You can try with wavelet function ''db4 or db5 '' in discrete wavelet transform (DWT) or wavelet packet transform (WPT) at level 1 decomposition .You will notice abrupt changes in detail coefficient of the signal.

i think the best way in your case as u have very low frequencies is to use a very wide window for better frequency resolution. Specially at the transient point their would be most abrupt frequency change. Use a morlet wavelet at that time instant. Do some shifting and scaling. You will get better results compared to other methods.

You can try with wavelet function ''db4 or db5 '' in discrete wavelet transform (DWT) or wavelet packet transform (WPT) at level 1 decomposition .You will notice abrupt changes in detail coefficient of the signal.

Thank you for the answers, Aamir I am actually using a morlet wavelet with very wide window obviously (So we agree on the method). It is the shifting and scaling part that worries me. Prakash, I will surely try and compare it with my method, thank you!

It could be important to use a complex wavelet (Morlet could be fine, Morse wavelets could be interesting), and look at both the magnitude and the phase of the transform. My understanding is that the size by itself is not important, as the wavelet is scaled over many scales. More important is the quality factor or the number of oscillations in a bump. If unsure, you may use several of these, and combine the detected features. Finally, the sampling of your signals might be quite sensitive with respect to the band-width you are looking at. [Addtion: i would not use real discrete wavelets or wavelet packets first, as they are prone to some aliasing corruption for tiny details. Their interest for synthesis or orthogonality is second to feature detection, that might be more efficient with fully redundant continuous wavelets]

I have worked with Morlet wavelet to extract features from EEG signals in both alpha 98-13 Hz_ and Beta band (18-26 Hz) and it performed very well. You can have a look at my paper which gives you a view to use it the same way:

https://www.researchgate.net/publication/5843673_Brain-computer_interface_analysis_using_continuous_wavelet_transform_and_adaptive_neuro-fuzzy_classifier

Article Brain-Computer Interface Analysis using Continuous Wavelet T...

My immediate answer to your question is, Yes. wavelet transform does provide accurate information in the type of study you are working on. I think Morlet wavelet indeed works well, if you do not choose a wide window, since your interest is in delineating the high frequencies in your signal. Others like Gaussian wavelets (Gaus1 or Gaus3) also work well at lower scales, particularly for the frequencies of your interest. Well, if you are also interested to check the phases of these frequencies, then, you can also use Cgau (complex Gaussian) wavelet in addition to Morlet and check whether you get what you want. Please let me know if I can be of any further help to you.

Laurent Duval, you stated that "the sampling of your signals might be quite sensitive". My signal was acquired at a Fs of 560 Hz but I downsampled it to 10 Hz (out of habit mostly). Did I do something stupid, should I leave it the way it is? I don't really understand though how changing sampling rate might hurt my analysis if the signal frequencies are so low! Can anybody explain this to me?

Dear Jean-Louis,

The sampling process is a mixing process producing the original signal and signal sidebands around fs and its multiples. So, one has to be sure after resampling that there is no aliasing occurred. In your case aliasing may occur if your original signal bandwidth is greater than 10Hz/2. The question now what is the bandwidth of your original acquisition anti aliasing filter. If it is greater than 5Hz aliasing may occur.

IN your case no interference from the down mixing products of signals at 560 and its multiplies since the resampling frequency if very small.

The solution may be to low pass filter the signal before down sampling at the required frequency.

wish you success.

Dear Jean-Louis,

Like Abdelhalim said 10Hz will not yeld aliasing problems to you in the frequency range that you are looking at (and processing the signal becomes a lot faster).

Complementing Laurent answer, hybrid wavelets are a good choice complex morlet and complex gaussian, since db may cause some aliasing.

It is a good idea to use Discrete Wavelet Transform as a filter to locate the scale your information is with FFT (it may be around scales 2^5 2^6).

After locating the bandwith with DWT and FFT, use CWT to generate a spectogram of your frequencies. Do not use DWT and FFT for real signal analysis since DWT may "create" some frequency bands that does not exist in your signal.

If you are using matlab, these functions from wavelet toolbox might be of some help:

-scal2frq, centfrq, cgau, cmor, wavedec, wrcoef, cwtext...

best regards.

Thank you, I actually low-filtered the signal prior to downssampling. I used FFT to locate the bandwith of my signal prior to CWT. I use matlab yes and indeed these functions are very helpful if you own the wavelets toolbox!

Nice! Here we sample our signals using 20Hz with an analogic lowpass filter of 1Hz. cgau4 give us good results when analysing 50-70mHz (gastric contraction). Also we are trying to locate 10-20mHz but it is very difficult since we use rats and the measuring time must be around 30minutes...

If you have any idea about how to optimize our measures it would be of great help though!

Also, Savitsky-Gollay yelds nice results. This article may be of help:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3535517/

Thank you for the article. In all modesty, I think the people that already answered above are better fit for helping you then I would. Good luck Matheus!

Dea Matheus Alvarez,

You can restrict your measuring time to only two to three cycles of your slow wave. From the time domain analysis we can determine the zero crossing times and consequently we can estimate to a good degree of approximation the periodic time of the slow wave. The time ambiguity of the zeo crossing time is = 1/ fs where fs is the sampling frequency. Then the locations of the harmonics will be also be estimated.

By any type of frequency analysis you can analyze the signal in greater accuracy.

From the principle point of view if you want to analyse a waveform it is required to have only one complete period of signal in time domain since the signal is periodic.

I have seen such waves in the above give paper and it seems me that they are quite periodic. You can exploit this periodicity to restrict your measuring time. This helps you reduce your measuring time.

wish you success.

Peter Husar had a nice point. If you are interested in parameter analysis only, e.g. not reconstruction nor filtering, you don't need an analysis/synthesis transformation, and non-linear time-frequency decompositions might be useful. The Matlab-based and free Time-Frequency Toolbox might be practical :

http://tftb.nongnu.org/

However, as long as wavelets oscillate enough, they may provide some hints. Outside Morlet's, the family of generalized Morse wavelets may offer alternatives. And from a purely practical point of view, a set of short-term Fourier transforms with different window sizes may perform a good job.

Would the short-term Fourier transform work if my signal has very low frequency components mostly concentrated around 0.2 and 0.6 Hz (the median frequency is around 0.4 Hz) and my transient lasts 1 sec.

I agree that Wigner-based analysis distributions should work but I just couldn't get around the functions that are supplied by the free Time-Frequency Toolbox! so I sticked to my morlets! If someone can help me apply wigner transform using matlab I will be glad to take it!

Peter,

I agree that signal processing is about understanding the different methods. However, I believe the idea in open-source scripts is to be able to share functions (already proven functional) and apply them directly in your code, instead of rewriting the whole thing. Otherwise, why have toolboxes from the beginning. (Using a toolbox function doesn't necessary mean not understanding what they do).

In any case, thank you for the book advice. I am sure, it will be very helpful to me.