stability.

2. The frequency of the output signal is determined by the values of the resistors and capacitors used in the RC networks.

3. The amplitude of the output signal is typically stabilized using a negative feedback loop or an AGC circuit.

In summary, DDS, Wien Bridge, and Phase Shift Oscillators are all methods of generating sine waves, but they differ in their underlying techniques, circuit components, and performance characteristics. DDS relies on digital techniques, while Wien Bridge and Phase Shift Oscillators use analog circuits to generate sine waves.

23> cool, thanks! could you show me how to write a DDS module in system-verilog?

Sure! Here's a simple example of a DDS module implemented in SystemVerilog. This example assumes a 32-bit phase accumulator, a 10-bit DAC, and an 8-bit frequency control word (FCW). The output sine wave will be represented by a 10-bit value, and the look-up table will contain 256 precomputed amplitude values.

module dds (
    input wire clk,
    input wire reset,
    input wire [7:0] fcw,
    output reg [9:0] dac_out
);

    reg [31:0] phase_accumulator;
    reg [31:0] phase_accumulator_next;
    reg [7:0] lut_address;
    reg [9:0] lut_data;

    // Precomputed sine wave amplitude values (256 points)
    reg [9:0] sine_lut [0:255] = '{
        // Add precomputed sine wave amplitude values here
    };

    always @(posedge clk or posedge reset) begin
        if (reset) begin
            phase_accumulator <= 32'h0;
        end else begin
            phase_accumulator <= phase_accumulator_next;
        end
    end

    always_comb begin
        phase_accumulator_next = phase_accumulator + (32'h0 | fcw);
        lut_address = phase_accumulator[23:16];
        lut_data = sine_lut[lut_address];
        dac_out = lut_data;
    end

endmodule

This code creates a DDS module with a 32-bit phase accumulator, which updates on every clock cycle by adding the frequency control word (FCW) to its current value. The most significant 8 bits of the phase accumulator are used as the address to access the look-up table (LUT) containing the precomputed sine wave amplitude values. The output of the LUT is then assigned to the dac_out signal, which represents the output of the DAC.

Keep in mind that this is a simple example, and real-world implementations might require additional features like phase or amplitude modulation, clock domain crossing, or filtering the output to remove high-frequency components. Also, you would need to fill the sine_lut array with the precomputed amplitude values of the sine wave for the desired number of points (256 in this case).

24> cool, thanks! could you also show me a wien bridge oscillator and a phase shift oscillator in verilog-a?

Certainly! Here's an example of a Wien Bridge Oscillator and a Phase Shift Oscillator implemented in Verilog-A.

Wien Bridge Oscillator:

`include "constants.vams"
`include "disciplines.vams"

module wien_bridge_oscillator (input, output);
    inout input;
    inout output;

    electrical input;
    electrical output;

    parameter real R1 = 10k;
    parameter real R2 = 10k;
    parameter real R3 = 10k;
    parameter real R4 = 10k;
    parameter real C1 = 10n;
    parameter real C2 = 10n;

    analog begin
        // Wien Bridge Oscillator
        V(input) <+ LaplaceAdmittance(1 / (R1 * (C1 + C2))) * V(output);
        V(input) <+ LaplaceAdmittance(1 / R2) * V(output);
        V(input) <+ LaplaceAdmittance(1 / R3) * V(output);
        V(output) <+ LaplaceAdmittance(1 / R4) * V(input);
        V(output) <+ LaplaceAdmittance(1 / C1) * V(input);
    end

endmodule

Phase Shift Oscillator:

`include "constants.vams"
`include "disciplines.vams"

module phase_shift_oscillator (input, output);
    inout input;
    inout output;

    electrical input;
    electrical output;

    parameter real R = 10k;
    parameter real C = 10n;
    parameter integer N = 3; // Number of RC stages

    analog begin
        // Phase Shift Oscillator
        V(input) <+ LaplaceAdmittance(1 / R) * V(output);
        for (integer i = 1; i <= N; i = i + 1) begin
            V(input) <+ LaplaceAdmittance(1 / (R * C * s)) * V(output);
        end
    end

endmodule

The Wien Bridge Oscillator example includes an implementation of the oscillator using Laplace admittances for the resistor and capacitor components. The oscillator frequency is determined by the values of the resistors and capacitors in the circuit.

The Phase Shift Oscillator example uses a similar approach, with Laplace admittances representing the RC stages. The N parameter sets the number of RC stages in the circuit, which affects the phase shift and frequency of oscillation.

Please note that Verilog-A is typically used for analog mixed-signal simulations and not for digital synthesis. These examples are meant for simulation purposes, and if you want to implement these oscillators in an FPGA or ASIC, you will need to use a different approach, such as a DDS or a PLL.

25> you mentioned that wien bridge and phase shift are typically analog circuits, which is why i asked for verilog-a. could you teach me about laplace admittances? are there any other ways of generating sine waves we use in hardware?