TAD - TSVM Advanced Audio Codec

A perceptually-optimised wavelet-based audio codec designed for resource-constrained systems, featuring CDF 9/7 wavelets, EZBC sparse coding, and sophisticated perceptual quantisation.

Overview

TAD (TSVM Advanced Audio) is a modern audio codec built on discrete wavelet transform (DWT) using Cohen-Daubechies-Feauveau (CDF) 9/7 biorthogonal wavelets. It combines perceptual quantisation, advanced entropy coding, and careful optimisation for resource-constrained systems.

Key Advantages

• Perceptual optimisation: HVS-aware quantisation preserves audio quality where it matters
• Efficient sparse coding: EZBC encoding exploits coefficient sparsity (86.9% zeros in typical content)
• Variable chunk sizes: Supports any chunk size ≥1024 samples, including non-power-of-2
• Stereo decorrelation: Mid/Side encoding exploits stereo correlation for better compression
• Hardware-friendly: Designed for efficient decoding on resource-constrained platforms

Features

Compression Technology

• CDF 9/7 Biorthogonal Wavelets

  • 9-level fixed decomposition for all chunk sizes
  • Lifting scheme implementation for efficient computation
  • Optimal frequency discrimination for audio signals

• Pre-processing

  • First-order IIR pre-emphasis filter (α=0.5) shifts quantisation noise to lower frequencies, where they are less objectionable to listeners
  • Gamma companding (γ=0.5) for dynamic range compression before quantisation
  • Mid/Side stereo transformation exploits stereo correlation
  • Lambda companding (λ=6.0) with Laplacian CDF mapping for full bit utilisation

• Perceptual Quantisation

  • Channel-specific (Mid/Side) frequency-dependent weights
  • Subband-aware quantisation preserves perceptually important frequencies

• EZBC Encoding

  • Binary tree embedded zero block coding
  • Exploits coefficient sparsity (86.9% Mid, 97.8% Side typical)
  • Progressive refinement structure
  • Spatial clustering of non-zero coefficients

• Entropy Coding

  • Zstandard compression (level 7) on concatenated EZBC bitstreams
  • Cross-channel compression optimisation
  • Optional Zstd bypass for debugging

Audio Format

• Sample Rate: 32 KHz (TSVM audio hardware native format)
• Channels: Stereo (L/R input, Mid/Side internal representation)
• Chunk Sizes: Variable, any size ≥1024 samples (including non-power-of-2)
• Bit Depth: 32-bit float internal, 8-bit unsigned PCM output with noise-shaped dithering
• Bandwidth: Full 0-16 KHz frequency range preserved

Quality Levels

Six quality levels (0-5) provide a wide range of compression/quality trade-offs:

• Level 0: Lowest quality, smallest file size
• Level 3: Default, balanced quality/compression (2.51:1 vs PCMu8)
• Level 5: Highest quality, largest file size

Quality levels are designed to be synchronised with TAV video codec for unified encoding.

Building

Prerequisites

• C compiler (GCC/Clang)
• Zstandard library (libzstd)
• Math library (libm)

Compilation

# Build TAD encoder/decoder
make tad

# Build all tools
make all

# Clean build artifacts
make clean

Build Targets

• encoder_tad - Standalone audio encoder with FFmpeg calls
• decoder_tad - Standalone audio decoder

Usage

Basic Encoding

Encoding requires FFmpeg executable installed in your system.

# Default encoding (quality level 3)
./encoder_tad -i input.mp3 -o output.tad

# Specify quality level (0-5)
./encoder_tad -i input.m4a -o output.tad -q 0    # Lowest quality
./encoder_tad -i input.ogg -o output.tad -q 5    # Highest quality

# Disable Zstd compression (for debugging)
./encoder_tad -i input.opus -o output.tad --no-zstd

# Verbose output with statistics
./encoder_tad -i input.flac -o output.tad -v

Decoding

# Decode to PCMu8
./decoder_tad -i input.tad -o output.pcm --raw-pcm

# Decode to WAV
./decoder_tad -i input.tad -o output.wav

Input Formats

TAD encoder accepts any audio format supported by FFmpeg:

• Audio files: WAV, MP3, FLAC, OGG, AAC, etc.
• Video files with audio streams: MP4, MKV, AVI, etc.
• Raw PCM formats

Audio is automatically resampled to 32 KHz stereo if necessary.

Technical Architecture

Encoder Pipeline

1. Input Processing

   • FFmpeg demuxing and audio stream extraction
   • Resampling to 32 KHz stereo
   • Conversion to PCM32f

2. Pre-emphasis Filter

   • First-order IIR filter with α=0.5
   • Shifts quantisation noise toward lower frequencies
   • Improves perceptual quality

3. Gamma Companding

   • Dynamic range compression with γ=0.5
   • Applied independently to each sample
   • Reduces quantisation error for low-amplitude signals

4. Stereo Decorrelation

   • Left/Right to Mid/Side transformation
   • Mid = (L + R) / 2
   • Side = (L - R) / 2
   • Exploits stereo correlation for better compression

5. 9-Level CDF 9/7 DWT

   • Fixed 9 decomposition levels for all chunk sizes
   • Forward lifting scheme implementation
   • Correct length tracking for non-power-of-2 sizes

6. Perceptual Quantisation

   • Channel-specific (Mid/Side) subband weights
   • Lambda companding with λ=6.0
   • Laplacian CDF mapping: sign(x) * floor(λ * log(1 + |x|/λ))
   • Quantised to int8 coefficients

7. EZBC Encoding

   • Binary tree structure per channel
   • Progressive refinement by bitplanes
   • Zero block coding exploits sparsity
   • Independent bitstreams for Mid and Side

8. Zstd Compression

   • Level 7 compression on concatenated [Mid_bitstream][Side_bitstream]
   • Cross-channel optimisation opportunities
   • Adaptive compression based on content

Decoder Pipeline

1. Container Parsing

   • TAD packet identification (type 0x24)
   • Chunk size extraction
   • Compressed data boundaries

2. Zstd Decompression

   • Decompress concatenated bitstreams
   • Split into Mid and Side EZBC streams

3. EZBC Decoding

   • Binary tree decoder per channel
   • Reconstruct quantised int8 coefficients
   • Progressive refinement reconstruction

4. Lambda Decompanding

   • Inverse Laplacian CDF with channel-specific weights
   • Reconstruct float32 DWT coefficients
   • Apply subband-specific perceptual weights

5. 9-Level Inverse CDF 9/7 DWT

   • Inverse lifting scheme implementation
   • Correct length tracking for non-power-of-2 chunk sizes
   • Pre-calculated length sequence from forward transform

6. Mid/Side to Left/Right

   • L = Mid + Side
   • R = Mid - Side
   • Reconstruct stereo channels

7. Gamma Decompanding

   • Inverse gamma with γ⁻¹=2.0
   • Restore original dynamic range

8. De-emphasis Filter

   • Reverse pre-emphasis with α=0.5
   • Remove frequency shaping
   • Restore flat frequency response

9. PCM32f to PCM8u Conversion

   • Noise-shaped dithering for 8-bit output
   • Clamping to valid range
   • Final output format

Wavelet Implementation

CDF 9/7 wavelet follows a two-stage lifting scheme:

// Forward Transform: Predict → Update
// Predict step (generate high-pass)
temp[half + i] = data[odd] - α * (data[even_left] + data[even_right]);

// Update step (generate low-pass)
temp[i] = data[even] + β * (temp[half + i - 1] + temp[half + i]);

// Normalization (K factor)
temp[i] *= K;
temp[half + i] /= K;

// Inverse Transform: Denormalize → Undo Update → Undo Predict (reversed order)
temp[i] /= K;
temp[half + i] *= K;

temp[i] -= β * (temp[half + i - 1] + temp[half + i]);
data[odd] = temp[half + i] + α * (temp[i] + temp[i + 1]);
data[even] = temp[i];

CDF 9/7 Coefficients:

• α = -1.586134342
• β = -0.052980118
• γ = +0.882911075
• δ = +0.443506852
• K = 1.230174105

Non-Power-of-2 Chunk Size Handling

Critical implementation detail for variable chunk sizes:

// Pre-calculate exact length sequence from forward transform
int lengths[MAX_LEVELS + 1];
lengths[0] = chunk_size;
for (int i = 1; i <= levels; i++) {
    lengths[i] = (lengths[i - 1] + 1) / 2;
}

// Apply inverse DWT using lengths[level] for each level
// NEVER use simple doubling (length *= 2) - incorrect for non-power-of-2!

Incorrect length tracking causes mirrored subband artefacts in decoded audio.

Perceptual Quantisation Weights

Channel-specific weights for Mid (channel 0) and Side (channel 1):

// Base quantiser weights per subband (9 levels + approximation)
float BASE_QUANTISER_WEIGHTS[2][10] = {
    // Mid channel (0)
    {4.0f, 2.0f, 1.8f, 1.6f, 1.4f, 1.2f, 1.0f, 1.0f, 1.3f, 2.0f},

    // Side channel (1)
    {6.0f, 5.0f, 2.6f, 2.4f, 1.8f, 1.3f, 1.0f, 1.0f, 1.6f, 3.2f}
};

// During dequantisation:
float weight = BASE_QUANTISER_WEIGHTS[channel][subband] * quantiser_scale;
coeffs[i] = normalised_val * TAD32_COEFF_SCALARS[subband] * weight;

Different weights for Mid and Side channels reflect perceptual importance of frequency bands in each channel. DC frequency has highest weight (4.0 Mid, 6.0 Side) due to energy concentration.

Performance Characteristics

Compression Efficiency

• Target Compression: 2:1 against PCMu8 baseline (4:1 against PCM16LE input)
• Achieved Compression: 2.51:1 against PCMu8 at quality level 3
• Audio Quality: Preserves full 0-16 KHz bandwidth
• Coefficient Sparsity: 86.9% zeros in Mid channel, 97.8% in Side channel (typical)
• EZBC Benefits: Exploits sparsity, progressive refinement, spatial clustering

Computational Complexity

• Encoding: O(n log n) per chunk for DWT, O(n) for EZBC encoding
• Decoding: O(n log n) per chunk for inverse DWT, O(n) for EZBC decoding
• Memory: O(n) working memory for chunk processing

Quality Characteristics

• Frequency Response: Flat 0-16 KHz within perceptual limits
• Dynamic Range: Preserved through gamma companding
• Stereo Imaging: Maintained through Mid/Side decorrelation
• Perceptual Quality: Optimised for human auditory system characteristics

Integration with TAV

TAD is designed as an includable API for TAV video encoder integration:

• Variable Chunk Sizes: Audio chunks can match video GOP boundaries (e.g., 32016 samples for 1-second TAV GOP)
• Unified Quality Levels: TAD quality 0-5 synchronised with TAV quality 0-5
• Embedded Packets: TAV embeds TAD-compressed audio using packet type 0x24
• Shared Container: Single .tav file contains both video and audio streams

TAV Integration Example

// TAD handles non-power-of-2 chunk size correctly
tad_encode_chunk(audio_buffer, audio_samples_per_gop, output_buffer, &output_size);

// TAV embeds TAD packet
tav_write_packet(TAV_PACKET_AUDIO, output_buffer, output_size);

Format Specification

For complete packet structure and bitstream format details, refer to format documentation.txt.

Key Packet Types

• 0x24: TAD audio packet (used in standalone .tad files and embedded in .tav files)

Related Projects

• TAV (TSVM Advanced Video): Wavelet-based video codec with integrated TAD audio
• TSVM: Target virtual machine platform for TAD playback

Licence

MIT.