Projects

IBT — MATLAB Implementation on SP Cup 2017 Database

A real-time tempo induction and beat tracking system implemented in MATLAB.
Based on: “IBT: A Real-Time Tempo and Beat Tracking System” — ISMIR 2010.

Overview

IBT is an agent-based tempo induction and beat tracking system that processes audio causally in real time. It extends the competing-agents strategy of BeatRoot to support continuous, frame-based spectral flux input — making it suitable for live audio, MIR pipelines, and robotic platforms.

The algorithm is evaluated on the ISMIR 2004 Tempo Induction Contest dataset (3199 instances) and a 1360-piece beat tracking benchmark, achieving results competitive with state-of-the-art systems.

Repository Structure

ibt/
├── beatVer1.m       # Main script: full IBT pipeline (pre-tracking + beat tracking)
├── specflux.m       # Spectral flux onset detection function (STFT-based)
├── peakpick.m       # Adaptive peak-picking on onset detection function
├── comp_dgt_fb.m    # Filter bank DGT (Gabor transform) — borrowed from LTFAT
├── winfuns.m        # Window function generator (Hamming, Hann, Blackman, etc.)
└── open_025.wav     # Example audio file for running beatVer1.m

Requirements

• MATLAB R2016b or later (uses designfilt, audioread, findpeaks)
• Signal Processing Toolbox
• No additional toolboxes required (LTFAT helper comp_dgt_fb is bundled)

Quick Start

1. Place all .m files and your .wav file in the same directory.
2. Update the filename in beatVer1.m if needed:

   [y, fs] = audioread('open_025.wav');
   

3. Run the script:

   >> beatVer1
   

4. The script outputs:
   • A plot of the autocorrelation periodicity function with detected tempo peaks
   • beat_final — a vector of estimated beat positions in milliseconds

Algorithm Pipeline

Audio WAV file
      │
      ▼
┌─────────────────────────────────────┐
│  1. AUDIO FEATURE EXTRACTION        │
│     specflux.m                      │
│     • Hamming window, 1024 samples  │
│     • Hop size: 512 samples         │
│     • Spectral flux (half-wave rect)│
│     • Zero-phase Butterworth LP     │
│       filter (2nd order, IIR)       │
└──────────────┬──────────────────────┘
               │
               ▼
┌─────────────────────────────────────┐
│  2. PRE-TRACKING (5s window)        │
│                                     │
│  a) Period Hypotheses Induction     │
│     • Autocorrelation of SF         │
│     • Peak-pick in [50, 250] BPM    │
│       (240–1200 ms at 44100 Hz)     │
│     • Threshold: δ × rms(A(τ))      │
│                                     │
│  b) Phase Hypotheses Selection      │
│     • 30 uniformly spaced phases    │
│     • Beat train template matching  │
│     • Best phase per period: φᵢ     │
│                                     │
│  c) Agent Scoring & Ranking         │
│     • Raw score: beat–onset error   │
│     • Relational score: rewards     │
│       integer metrical ratios       │
│     • Final score Sᵢ = Sᵢrel / max │
└──────────────┬──────────────────────┘
               │
               ▼
┌─────────────────────────────────────┐
│  3. BEAT TRACKING (causal)          │
│     beatVer1.m                      │
│                                     │
│  Multi-agent system (max 30 agents) │
│  For each onset event:              │
│  • Best agent emits beat to output  │
│  • Inner window (±46.4 ms):         │
│    period & phase correction        │
│    P ← P + 0.25·err                 │
│    φ ← φ + P + 0.25·err            │
│  • Outer window (−0.2P, +0.4P):     │
│    spawn 3 child agents (C1, C2, C3)│
│    – C1: phase correction only      │
│    – C2: period + phase correction  │
│    – C3: half-correction (both)     │
│  • Agent culling: redundancy,       │
│    score gap > 80%, out-of-range    │
└──────────────┬──────────────────────┘
               │
               ▼
         beat_final (ms)

Key Parameters

All parameters are set at the top of beatVer1.m and are easy to modify:

File Reference

beatVer1.m

Main script. Runs the full IBT pipeline end-to-end:

• Loads audio, computes spectral flux, applies LP filter
• Detects onsets via peakpick
• Initialises beat agents from period/phase hypotheses
• Runs the causal multi-agent beat tracking loop
• Outputs beat_final (beat positions in ms)

specflux.m

[SF, V0] = specflux(f, win_length, tgap)

Computes the spectral flux onset detection function of signal f using a Hamming-windowed Gabor transform. Half-wave rectifies the magnitude difference between consecutive frames.

peakpick.m

peaks = peakpick(SF, thre, range, multi)

Picks significant local maxima from the onset detection function. A peak is accepted only if it exceeds the local mean over an asymmetric neighbourhood [−multi×range, +range] by more than thre.

comp_dgt_fb.m

coef = comp_dgt_fb(f, g, a, M)

Computes the Discrete Gabor Transform using a filter bank approach. Borrowed from the LTFAT toolbox by Peter L. Søndergaard (GPL). Handles boundary conditions periodically for both leading and trailing edges.

winfuns.m

g = winfuns(name, N)
g = winfuns(name, N, L)
g = winfuns(name, x)

Generates standard window functions by name. Used internally by specflux to produce the Hamming window for the STFT.

Supported windows: hann, hamming, blackman, blackharr, nuttall, gauss, cos, rec, tri, and many Nuttall variants (nuttall10 through nuttall03).

Agent Score Functions

Raw score (within induction window)

For each beat prediction bp vs. local spectral flux maximum m:

If m ∈ Tᵢₙ:   Δs =  (1 − |err|/Tr_out) · (Pᵢ/Pmax) · SF(m)
If m ∈ Tₒᵤₜ:  Δs = −(|err|/Tr_out)     · (Pᵢ/Pmax) · SF(m)

Relational score (agent ranking)

Sᵢrel = 10 · Sᵢraw + Σⱼ≠ᵢ r(nᵢⱼ) · Sⱼraw

       ⎧ 6 − n,   1 ≤ n ≤ 4
r(n) = ⎨ 1,       5 ≤ n ≤ 8
       ⎩ 0,       otherwise

where nᵢⱼ is the nearest integer ratio between periods Pᵢ and Pⱼ.

Child agent generation (outer window)

Source