Project 3: The Huffman Decoder & IMDCT

A function that takes the compressed data portion of a single MP3 frame, decodes the Huffman-encoded values, performs inverse quantization, and runs the Inverse Modified Discrete Cosine Transform (IMDCT) and synthesis filterbank to produce a block of 1152 PCM samples.

Quick Reference

Attribute Value
Primary Language C
Alternative Languages N/A
Difficulty Level 5: Master
Time Estimate 1-2 months
Knowledge Area Data Compression / Digital Signal Processing
Tooling C, GDB
Prerequisites Project 2, strong C skills, and a willingness to read dense technical/mathematical documents.

What You Will Build

A function that takes the compressed data portion of a single MP3 frame, decodes the Huffman-encoded values, performs inverse quantization, and runs the Inverse Modified Discrete Cosine Transform (IMDCT) and synthesis filterbank to produce a block of 1152 PCM samples.

Why It Matters

This project builds core skills that appear repeatedly in real-world systems and tooling.

Core Challenges

  • Implementing the bit reservoir → maps to understanding that a frame’s data may not start at the beginning of the frame’s data section
  • Implementing Huffman decoding → maps to reading a bitstream and walking down a decoding tree to find the quantized coefficients
  • Inverse Quantization → maps to a series of nested loops and power-of-2 calculations
  • Implementing the IMDCT and Synthesis Filterbank → maps to the most math-intensive part. You will be implementing complex formulas involving sine windows and matrix-like operations.

Key Concepts

  • Huffman Coding: A classic data structures & algorithms topic.
  • Modified Discrete Cosine Transform (MDCT): The core mathematical transform of MP3, AAC, and other formats.
  • Digital Signal Processing (DSP): The field of processing digitized signals.

Real-World Outcome

Deliver a working demo with observable output that proves the feature is correct.

Implementation Guide

  1. Reproduce the simplest happy-path scenario.
  2. Build the smallest working version of the core feature.
  3. Add input validation and error handling.
  4. Add instrumentation/logging to confirm behavior.
  5. Refactor into clean modules with tests.

Milestones

  • Milestone 1: Minimal working program that runs end-to-end.
  • Milestone 2: Correct outputs for typical inputs.
  • Milestone 3: Robust handling of edge cases.
  • Milestone 4: Clean structure and documented usage.

Validation Checklist

  • Output matches the real-world outcome example
  • Handles invalid inputs safely
  • Provides clear errors and exit codes
  • Repeatable results across runs

References

  • Main guide: LEARN_C_MP3_PLAYER_FROM_SCRATCH.md
  • The MP3 specification (ISO/IEC 11172-3), DSP guides.