Post by thread:Wavelet spectral analysis for guitar tuner?

Has anyone thought of or have code for using wavelets on PIC's? Since wavelts deal with octaves, or power's of 2 frequency ratio, these would seem to be a natural choice. For those who don't know, wavelet analysis is similar to fourier analysis, with the differences being wavelets are based on a pulse rather than sinusoid, and octave rather than decade frequency spans. That is, any waveform is expressed as a series of pulses, of varying pulse dilation (pulse width), translation (phase) and amplitude. The calculations required go much faster that with the fourier transform, speeding up signal compression and analysis applications. I'm interested in this for an inexpensive EEG/Biofeedback monitor, which spectrum is also based on octaves rather than decades. Here's an ftp site with info about wavelets: ceres.math.yale.edu, ~ftp/pub/wavelets/ The Aprill 92 issue of Dr Dobbs Journal has an article, with example C code and executables on their BBS.

stephnss@XNET.COM wrote Has anyone thought of or have code for using wavelets on PIC's? Since wavelts deal with octaves, or power's of 2 frequency ratio, these would seem to be a natural choice. For those who don't know, wavelet analysis is similar to fourier analysis, with the differences being wavelets are based on a pulse rather than sinusoid, and octave rather than decade frequency I think you may have misconceptions about fourier vs. wavelet transform. Fourier transform decomposes signal into its spectral components as normally understood (a fundamental frequency and its harmonics). Wavelets decompose signal into different set of primitives, based on 'fractal' shapes. Therefore, fourier transform is better for periodic signals, while wavelets work better for non-periodic, noisy signals with sharp transitions. As far as speed difference, both methods are fundamentally similar: they both represent your function f(t) as a sum of transform base functions T(w,t) multiplied by transform coefficients F(w) i i _N__ _N__ \ \ f(t) = > F(w) T(w,t), where F(w,t) = > f(t ) T(w,t) /___ i i i /___ i i i=1 i=1 (moreless). przemek klosowski (spam_OUTprzemekTakeThisOuTrrdstrad.nist.gov) Reactor Division (bldg. 235), E111 National Institute of Standards and Technology Gaithersburg, MD 20899, USA (301) 975 6249

In article .....stephnssKILLspam@spam@XNET.COM writes: >Has anyone thought of or have code for using wavelets on PIC's? Since >wavelts deal with octaves, or power's of 2 frequency ratio, these would seem Wavelets on a single PIC seems to be a bit much. However, an implementation of the Discrete Wavelet Transform could be done on a cascade of PICs. The 17C44 with its hardware multiply would be a good choice for each of the mirror filters. In such a fashion you would then have the PICs forming a pipeline. This might be less expensive than using DSP chips. Lee Holeva

> > I think you may have misconceptions about fourier vs. wavelet transform. > Fourier transform decomposes signal into its spectral components as normally > understood (a fundamental frequency and its harmonics). Wavelets decompose > signal into different set of primitives, based on 'fractal' shapes. > > Therefore, fourier transform is better for periodic signals, while > wavelets work better for non-periodic, noisy signals with sharp > transitions. Sorry, but what you mean is the fourier series. The fourier transform can also be done continuously for non-periodic signals. Erwin -------------------------------------------------------------- Erwin Petter Fraunhofer Institute for biomedical Engineering Ensheimerstr 48 ////// 66386 St.Ingbert /_~~~_\ Germany q o | o p tel. +49 6894 980158 | === | \ / -------------------------------ooOo----oOoo--------------------------

On Sun, 16 Jul 1995, Erwin Petter wrote: > > Therefore, fourier transform is better for periodic signals, while > > wavelets work better for non-periodic, noisy signals with sharp > > transitions. > > Sorry, but what you mean is the fourier series. The fourier > transform can also be done continuously for non-periodic signals. > > Erwin The Fourier transform *implicitly* assumes a periodic signal. You explicitly specify the period when you choose the length of your sample set. In other words, the sample window or the number of samples you use (in a digital transform) on which you perform the transform *is* the period (and the *only* period) of your signal, as far as the transform is concerned. Sure, you can perform a Fourier transform on non-periodic signals. Just be sure to realise that you are *forcing* a periodicity on it. Note that this periodicity becomes the sampling density in the transform space (usually "frequency bins" in the common usage of the transform). Paul Picot ppicotKILLspamirus.rri.uwo.ca Imaging Research Labs, Robarts Research Institute. London, Ontario, Canada Affiliated with University Hospital and the University of Western Ontario

Erwin is right: the Fourier TRANSFORM does not assume periodicity, because it calculates the fourier 'coefficients' for every frequency on the real axis (i.e. a transform of a function f(t) is another function F(omega): for instance the fourier transform of a sin(omega_zero*t) is a delta function with peak at 'omega_zero'; in a complementary way a transform of an impulse has constant power density for all frequencies). Now Fourier SERIES do assume a period (i.e. a fundamental frequency). Having said that, even Fourier transform 'likes' the periodic functions, in the sense that the transforms of them have nicer properties than transforms of arbitrary f(t).

> Erwin is right: the Fourier TRANSFORM does not assume periodicity, > because it calculates the fourier 'coefficients' for every frequency > on the real axis. Sure? Well, the DISCRETE fourier transform DOES assume periodicity, because with a finite number of base vectors which are all periodic (sin and cos), all you can get is a periodic function. In programming, you always deal with the discrete FT (unless you do computer algebra ;-), not the continuous one with the integral. What is the moral of this? If you want to to use the discrete fourier transform on a finite signal, then you have to make this finite signal artificially periodic. The FT always consideres the data block you give it as a periodic signal and you you are not carefull, you will see the probably large edge between the last and the first sample in your spectrum -> you get a pretty weird spectrum. What can you do against this? Just multiply your data block with a 'windowing function', which makes your data periodic (i.e. last sample = first sample = 0) without doing too much harm to the spectrum. A number of good windowing functions are described in every signal processing textbook. They are called Welch, Hann, Hamming, Barlet, etc. window functions. With them, you get really good spectral estimation using the DFT. All this is old well-established standard technology explained in detail in every book about digital signal processing. There's also a nice easy to understand chapter 13.4 in "Numerical Recipes in C" by W. H. Press et. al., ISBN 0-521-43108-5 about spectral estimation using the FFT. Markus -- Markus Kuhn, Computer Science student -- University of Erlangen, Internet Mail: <.....mskuhnKILLspam.....cip.informatik.uni-erlangen.de> - Germany WWW Home: <http://wwwcip.informatik.uni-erlangen.de/user/mskuhn>