Wavefield-Core: The Foundation of Holophonic Sound

A Fastcomcorp Digital Audio Reference Implementation
Copyright © 2008–2025 Francisco F. Pinochet
Version 1.7.0 (Production Engine)

In the pursuit of perfect acoustic reconstruction, we often find ourselves limited by the systems of the past. While contemporary spatial audio standards have made remarkable strides in bringing immersive sound to the masses, Wavefield-Core represents a humble yet rigorous return to the mathematical roots of wavefield synthesis and high-order holophonic reproduction.

Built upon the Pinochet–Gerzon Law and the foundational 2008 Geometry System, Wavefield-Core is a portable C++ library designed to recreate sound fields with a level of physical accuracy that respects the true nature of propagation. This isn't just about "surround sound"—it's about the precise reconstruction of an acoustic hologram.

A New Standard of Precision

Where existing formats often cap at low orders of Ambisonics, Wavefield-Core provides a foundation that scales gracefully into high-order research domains. This is not a replacement for common standards, but an invitation to explore the scientific limits of what is possible. By prioritizing physical correctness through Near-Field Compensation (NFC-HOA) and scientifically derived speaker arrays, we provide a toolset that high-fidelity enthusiasts and professional audio engineers have been seeking: a way to step beyond the limitations of "points in space" and into a true holophonic reality.

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Key Features

• Pinochet–Gerzon Law: Native support for $(n+1)^2$ channel scaling.
• File Support: Native decoding for .fda files (32-bit Float RAW PCM/WAV).
• NFC-HOA: Near-Field Compensated radial filters for accurate distance perception.
• Binaural Rendering: High-quality virtual speaker downmix for headphones.
• Geometry Providers: Exact 2008 49-point sphere and generated Lebedev grids.
• Zero Dependencies: Pure C++17 (requires only standard math headers).

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The Pinochet–Gerzon Law

At the heart of Wavefield-Core is the Pinochet–Gerzon Law, a mathematical requirement for stable holophonic reconstruction. While traditional Ambisonics provides a general framework for spatial sound, the reconstruction of a physically accurate wavefield requires a specific density of information.

The law dictates that for a given Ambisonic order $n$, the minimum number of independent channels $C$ required for a complete spherical reconstruction is: $$C = (n+1)^2$$

Mathematical Stability & Spatial Aliasing

A key differentiator of Fastcomcorp's approach is the prevention of spatial aliasing. By adhering strictly to the Pinochet–Gerzon Law, the library ensures that the wavefronts reconstructed by the speaker array do not interfere destructively within the "sweet spot." This relationship ensures that the sound field remains physically stable across the entire listening area.

By adhering to this law, Wavefield-Core maintains the mathematical integrity established by Michael Gerzon while incorporating the practical geometry and radial filtering optimizations (NFC-HOA) developed by Francisco Pinochet.

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🛠 For Software Developers

Integration

Wavefield-Core uses CMake for easy integration.

# Add to your CMakeLists.txt
add_subdirectory(Wavefield-Core)
target_link_libraries(your_app PRIVATE wavefield_core)

Basic API Usage

The PlaybackEngine is the primary interface for decoding.

#include "include/FDA_PlaybackEngine.hpp"
#include "include/FDA_FormatParser.hpp"

// 1. Initialize engine (e.g., 6th order for .fda)
WavefieldCore::PlaybackEngine engine(6, 44100.0f);
engine.setDistance(2.0f); // Set listening distance

// 2. Decode Ambisonic buffer to Stereo (Binaural)
// ambisonicIn: interleaved floating point [frameCount * 49]
// stereoOut:   interleaved stereo [frameCount * 2]
engine.decodeBinaural(ambisonicIn, stereoOut, frameCount);

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🧪 Testing & Verification

To verify your environment, you can generate a test .fda file and play it using the included headless utility:

# 1. Build everything
mkdir build && cd build
cmake .. && make

# 2. Generate a 49-channel test file
./fda_generate_test

# 3. Decode it to stereo
./fda_play_headless test_49ch.fda

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🔌 For Hardware Developers (DSP/Embedded)

Portability & Performance

The library is designed with hardware constraints in mind:

• Optimized Binary: The core processing is compiled into a lightweight static library for maximum performance.
• Memory Footprint: The PlaybackEngine uses a pre-calculated decoding matrix to minimize run-time CPU cycles.
• Float32 Precision: Fully compatible with single-precision floating point units (FPUs) common in modern audio DSPs.

Tip

SIMD Optimization: You can accelerate the decoding loops in FDA_PlaybackEngine.cpp using platform-specific SIMD instructions (e.g., NEON, AVX) for high-order FDAX streams.

Hardware Mapping

To map decoded signals to physical speaker outputs, use m_speakerPositions to get the target coordinates:

auto positions = engine.getSpeakerPositions();
// Each position contains: .azimuth, .elevation, .radius

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📁 File Structure

• include/: Public API and headers.
• src/: Implementation of math and engines.
• examples/: Minimal headless playback utility.
• CMakeLists.txt: Build configuration.

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🔒 Proprietary Reference Implementation

Wavefield-Core is the proprietary reference library for FDA/FDAX playback. It is designed to provide authorized hardware and software distributors with a secure, high-performance interface for holophonic audio rendering.

This architecture enables both commercial hardware manufacturers and authorized open-source media players to integrate high-order FDA/FDAX support into their ecosystems.

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📜 Legal & Licensing

This software realizes the technical specifications of U.S. Provisional Patent 63/932437. All rights reserved by Francisco F. Pinochet. For commercial integration or hardware manufacturing licenses, please contact Fastcomcorp.