I'm interested in finding out more about refining time-resolution by use of multiple window widths for STFT's. In other words, wider windows for lower frequencies, narrower for better time-resolution for highs. Any recommendations for starting points? Also, are there any pitfalls to watch for? It seems an obvious thing to do, but most of the time, when I see mention of STFT's, one window size is used for all frequencies.
Adaptive window size for STFT
Started by ●December 9, 2015
Reply by ●December 9, 20152015-12-09
On Wednesday, December 9, 2015 at 10:15:16 AM UTC-6, Max wrote:> I'm interested in finding out more about refining time-resolution by > use of multiple window widths for STFT's. In other words, wider > windows for lower frequencies, narrower for better time-resolution for > highs. > > Any recommendations for starting points? > > Also, are there any pitfalls to watch for? It seems an obvious thing > to do, but most of the time, when I see mention of STFT's, one window > size is used for all frequencies.Check out dilation
Reply by ●December 9, 20152015-12-09
Some audio compression standards uses adaptive window lengths for the DCT, and they switch to a shorter window when a transient is detected. The reason for this is that a transient may not have enough temporal masking so if your window size corresponds to, say, 20ms, you may hear a puff of noise around a transient, so it's desirable to use a shorter window just for that one frame. If you are going to use both short and long stft's in parallel and you want to reconstruct a time domain signal without any error, then you might need to do a bit of work to figure out how to combine them. Bob
Reply by ●December 9, 20152015-12-09
>I'm interested in finding out more about refining time-resolution by >use of multiple window widths for STFT's. In other words, wider >windows for lower frequencies, narrower for better time-resolution for >highs. > >Any recommendations for starting points? > >Also, are there any pitfalls to watch for? It seems an obvious thing >to do, but most of the time, when I see mention of STFT's, one window >size is used for all frequencies.Hi Max, I may have a good news for you: what you are searching for indeed already exists: it is called "Constant Q transform" (Q is the quality factor), for which the frequency resolution is different for low and high frequencies : - at low frequencies, wider analysis windows, so better frequency resolution and worse time resolution - at high frequencies, narrower analysis windows, so reverse behavior. Here are some references: - Original paper from J.C. Brown on the subject: http://www.ee.columbia.edu/~dpwe/papers/Brown91-cqt.pdf - Second paper (optimizations): http://academics.wellesley.edu/Physics/brown/pubs/effalgV92P2698-P2701.pdf - Implementation in Matlab with Sparse matrix: http://wwwmath.uni-muenster.de/logik/Personen/blankertz/constQ/constQ.pdf The limitation for the last implementation is that it is only a frequency analysis, not a time-frequency analysis. I had coded some time ago the optimized constant-Q transform implementation for time-frequency analysis in SCILAB (see http://www.tsdconseil.fr/log/scriptscilab/cqt/index-en.html ; look for instance at the screenshot of time-frequency analysis of piano scale), but now that I look at it, the code not very clean! Yet, it may help as a starting point. Regards, Julien --------------------------------------- Posted through http://www.DSPRelated.com
Reply by ●December 9, 20152015-12-09
On Wednesday, December 9, 2015 at 8:15:16 AM UTC-8, Max wrote:> I'm interested in finding out more about refining time-resolution by > use of multiple window widths for STFT's. In other words, wider > windows for lower frequencies, narrower for better time-resolution for > highs. > > Any recommendations for starting points? > > Also, are there any pitfalls to watch for? It seems an obvious thing > to do, but most of the time, when I see mention of STFT's, one window > size is used for all frequencies.A commonly used and well supported approach is the S-Transform. Stockwell, RG, L Mansinha, and RP Lowe (1996). Localization of the complex spectrum: the S transform, IEEE Transactions on Signal Processing 44 (4), p 998-1001. Abstract The S transform, which is introduced in this correspondence, is an extension of the ideas of the continuous wavelet transform (CWT) and is based on a moving and scalable localizing Gaussian window. It is shown here to have some desirable characteristics that are absent in the continuous wavelet transform. The S transform is unique in that it provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. These advantages of the S transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis, whereas the localizing scalable Gaussian window dilates and translates. A simpler discussion: International Journal of Signal Processing, Image Processing and Pattern Recognition Vol.6, No.5 (2013), pp.245 Time-frequency Analysis Based on the S-transform Lin Yun*, Xu Xiaochun, Li Bin and Pang Jinfeng College of Information and Communication Engineering Harbin Engineering University Harbin, China Abstract S-transform is a new time-frequency analysis method, which is deduced from short-time Fourier transform and continue Wavelet transform. It has much better performance than traditional time-frequency method. Therefore, in this paper, the basic principle of is briefly introduced and the relationships between is analyzed by theoretical derivation. According to the simulation experiments, the time-frequency space characteristics of short-time Fourier transform, Wigner-Ville distribution and S-transform are contrasted. As the results shown, the window of S-transform has a progressive frequency dependent resolution. So the S-transform has a great flexibility and utility in the processing of non-stationary signal. Compare with the time-frequency spectrum of three different analysis methods under various noise conditions, it is obvious that S-transform has much better anti-noise performance than that of traditional methods for non-stationary signal processing. Based on the superior time-frequency resolution, the S-transform spectrum can be used to describe the structure of incoming signal effectively At: http://www.sersc.org/journals/IJSIP/vol6_no5/22.pdf Dale B. Dalrymple
Reply by ●December 12, 20152015-12-12
On Wed, 9 Dec 2015 11:35:46 -0800 (PST), radams2000@gmail.com wrote:>Some audio compression standards uses adaptive window lengths for the DCT, and they switch to a shorter window when a transient is detected. The reason for this is that a transient may not have enough temporal masking so if your window size corresponds to, say, 20ms, you may hear a puff of noise around a transient, so it's desirable to use a shorter window just for that one frame.Interesting!>If you are going to use both short and long stft's in parallel and you want to reconstruct a time domain signal without any error, then you might need to do a bit of work to figure out how to combine them. > >BobYeah, that's one of the things I was hoping to find out. Hard to get any traction with limited info out there. I was expecting to find more cases where this is used.
Reply by ●December 12, 20152015-12-12
On Wed, 09 Dec 2015 14:20:07 -0600, "tsd822" <110497@DSPRelated> wrote:>>I'm interested in finding out more about refining time-resolution by >>use of multiple window widths for STFT's. In other words, wider >>windows for lower frequencies, narrower for better time-resolution for >>highs. >> >>Any recommendations for starting points? >> >>Also, are there any pitfalls to watch for? It seems an obvious thing >>to do, but most of the time, when I see mention of STFT's, one window >>size is used for all frequencies. > >Hi Max, > >I may have a good news for you: what you are searching for indeed already >exists: it is called "Constant Q transform" (Q is the quality factor), for >which the frequency resolution is different for low and high frequencies >: > - at low frequencies, wider analysis windows, so better frequency >resolution and worse time resolution > - at high frequencies, narrower analysis windows, so reverse behavior. > >Here are some references: > - Original paper from J.C. Brown on the subject: >http://www.ee.columbia.edu/~dpwe/papers/Brown91-cqt.pdf > - Second paper (optimizations): >http://academics.wellesley.edu/Physics/brown/pubs/effalgV92P2698-P2701.pdf > - Implementation in Matlab with Sparse matrix: > >http://wwwmath.uni-muenster.de/logik/Personen/blankertz/constQ/constQ.pdf > >The limitation for the last implementation is that it is only a frequency >analysis, not a time-frequency analysis. > >I had coded some time ago the optimized constant-Q transform >implementation for time-frequency analysis in SCILAB (see >http://www.tsdconseil.fr/log/scriptscilab/cqt/index-en.html ; look for >instance at the screenshot of time-frequency analysis of piano scale), but >now that I look at it, the code not very clean! Yet, it may help as a >starting point. > >Regards, > >Julien > >--------------------------------------- >Posted through http://www.DSPRelated.comThanks much for the references, Julien. I had seen mention of "constant-Q" at one time, but I had the impression that it related only to wavelets. I'll take a second look, and I'll check the papers and code that you referenced.
Reply by ●December 12, 20152015-12-12
On Wed, 9 Dec 2015 15:22:05 -0800 (PST), dbd <d.dalrymple@sbcglobal.net> wrote:>On Wednesday, December 9, 2015 at 8:15:16 AM UTC-8, Max wrote: >> I'm interested in finding out more about refining time-resolution by >> use of multiple window widths for STFT's. In other words, wider >> windows for lower frequencies, narrower for better time-resolution for >> highs. >> >> Any recommendations for starting points? >> >> Also, are there any pitfalls to watch for? It seems an obvious thing >> to do, but most of the time, when I see mention of STFT's, one window >> size is used for all frequencies. > >A commonly used and well supported approach is the S-Transform. > >Stockwell, RG, L Mansinha, and RP Lowe (1996). Localization of the complex spectrum: the S transform, IEEE Transactions on Signal Processing 44 (4), p 998-1001. >Abstract >The S transform, which is introduced in this correspondence, >is an extension of the ideas of the continuous wavelet transform (CWT) >and is based on a moving and scalable localizing Gaussian window. It >is shown here to have some desirable characteristics that are absent in >the continuous wavelet transform. The S transform is unique in that >it provides frequency-dependent resolution while maintaining a direct >relationship with the Fourier spectrum. These advantages of the S >transform are due to the fact that the modulating sinusoids are fixed >with respect to the time axis, whereas the localizing scalable Gaussian >window dilates and translates. > > >A simpler discussion: > >International Journal of Signal Processing, Image Processing and Pattern Recognition Vol.6, No.5 (2013), pp.245 > >Time-frequency Analysis Based on the S-transform >Lin Yun*, Xu Xiaochun, Li Bin and Pang Jinfeng >College of Information and Communication Engineering >Harbin Engineering University >Harbin, China > >Abstract >S-transform is a new time-frequency analysis method, which is deduced from short-time Fourier transform and continue Wavelet transform. It has much better performance than traditional time-frequency method. Therefore, in this paper, the basic principle of is briefly introduced and the relationships between is analyzed by theoretical derivation. According to the simulation experiments, the time-frequency space characteristics of short-time Fourier transform, Wigner-Ville distribution and S-transform are contrasted. As the results shown, the window of S-transform has a progressive frequency dependent resolution. So the S-transform has a great flexibility and utility in the processing of non-stationary signal. >Compare with the time-frequency spectrum of three different analysis methods under various noise conditions, it is obvious that S-transform has much better anti-noise performance than that of traditional methods for non-stationary signal processing. Based on the superior time-frequency resolution, the S-transform spectrum can be used to describe the structure of incoming signal effectively > >At: >http://www.sersc.org/journals/IJSIP/vol6_no5/22.pdf > >Dale B. DalrympleHi Dale, The S-transform sounds like a cross between wavelets and STFTs. That should be a good start. The link above didn't work though: 403 error, which I assume means that authorization is required. I just found a couple other refs that refer the the variable window STFT method as "multiresolution analysis." It's covered briefly in Julius O. Smith's "Spectral" book. I haven't had a chance to go through it yet. I'll probably have to do a lot of studying of concepts leading up to it.
Reply by ●December 14, 20152015-12-14
There are methods, developed for low-delay noise reduction in audio: You could look up the STFT window switching by Mauler & Martin: http://www.asp.eurasipjournals.com/content/pdf/1687-6180-2009-469480.pdf Another method, which also allows frequency selective resolution: http://ftp.esat.kuleuven.be/pub/SISTA/ida/reports/13-228.pdf Generally: These methods do work. In practice, restrictions may arise if the time-frequency analysis-synthesis is not only for a single-purpuse, such as noise reduction but rather more objectives apply. Will a variable scheme be suitable for all applications? On 12/09/2015 05:15 PM, Max wrote:> I'm interested in finding out more about refining time-resolution by > use of multiple window widths for STFT's. In other words, wider > windows for lower frequencies, narrower for better time-resolution for > highs. > > Any recommendations for starting points? > > Also, are there any pitfalls to watch for? It seems an obvious thing > to do, but most of the time, when I see mention of STFT's, one window > size is used for all frequencies. >
Reply by ●December 16, 20152015-12-16
On Friday, December 11, 2015 at 9:07:09 PM UTC-8, Max wrote:> On Wed, 9 Dec 2015 15:22:05 -0800 (PST), dbd wrote: > > >On Wednesday, December 9, 2015 at 8:15:16 AM UTC-8, Max wrote: > >> I'm interested in finding out more about refining time-resolution by > >> use of multiple window widths for STFT's. In other words, wider > >> windows for lower frequencies, narrower for better time-resolution for > >> highs. > >> > >> Any recommendations for starting points? > >> > >> Also, are there any pitfalls to watch for? It seems an obvious thing > >> to do, but most of the time, when I see mention of STFT's, one window > >> size is used for all frequencies. > > > >A commonly used and well supported approach is the S-Transform. > > > >Stockwell, RG, L Mansinha, and RP Lowe (1996). Localization of the complex spectrum: the S transform, IEEE Transactions on Signal Processing 44 (4), p 998-1001. > >Abstract > >The S transform, which is introduced in this correspondence, > >is an extension of the ideas of the continuous wavelet transform (CWT) > >and is based on a moving and scalable localizing Gaussian window. It > >is shown here to have some desirable characteristics that are absent in > >the continuous wavelet transform. The S transform is unique in that > >it provides frequency-dependent resolution while maintaining a direct > >relationship with the Fourier spectrum. These advantages of the S > >transform are due to the fact that the modulating sinusoids are fixed > >with respect to the time axis, whereas the localizing scalable Gaussian > >window dilates and translates. > > > >...> > Hi Dale, > > The S-transform sounds like a cross between wavelets and STFTs. That > should be a good start. The link above didn't work though: 403 error, > which I assume means that authorization is required.The url is a free journal. I haven't paid for access. Perhaps your ISP has been blacklisted.> > I just found a couple other refs that refer the the variable window > STFT method as "multiresolution analysis." It's covered briefly in > Julius O. Smith's "Spectral" book. I haven't had a chance to go > through it yet. I'll probably have to do a lot of studying of > concepts leading up to it.A simple google finds the original S-Transform paper: Stockwell, RG, L Mansinha, and RP Lowe (1996). Localization of the complex spectrum: the S transform, IEEE Transactions on Signal Processing 44 (4), p 998-1001. Available (today at least)at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.462.1500&rep=rep1&type=pdf Some other general papers that might be of interest are: E. Sejdić, I. Djurović, J. Jiang, “Time-frequency feature representation using energy concentration: An overview of recent advances,” Digital Signal Processing, vol. 19, no. 1, pp. 153-183, January 2009. http://www.imedlab.org/publications/tfr%20review.pdf R. A. Brown and R. Frayne, "A fast discrete S-transform for biomedical signal processing", University of Calgary Seaman Family MR Research Centre Foothills Medical Centre, Canada. http://www.ncbi.nlm.nih.gov/pubmed/19163232 Dale B. Dalrymple
