WTF!? Wavelet TransForm for audio measurements - What-is? and How-to?

[Elias]

Hello,

I think wavelets are the wave of the future also in audio measurements. There has been some interest on the wavelets recently in diyaudio and some of the benefits over other analysis methods have been noted. Take a look here for a snapshot what wavelets can do keeping in mind it only shows a part of what is possible
Horn Honk $$ WANTED $$


What-is?

I'll keep the introduction short because everyone wants to get into the point fast

Shortly put, a wavelet is a piece of 'wave' essentially having a defined center frequency and time duration. That's it!

Typically for this purpose the time domain waveform of the wavelet is 'smooth' avoiding abrupt changes.

The benefit using wavelets is to have improved resolution of the time-frequency domain information.





How-to?

A wavelet in the time domain looks for example like this:



What we are interested in wavelets is the time-frequency information so we want to see the amplitude versus time. Amplitude of the wavelet can be seen in the envelope like this:



To analyse a whole frequency band we generate a family of wavelets. Here is seen from 100Hz to 10kHz in 5 steps:



And for the ampitude information we calculate the envelope for each like this:



From now on in this case we are only interested of the envelope so we select only that and we have:



Because a human is a logarithmic device, we take LOG of the above and see the envelope in 20dB scale here:



Now we have some fun and visit the indian bazaar and get one of those colorful blankets and throw it on the top:



And now we are almost done! For better visibility we choose the view angle at the zenith and finally we have this:




- Elias

[Elias]

I found out the 'best' software to analyse wavelets is GNU Octave
Octave

Why it's the 'best'? It's free! It gives you almost everything that Matlab The MathWorks - MATLAB and Simulink for Technical Computing does with no cost. The visualisation tools are great. In mathematical capabilities only You are the limit.


Here's the code to plot the previous wavelets:
http://dl.dropbox.com/u/2400456/diyaudio/waveletdemo.m

How to run the code:

1) Download and instal Octave

2) In Octave command promt you can go the location of the waveletdemo.m file for example 'cd C:/your_folder'

3) Then type the name of the script file without the .m waveletdemo


Now you should be able to see the plots!


Ok, this was how-to generate a wavelet.

Next comes how-to get the use of it in analysing a loudspeaker impulse response for example.


- Elias

[Pano]

Thanks Elias. Very nice. =)

[doug20]

Wow, Thank you so much!

[gedlee]

Basically wavelets and CSD are the same thing, although there is a subtle difference. The CSD truncates from a certain point and the wavelet does not, its full window slides so to speak. This is not a huge difference.

Mathematically wavelets can be defined and manipulated theoretically in an exact manner, but CSD cannot. This definately gives the wavelets an advantage in certain situations.

Octave is not very useful for windows users, it more of a unix based platform.

Wavelets can also be done in MathCAD and Mathmatica.

[doug20]

The honk horn thread has all of this discussion and yes Wavelets are CSDs. I just want be able to create the same wavelets that Elias was creating. They are much cleaner then the CSDs ARTA creates. I have many waveguides, many CDs and many crossovers to play around with.

Octave runs just fine in Vista and its free.

Is MathCAD or Mathmatica free?

[gedlee]

I'll avoid that thread, thanks.

I was looking at Octave and from what I read it was not stable under windows and all my platforms are now Win 7. You have installed it on Vista and it runs with no trouble? That was not what I was reading, nor what Elias alluded to when I asked him.

No, neither MathCAD or Mathmatica is free, but I just find that in the long run free software fails to be well supported and my time is worth too much to waste on software that is going to become obsolete.

[mige0]

Thanks, Elias.

Your example run smooth on my XOctave setup described here:

Help on making MULTIRESOLUTION WAVELET ANALYSIS available ?

Great start!



I'll have a look into the code later, as I'm short in time right now...



Michael

[Jmmlc]

Hello,

I used to wrote under Matlab a spectrogram routine which gives very similar results to the continuous wavelets analysis illustrated by Elias.

It is based on the use of a gaussian envelop pulse having a constant number of periods (for what it seems theorically this pulse cannot be accepted as a wavelet though...).

You'll find my routine as an attached txt file that you can easily paste and run into Matlab.

Best regards from Paris, France

Jean-Michel Le Cléac'h

[doug20]

Originally Posted by gedlee

I'll avoid that thread, thanks.

I was looking at Octave and from what I read it was not stable under windows and all my platforms are now Win 7. You have installed it on Vista and it runs with no trouble? That was not what I was reading, nor what Elias alluded to when I asked him.

No, neither MathCAD or Mathmatica is free, but I just find that in the long run free software fails to be well supported and my time is worth too much to waste on software that is going to become obsolete.

For my limited use, I had zero issues with Octave on Vista (SP2). I will find out if his package works without issues on Vista too.

Btw, You have limited experience with open source communities if you beleve free = obsolete because its not true in all cases.

1. The best webserver is apache, its free!! Its been around and stable for years with a big open source community.

2. Linux has been free forever (biggest open source community period). Companies just do not get the free idea because they like to pay and then blame someone when they screw up.

3. One of the best programming languages out there is called Python. Its free, it has A HUGE open source community and its everywhere, you would be amazed who uses it and what it can do. We run automated picking systems with it 24/7, Automation/PLC integration is easy with it. Its an extremely powerful language.

Conclusion, open source has proven itself to be extremely viable in the business world.

Thank you again Elias, I look forward to reading and understanding this stuff!