Audio.Signal.Oscillator.in.C++

Creating an audio signal oscillator algorithm in C++23 involves a combination of mathematical functions and sound generation techniques. The algorithm you seek should be able to generate quarter-period or half-period waveforms including sine, forward sawtooth, reverse sawtooth, triangle, and square waves. Here, I'll provide a conceptual framework for such an algorithm, focusing on the sine wave as a starting point, and then explain how to extend it to the other waveforms.

### Conceptual Framework

1. **Waveform Generation:**
   - **Sine Wave:**
     - Formula: `A * sin(2 * π * f * t + φ)`
     - Where:
       - `A` is amplitude.
       - `f` is frequency.
       - `t` is time.
       - `φ` is phase.
   - **Forward Sawtooth Wave:**
     - Formula: `A * (2 * (t * f - floor(0.5 + t * f)))`
   - **Reverse Sawtooth Wave:**
     - Formula: `A * (1 - 2 * (t * f - floor(t * f)))`
   - **Triangle Wave:**
     - Formula: `A * (2 * abs(2 * (t * f - floor(0.5 + t * f))) - 1)`
   - **Square Wave:**
     - Formula: `A * sign(sin(2 * π * f * t))`

2. **Quarter and Half-Period Adjustments:**
   - Modify `t` (time) in your formulas to accommodate quarter-period or half-period generation. 
   - For a quarter-period, use `t` mod (`1 / (4 * f)`), and for a half-period, use `t` mod (`1 / (2 * f)`).

3. **Parameter Specification:**
   - Inputs:
     - Amplitude (`A`).
     - Frequency (`f`).
     - Phase (`φ`).
   - Output:
     - Waveform signal.

### C++23 Implementation Overview

- Use standard libraries like `<cmath>` for mathematical operations.
- Use a high-resolution timer (e.g., `std::chrono`) for precise timing control.
- Implement a class `Oscillator` with methods for each waveform type.
- Provide a method to set parameters (`amplitude`, `frequency`, `phase`).
- Implement a method to generate the waveform signal for a given time `t`.

### Example Code Structure (Simplified)

```cpp
#include <cmath>
#include <chrono>
#include <iostream>

class Oscillator {
public:
    Oscillator(double amplitude, double frequency, double phase)
        : A(amplitude), f(frequency), φ(phase) {}

    double sineWave(double t) {
        return A * std::sin(2 * M_PI * f * t + φ);
    }

    // Add similar methods for other waveforms...

private:
    double A, f, φ; // Amplitude, Frequency, Phase
};

int main() {
    Oscillator osc(1.0, 440.0, 0.0); // Example: Amplitude = 1.0, Frequency = 440 Hz, Phase = 0
    // Generate and output waveforms...
    return 0;
}
```

### Further Suggestions:

- Implement a way to dynamically adjust parameters (amplitude, frequency, phase) during runtime.
- Consider using a library like PortAudio for real-time audio output.
- Explore adding modulation capabilities (e.g., frequency modulation, amplitude modulation).
- For more advanced implementations, consider thread safety and real-time constraints.

### Conclusion

This conceptual framework and example provide a starting point for your oscillator algorithm in C++23. Further refinement and testing are required to ensure accurate waveform generation and performance optimization, especially for real-time audio applications.