Hi, This is my first post to this interesting newgroup. I have been analyzing sound samples (muic) using FFT with some success. I can calculate frequency, amplitude and phase for the frames. But I face the known frequency / time resolution dilemma. This has made me experiment with wavelets. So far I have only tried the Haar wavelet. I have made test files with sine waves of frequencies 440 Hz, 880 and the sum of those and different amplitudes. I have used 2048 samples and a windowing function. The resulting array mystifies me. There are a lot of non-zero values. How do I interprete the values ? I program in VB and can post my code if that can help my explanation. Best regards Michael

# Going from FFT to Wavelets

Started by ●October 17, 2004

Reply by ●October 19, 20042004-10-19

"DSP curious" <dsp@iname.com> wrote in message news:fcydnez7n-7KWe_cRVn-qw@giganews.com...> Hi, > > This is my first post to this interesting newgroup. > > I have been analyzing sound samples (muic) using FFT with some success. > I can calculate frequency, amplitude and phase for the frames. > But I face the known frequency / time resolution dilemma. > > This has made me experiment with wavelets. > So far I have only tried the Haar wavelet. > I have made test files with sine waves of frequencies 440 Hz, 880 and the > sum of those > and different amplitudes. > I have used 2048 samples and a windowing function. > The resulting array mystifies me. There are a lot of non-zero values. > How do I interprete the values ? > > I program in VB and can post my code if that can help my explanation. > > Best regards > Michael > >If the answer is not straightforward, maybe some of you can recommend some good books on wavelets (there are 250 on amazon) or direct me to good websites. Which wavelets are best suited to analyzing sound? Thanks in advance, Michael

Reply by ●October 19, 20042004-10-19

"DSP curious" <dsp@iname.com> wrote in message news:yNOdnV6Lbdj_6OjcRVn-tg@giganews.com...> > "DSP curious" <dsp@iname.com> wrote in message > news:fcydnez7n-7KWe_cRVn-qw@giganews.com... >> Hi, >> >> This is my first post to this interesting newgroup. >> >> I have been analyzing sound samples (muic) using FFT with some success. >> I can calculate frequency, amplitude and phase for the frames. >> But I face the known frequency / time resolution dilemma. >> >> This has made me experiment with wavelets. >> So far I have only tried the Haar wavelet. >> I have made test files with sine waves of frequencies 440 Hz, 880 and the >> sum of those >> and different amplitudes. >> I have used 2048 samples and a windowing function. >> The resulting array mystifies me. There are a lot of non-zero values. >> How do I interprete the values ? >> >> I program in VB and can post my code if that can help my explanation. >> >> Best regards >> Michael >> >> > > If the answer is not straightforward, maybe some of you can recommend > some good books on wavelets (there are 250 on amazon) or direct me to > good websites. > Which wavelets are best suited to analyzing sound? > > Thanks in advance, > MichaelMichael, The Haar wavelet is good as a simple example to use to understand some of the basics of wavelets such as orthonormality, perfect reconstruction, etc. However, it is usually too simplistic to really provide any really interesting results. It's basically consists of splitting the signal into a sum and difference signal... You may want to try using the Daubechies family of wavelets for your experiments. In Matlab you can use the wfilters command to create a Daubechies filter. For example: [lo_d, hi_d, lo_r, hi_r] = wfilters('db20'); You can then use the dwt command to do the wavelet decomposition itself. Brad

Reply by ●October 20, 20042004-10-20

DSP curious wrote:> If the answer is not straightforward, maybe some of you can recommend > some good books on waveletsWavelet theory is not straightforward. Its core is funtional analysis, a reasonably hairy subject. For the extreme in depth and mathematical formality see: A Wavelet Tour of Signal Processing Stephane Mallat For one of the more accessable for an engineer yet reasonably complete see: Wavelets and Filter Banks Gilbert Strang and Truong Nguyen Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein

Reply by ●October 20, 20042004-10-20

Try Amara's wavelet page, it's definitely one of the best online resources on the topic: http://www.amara.com/current/wavelet.html -- Stephan M. Bernsee http://www.dspdimension.com

Reply by ●October 20, 20042004-10-20

"Stephan M. Bernsee" <spam@dspdimension.com> wrote in message news:2tmeuuF206fdlU1@uni-berlin.de...> Try Amara's wavelet page, it's definitely one of the best online > resources on the topic: > > http://www.amara.com/current/wavelet.html > -- > Stephan M. Bernsee > http://www.dspdimension.com >Hi Stephan Thank you for the link. The page looks very interesting. Regards, Michael

Reply by ●October 20, 20042004-10-20

"Bob Cain" <arcane@arcanemethods.com> wrote in message news:cl4rao02r2i@enews2.newsguy.com...> > > DSP curious wrote: > > > > If the answer is not straightforward, maybe some of you can recommend > > some good books on wavelets > > Wavelet theory is not straightforward. Its core is > funtional analysis, a reasonably hairy subject. For the > extreme in depth and mathematical formality see: > > A Wavelet Tour of Signal Processing > Stephane Mallat > > For one of the more accessable for an engineer yet > reasonably complete see: > > Wavelets and Filter Banks > Gilbert Strang and Truong Nguyen > > > Bob > -- > > "Things should be described as simply as possible, but no > simpler." > > A. EinsteinThanks Bob, I'll have a look at both books. I am a programmer with a mathematical background. What I have done so far is to make a program that transforms wave files from time to frequency domain, manipulate or estimate frequencies, and then back to the time domain. I did this with ideas from the great (now down) Don Cross website. My problem with this is that I would like to estimate frequencies more precisely (relatively). I understand that wavelets "are" logarithmic instead of linear, so that solves my problem. As mentioned, I have made a simple test using the method described on the page http://dmr.ath.cx/gfx/haar/. I just don't know what to make of the resulting array. What I need is a description of how to interprete the result of a wavelet transform in terms of frequency. Will the above books do that? Regards, Michael

Reply by ●October 20, 20042004-10-20

On 2004-10-20 15:00:12 +0200, "DSP curious" <dsp@iname.com> said:> "Bob Cain" <arcane@arcanemethods.com> wrote >> Wavelet theory is not straightforward. Its core is >> funtional analysis, a reasonably hairy subject.I agree it's a Haar-y subject :-)> What I need is a description of how to interprete the result of a wavelet > transform in terms > of frequency. Will the above books do that?Yes and no. Wavelets exploit localization in both time and frequency domain to achieve an advantage in certain areas over the DFT (which uses a complex exponential as basis that is not localized in time). Because of this, they're not easily interpreted in the frequency domain alone. Still I would consider the books mentioned by Bob a good reading, in addition to Amara's Wavelet page (see my other post) which is an excellent collection of web resources and articles on the subject. -- Stephan M. Bernsee http://www.dspdimension.com

Reply by ●October 20, 20042004-10-20

"DSP curious" <dsp@iname.com> wrote in message news:41765133$0$215$edfadb0f@dread16.news.tele.dk...> > "Stephan M. Bernsee" <spam@dspdimension.com> wrote in message > news:2tmeuuF206fdlU1@uni-berlin.de... > > Try Amara's wavelet page, it's definitely one of the best online > > resources on the topic: > > > > http://www.amara.com/current/wavelet.html > > -- > > Stephan M. Bernsee > > http://www.dspdimension.com > > > > Hi Stephan > > Thank you for the link. The page looks very interesting. > > Regards, > Michael > >Don't forget your own site Stephan ;-) Lots of valuable information there too. Michael

Reply by ●October 21, 20042004-10-21

On 2004-10-20 21:53:16 +0200, "DSP curious" <dsp@iname.com> said:> Don't forget your own site Stephan ;-) > Lots of valuable information there too. > > MichaelThanks! Most of it isn't about wavelets though, so I thought it wasn't that relevant. -- Stephan M. Bernsee http://www.dspdimension.com