Subject: Re: Uncertainty principle debate From: Dmitry Terez <terez(at)SOUNDMATHTECH.COM> Date: Wed, 11 Feb 2004 18:18:26 -0000 X-Mailer:Netfirms Mailing - http://www.netfirms.comHi, everybody, This question was asked on comp.dsp user group last year. I hate to waste a good answer. So here it is, and believe it or not, it directly applies to the subject of your discussion. __Subject__: Can I Extract Fundamental from Partial Sine Wave? __Date__: Sun, 16 Nov 2003 03:55:36 -0600 > I have some experimental data for In-phase and quadrature signals. > Sometimes the data covers only half or less, of a full cycle. There are > usually about 100 - 140 equally spaced (in time) points, but a few > points are often missing. > > What technique can I use to calculate the fundamental frequency of the > sine wave? I would like to write a program, or use a spread sheet, > which ever is appropriate, or use an existing procedure. > > Any help would be appreciated. > > -- > Regards > > Clive G3CWV > > Hitchin, North Hertfordshire, UK. Jerry Avins <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > Vladimir Vassilevsky wrote: > > > Clive, > > > > What you are trying to find are the A, w and fi parameters for the > > equation: > > A*exp(jwt + fi) > > which makes the best fit with your data. You can do it with > > autoregression. > > > > Vladimir Vassilevsky > > > > DSP and Mixed Signal Design Consultant > > > > http://www.abvolt.com > > It's not quite that simple. As given, the waveform can have harmonics. > > Jerry If your signal is a pure sine wave (maybe noisy), then try to best-fit the equation as proposed by Vladimir. If your signal is periodic but has an unknown harmonic structure, then you need more than one period to determine the fundamental period of a signal. All of the conventional methods (correlation, spectrum, cepstrum-based etc.) used for detecting fundamental period of a signal require at least 2 complete periods to be included in the analysis window (Well, you can try to reduce your window size with cross-correlation, but this is not a way to go). The only method which can reliably get you the period (or its inverse – fundamental frequency) of a periodic signal using analysis window slightly longer than one complete period (at least for clean periodic signals) is the method based on signal embedding in multi-dimensional state space followed by a nearest-neighbor search. It was first presented at ICASSP last year. Go to http://www.soundmathtech.com/pitch Download the ICASSP 2002 paper and the Matlab demo. Although it may look complicated, in reality it is very simple and you can easily implement it for your purposes in about half an hour. Regards, Dmitry Terez SoundMath Technologies, LLC P.O. Box 846 Cherry Hill, NJ 08003 USA