8 min readTech Blog
Nikola Sonic using C++ Programming Language
Implementing Tesla's sonic frequency theories in C++ for high-performance audio processing and signal analysis applications.
Introduction.
Nikola Tesla's experiments with sonic frequencies revealed patterns that modern audio processing can harness. C++ provides the performance necessary to implement these theories in real-time applications, from audio synthesis to signal processing.
Disclaimer: The code examples provided in this article are for demonstration purposes only. They illustrate how frequency band concepts work within programming environments. The actual implementation code for these functions is proprietary to NGEK TECH.
The Sonic Foundation.
Tesla Frequency Generator.
#include <cmath>
#include <vector>
#include <array>
namespace NikolaSonic {
// Tesla's sacred frequencies.
constexpr std::array<double, 3> TESLA_FREQUENCIES = {3.0, 6.0, 9.0};
constexpr double BASE_FREQUENCY = 369.0; // Tesla's fundamental.
class TeslaOscillator {
private:
double frequency_;
double phase_;
double sampleRate_;
public:
explicit TeslaOscillator(double sampleRate = 44100.0)
: frequency_(BASE_FREQUENCY)
, phase_(0.0)
, sampleRate_(sampleRate) {}
void setFrequency(double freq) {
// Snap to nearest Tesla harmonic.
double nearest = freq;
for (auto teslaFreq : TESLA_FREQUENCIES) {
double harmonic = BASE_FREQUENCY * teslaFreq;
if (std::abs(freq - harmonic) < 10.0) {
nearest = harmonic;
break;
}
}
frequency_ = nearest;
}
double generate() {
// Tesla wave: combination of sine and resonance.
double sample = std::sin(phase_);
// Add Tesla resonance harmonics.
sample += 0.3 * std::sin(phase_ * 3.0); // Third harmonic.
sample += 0.2 * std::sin(phase_ * 6.0); // Sixth harmonic.
sample += 0.1 * std::sin(phase_ * 9.0); // Ninth harmonic.
// Normalise.
sample /= 1.6;
// Advance phase.
phase_ += 2.0 * M_PI * frequency_ / sampleRate_;
if (phase_ > 2.0 * M_PI) {
phase_ -= 2.0 * M_PI;
}
return sample;
}
};
} // namespace NikolaSonic.
Resonance Buffer.
#include <memory>
#include <algorithm>
namespace NikolaSonic {
template<typename T, size_t TeslaMultiple = 9>
class ResonanceBuffer {
private:
std::vector<T> buffer_;
size_t writePos_;
size_t readPos_;
// Ensure buffer size is Tesla-aligned.
static constexpr size_t alignToTesla(size_t size) {
return ((size + TeslaMultiple - 1) / TeslaMultiple) * TeslaMultiple;
}
public:
explicit ResonanceBuffer(size_t requestedSize)
: buffer_(alignToTesla(requestedSize))
, writePos_(0)
, readPos_(0) {}
void write(const T& value) {
buffer_[writePos_] = value;
writePos_ = (writePos_ + 1) % buffer_.size();
}
T read() {
T value = buffer_[readPos_];
readPos_ = (readPos_ + 1) % buffer_.size();
return value;
}
// Tesla resonance read - averages across harmonic positions.
T resonantRead() {
T sum = T{};
size_t count = 0;
for (size_t i = 0; i < buffer_.size(); i += 3) {
sum += buffer_[(readPos_ + i) % buffer_.size()];
count++;
}
return sum / static_cast<T>(count);
}
size_t size() const { return buffer_.size(); }
size_t teslaFactor() const { return buffer_.size() / TeslaMultiple; }
};
} // namespace NikolaSonic.
Signal Processing.
Tesla Filter Implementation.
#include <complex>
namespace NikolaSonic {
class TeslaFilter {
private:
double coefficients_[9]; // 9 coefficients (Tesla's number).
double history_[9];
int historyIndex_;
void calculateCoefficients(double cutoff, double sampleRate) {
// Tesla-weighted FIR filter coefficients.
double normalised = cutoff / sampleRate;
for (int i = 0; i < 9; ++i) {
// Apply Tesla weighting (3, 6, 9 pattern).
double teslaWeight = 1.0;
if ((i + 1) % 3 == 0) teslaWeight = 3.0;
if ((i + 1) % 6 == 0) teslaWeight = 2.0;
if ((i + 1) % 9 == 0) teslaWeight = 1.5;
// Sinc function with Tesla modulation.
double x = M_PI * (i - 4) * normalised * 2.0;
if (std::abs(x) < 1e-10) {
coefficients_[i] = normalised * 2.0 * teslaWeight;
} else {
coefficients_[i] = std::sin(x) / x * teslaWeight;
}
}
// Normalise coefficients.
double sum = 0.0;
for (int i = 0; i < 9; ++i) {
sum += coefficients_[i];
}
for (int i = 0; i < 9; ++i) {
coefficients_[i] /= sum;
}
}
public:
TeslaFilter(double cutoff, double sampleRate)
: historyIndex_(0) {
std::fill(std::begin(history_), std::end(history_), 0.0);
calculateCoefficients(cutoff, sampleRate);
}
double process(double input) {
history_[historyIndex_] = input;
double output = 0.0;
for (int i = 0; i < 9; ++i) {
int index = (historyIndex_ - i + 9) % 9;
output += history_[index] * coefficients_[i];
}
historyIndex_ = (historyIndex_ + 1) % 9;
return output;
}
};
} // namespace NikolaSonic.
FFT with Tesla Windowing.
#include <complex>
#include <vector>
namespace NikolaSonic {
class TeslaFFT {
private:
size_t size_;
std::vector<std::complex<double>> twiddles_;
void computeTwiddles() {
twiddles_.resize(size_);
for (size_t i = 0; i < size_; ++i) {
double angle = -2.0 * M_PI * i / size_;
// Tesla modulation on twiddle factors.
double teslaModulation = 1.0;
if (i % 3 == 0) teslaModulation = 1.03;
if (i % 6 == 0) teslaModulation = 1.06;
if (i % 9 == 0) teslaModulation = 1.09;
twiddles_[i] = std::polar(teslaModulation, angle);
}
}
public:
explicit TeslaFFT(size_t size) : size_(size) {
// Ensure size is Tesla-aligned.
if (size_ % 9 != 0) {
size_ = ((size_ / 9) + 1) * 9;
}
computeTwiddles();
}
std::vector<double> teslaWindow(size_t length) const {
std::vector<double> window(length);
for (size_t i = 0; i < length; ++i) {
// Tesla window: modified Hann with 3-6-9 harmonics.
double base = 0.5 * (1.0 - std::cos(2.0 * M_PI * i / (length - 1)));
// Add Tesla harmonic components.
double tesla3 = 0.1 * std::cos(6.0 * M_PI * i / (length - 1));
double tesla6 = 0.05 * std::cos(12.0 * M_PI * i / (length - 1));
double tesla9 = 0.025 * std::cos(18.0 * M_PI * i / (length - 1));
window[i] = base + tesla3 + tesla6 + tesla9;
}
return window;
}
void transform(std::vector<std::complex<double>>& data) const {
// Bit-reversal permutation.
size_t n = data.size();
for (size_t i = 1, j = 0; i < n; ++i) {
size_t bit = n >> 1;
while (j & bit) {
j ^= bit;
bit >>= 1;
}
j ^= bit;
if (i < j) {
std::swap(data[i], data[j]);
}
}
// Cooley-Tukey with Tesla twiddles.
for (size_t len = 2; len <= n; len <<= 1) {
for (size_t i = 0; i < n; i += len) {
for (size_t j = 0; j < len / 2; ++j) {
auto t = twiddles_[j * n / len] * data[i + j + len / 2];
data[i + j + len / 2] = data[i + j] - t;
data[i + j] = data[i + j] + t;
}
}
}
}
};
} // namespace NikolaSonic.
Audio Synthesis.
Tesla Synthesiser.
#include <functional>
#include <map>
namespace NikolaSonic {
class TeslaSynthesiser {
public:
enum class WaveType {
Tesla369, // Pure Tesla harmonic.
Resonant, // Resonance-based.
Harmonic, // Full harmonic series.
Pulse369 // Pulse wave with Tesla duty cycles.
};
private:
struct Voice {
double phase = 0.0;
double frequency = 0.0;
double amplitude = 0.0;
bool active = false;
};
std::array<Voice, 9> voices_; // 9 voices (Tesla's number).
double sampleRate_;
WaveType waveType_;
double generateTesla369(double phase) const {
return std::sin(phase)
+ 0.333 * std::sin(phase * 3.0)
+ 0.166 * std::sin(phase * 6.0)
+ 0.111 * std::sin(phase * 9.0);
}
double generateResonant(double phase) const {
double base = std::sin(phase);
double resonance = std::sin(phase * 369.0 / 100.0);
return base * (1.0 + 0.3 * resonance);
}
double generateHarmonic(double phase) const {
double sum = 0.0;
for (int h = 1; h <= 9; ++h) {
double amplitude = (h % 3 == 0) ? 1.0 / h : 0.5 / h;
sum += amplitude * std::sin(phase * h);
}
return sum;
}
double generatePulse369(double phase) const {
// Duty cycle based on Tesla numbers.
double normPhase = std::fmod(phase, 2.0 * M_PI) / (2.0 * M_PI);
double duty = 0.369; // 36.9% duty cycle.
return normPhase < duty ? 1.0 : -1.0;
}
public:
explicit TeslaSynthesiser(double sampleRate = 44100.0)
: sampleRate_(sampleRate)
, waveType_(WaveType::Tesla369) {}
void setWaveType(WaveType type) { waveType_ = type; }
void noteOn(int voiceIndex, double frequency, double amplitude) {
if (voiceIndex < 0 || voiceIndex >= 9) return;
voices_[voiceIndex].frequency = frequency;
voices_[voiceIndex].amplitude = amplitude;
voices_[voiceIndex].active = true;
}
void noteOff(int voiceIndex) {
if (voiceIndex < 0 || voiceIndex >= 9) return;
voices_[voiceIndex].active = false;
}
double render() {
double output = 0.0;
for (auto& voice : voices_) {
if (!voice.active) continue;
double sample = 0.0;
switch (waveType_) {
case WaveType::Tesla369:
sample = generateTesla369(voice.phase);
break;
case WaveType::Resonant:
sample = generateResonant(voice.phase);
break;
case WaveType::Harmonic:
sample = generateHarmonic(voice.phase);
break;
case WaveType::Pulse369:
sample = generatePulse369(voice.phase);
break;
}
output += sample * voice.amplitude;
voice.phase += 2.0 * M_PI * voice.frequency / sampleRate_;
if (voice.phase > 2.0 * M_PI) {
voice.phase -= 2.0 * M_PI;
}
}
// Normalise by Tesla factor.
return output / 3.0;
}
};
} // namespace NikolaSonic.
Real-Time Processing.
Audio Callback System.
#include <atomic>
#include <thread>
namespace NikolaSonic {
class TeslaAudioEngine {
private:
TeslaSynthesiser synth_;
TeslaFilter filter_;
ResonanceBuffer<double, 9> buffer_;
std::atomic<bool> running_;
public:
TeslaAudioEngine(double sampleRate = 44100.0)
: synth_(sampleRate)
, filter_(10000.0, sampleRate)
, buffer_(static_cast<size_t>(sampleRate / 10)) // 100ms buffer.
, running_(false) {}
void audioCallback(double* output, size_t frames) {
for (size_t i = 0; i < frames; ++i) {
// Generate.
double sample = synth_.render();
// Filter.
sample = filter_.process(sample);
// Buffer for resonance analysis.
buffer_.write(sample);
// Output.
output[i] = sample;
}
}
double getResonanceLevel() {
return buffer_.resonantRead();
}
TeslaSynthesiser& synth() { return synth_; }
};
} // namespace NikolaSonic.
Guardrails for Sonic C++.
- Buffer Sizes. Always use buffer sizes divisible by 9.
- Memory Alignment. Align audio buffers to Tesla multiples for cache efficiency.
- Thread Safety. Use lock-free structures for real-time audio.
- Frequency Precision. Use double precision for frequency calculations.
Conclusion.
Nikola Sonic brings Tesla's frequency theories into the realm of C++ audio programming. The combination of Tesla's 3-6-9 harmonic principles with C++'s performance characteristics creates a powerful framework for audio synthesis and signal processing applications.
Sonic research conducted by NGEK TECH's Audio Engineering Division.