Re: [music-dsp] Frequency based analysis alternatives?
STransform, see e.g. http://djj.ee.ntu.edu.tw/S_Transform.pdf -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Frequency based analysis alternatives?
This does not seem much different than FFT. The windowing function is now Gaussian. They vary window sizes to resolve time. From:Uli Brueggemann uli.brueggem...@gmail.com Sent:A discussion list for music-related DSP music-dsp@music.columbia.edu Date:Thu, July 10, 2014 12:05 pm Subject:Re: [music-dsp] Frequency based analysis alternatives? STransform, see e.g. http://djj.ee.ntu.edu.tw/S_Transform.pdf -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Frequency based analysis alternatives?
If I was to model music in general, it would be a sequence of 2 type segments, non-stationary transitions would be the first and quasi stationary tones the second type. This would get more involved with more instruments, but for just one sound source this would work quite well. Assuming we had a good classifier that detected the type and extent of segs, we could then use chirplets on the transitions and the old FFT for the tonal segs. Hopefully the chirplets would help classify the different type transitions for a sound source, based on their properties in the transform space. From:Olli Niemitalo o...@iki.fi Sent:A discussion list for music-related DSP music-dsp@music.columbia.edu Date:Thu, July 10, 2014 6:08 pm Subject:Re: [music-dsp] Frequency based analysis alternatives? There are chirp(let) transforms that represent the signal as a sum of Gaussian-enveloped bursts of (typically) linearly time-varying frequency. They work better than windowed short-time Fourier transforms for signals that are non-stationary. See for example: http://www.eurasip.org/Proceedings/Eusipco/Eusipco2004/defevent/papers/cr1374.pdf The fan-chirp transform takes this further to include in the burst a Gaussian-weighted range of harmonic frequencies: Luis Weruaga, Márian Képesi, The fan-chirp transform for non-stationary harmonic signals, Signal Processing, Volume 87, Issue 6, June 2007, Pages 1504-1522, ISSN 0165-1684, http://dx.doi.org/10.1016/j.sigpro.2007.01.006 There are FFT-based implementations for both, probably quite slow still. -olli On Wed, Jul 9, 2014 at 3:03 PM, Rohit Agarwal ro...@khitchdee.com wrote: What are the alternatives to the FFT? -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
[music-dsp] Instant frequency recognition
Hi all, a recent question to the list regarding the frequency analysis and my recent posts concerning the BLEP led me to an idea, concerning the theoretical possibility of instant recognition of the signal spectrum. The idea is very raw, and possibly not new (if so, I'd appreciate any pointers). Just publishing it here for the sake of discussion/brainstorming/etc. For simplicity I'm considering only continuous time signals. Even here the idea is far from being ripe. In discrete time further complications will arise. According to the Fourier theory we need to know the entire signal from t=-inf to t=+inf in order to reconstruct its spectrum (even if we talk Fourier series rather than Fourier transform, by stating the periodicity of the signal we make it known at any t). OTOH, intuitively thinking, if I'm having just a windowed sine tone, the intuitive idea of its spectrum would be just the frequency of the underlying sine rather than the smeared peak arising from the Fourier transform of the windowed sine. This has been commonly the source of beginner's misconception in the frequency analysis, but I hope you can agree, that that misconception has reasonable foundations. Now, recall that in the recent BLEP discussion I conjectured the following alternative definition of bandlimited signals: an entire complex function is bandlimited (as a function of purely real argument t) if its derivatives at any chosen point are O(B^N) for some B, where B is the band limit. Thinking along the same lines, an entire function is fully defined by its derivatives at any given point and (therefore) so is its spectrum. So, we could reconstruct the signal just from its derivatives at one chosen point and apply Fourier transform to the reconstructed signal. In a more practical setting of a realtime input (the time is still continuous, though), we could work under an assumption of the signal being entire *until* proven otherwise. Particularly, if we get a mixture of several static sinusoidal signals, they all will be properly restored from an arbitrarily short fragment of the signal. Now suppose that instead of sinusoidal signals we get a sawtooth. In the beginning we detect just a linear segment. This is an entire function, but of a special class: its derivatives do not fall off smoothly as O(B^N), but stop immediately at the 2nd derivative. From the BLEP discussion we know, that so far this signal is just a generalized version of the DC offset, thus containing only a zero frequency partial. As the sawtooth transition comes we can detect the discontinuity in the signal, therefore dropping the assumption of an entire signal and use some other (yet undeveloped) approach for the short-time frequency detection. Any further thoughts? Regards, Vadim -- Vadim Zavalishin Reaktor Application Architect Native Instruments GmbH +49-30-611035-0 www.native-instruments.com -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
