Take the 2-minute tour ×
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It's 100% free, no registration required.

I'm trying to synchronize (overlap) two audio recordings of the same song: a complete HQ version, and an incomplete, noisy version (phone recording for example). The noisy recording may have had its tempo increased/decreased.

Currently I have something working based on this 2001 paper: "The Beat Spectrum: a New Approach To Rhythm Analysis"

In short:

  • Get a self-similarity vector for each song, which will contain peaks at every multiple of the song bar duration (every 4 or 8 beats for latin music for example)
  • For each r (relative tempo ratio) from 0.7 to 1.3, scale the second vector and then do a dot product on the two vectors, using v1[i]·v2[i] = d1[i]*d2[i] (where d1[i] is the sign of v1's derivative; same for d2)

When the beats are clear in the recordings, I get a clear maximum at the correct ratio (usually 1.0). The problem is that when the beats are lost (due to EQ, bad mics, noise) the self-similarity chart stops showing the periodic bars and I get maximums in the wrong places in the dot product.

My question is, what else could I use instead of the dot-product-of-the-derivative-sign, and what other robust ways are there to determine the tempo change ratio in the presence of noise, besides doing BPM(song1) / BPM(song2).

In case someone can take this further: computing self-similarity by overlapping the sample twice (at [0, ofs, ofs+ofs] instead of just [0, ofs]) gives much more accurate maximums for each beat duration. But I haven't tested it yet on all the samples I have.

share|improve this question

migrated from math.stackexchange.com Nov 6 '12 at 11:31

This question came from our site for people studying math at any level and professionals in related fields.

The issue may be that the scaling isn't uniform across the entire track? Maybe try splitting the tracks into smaller parts (say 5-10 seconds) and compute $r$ for each independently. Then discard outliers, compute a moving average, and let then scaling parameter vary over time as you apply the transformation. –  Dan Brumleve Nov 5 '12 at 21:10
I have contacted the moderators on Signal Processing regarding migration. –  robjohn Nov 5 '12 at 23:57
Dan, shorter samples + discarding outliers definitely seems to help, I get more prominent maximums. I can't figure out how to account for r(t) as a non-constant (and it doesn't appear in any songs). –  patraulea Nov 6 '12 at 9:04
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.