hybrid_cqt magnitude scaling is inconsistent

Hi, With @CarmineCella we’ve tried running the CQT on synthetic sounds, such as white noise (np.random.randn) as well as Diracs. It looks like the cqt function, which relies on the pyramid algorithm of Schoerkuber and Klapuri, is not appropriately scaled in magnitude across octaves.

Below is the code to compute the CQT of a Dirac and the corresponding figure:

import librosa
import numpy as np
x = np.zeros(32768)
x[16384] = 1.0
sr = 22050.0
c = librosa.cqt(x, sr=sr)
librosa.display.specshow(c)

Am I mistaken to think that the magnitudes should stay equal across octaves instead ?

[dpwe]

It’s odd that it’s not time-symmetric. Setting x[0] to 1 looks about right, x[-1], not so much:[image: Inline image 1] I agree that the noise in the different HF bands is also a problem.

DAn.

On Fri, Apr 29, 2016 at 9:57 AM, Vincent Lostanlen <[e-mail]

wrote:

I was using librosa v0.4.1. After upgrading to librosa v0.4.2, I can reproduce @bmcfee https://github.com/bmcfee’s figure. This was indeed solved in #307 https://github.com/bmcfee/librosa/issues/307. Sorry for the inconvenience.

Mapping the amplitudes to a dB scale, like you did, makes the artifacts perfectly acceptable. Still, there is a sharp 8x magnitude difference (18 dB) in hybrid_cqt at the frequential boundary between the two methods.

For the record, below is the magnitude (not in dB) at the impulse location with new librosa 0.4.2. Green is hybrid CQT, blue is CQT.

c = librosa.cqt(x, sr=sr) plt.plot(c[:, 32]) hybrid_c = librosa.hybrid_cqt(x, sr=sr) plt.plot(hybrid_c[:, 32])

[image: hybrid_versus_cqt] https://cloud.githubusercontent.com/assets/3943142/14918164/b6a33364-0e22-11e6-8ed9-33c485e056a0.png

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[lostanlen]

[I wrote this message after the “sound good ?” of @bmcfee but have just realized that I had not been sent. Better late than never…] Sounds good to me. Most of what I need right now was already fixed in #307 anyway. Then, what do you think about @dpwe 's experiments on moving the impulse location and getting a result that is not covariant with translation ?