There is no doubt that EMD, EEMD, and Wavelet are signal decomposition techniques for non-stationary and non-linear signals. Now, a question arise whether it is possible to apply these techniques for stationary signals?
The signals used in my problem are vibration time-domain data (acceleration time histories). Some of them are non-stationary and other ones are stationary (proved by Kwiatkowski–Phillips–Schmidt–Shin (KPSS) hypothesis test). With a simple de-trending process, all signals to be stationary.
Thank you
Hi,
I do not know what are the nature (discrete/continuous) and/or the source of your signal (biological/physical process). Nonetheless, considering that your signal varies over time, it is definitely feasible to apply wavelets transforms for stationary signals decomposition. Actually, this is a very interesting and attractive approach as you will be able to find eventually fluctuations in the frequency content along the signal. To accomplish this task, you will have to define, in advance, the analyzing wavelet that better suites your application. And, likewise, it will be necessary to appropriately trade between time and frequency resolutions along the signal. Definitely, not a big deal!
Peace and blessings.
Hi Hassam,
I would like to introduce some keynotes about your question. To deal with non-stationarity, the most common approaches are adaptive models and time-frequency representation. Both the approaches deal with the non-stationarity using the trick to consider (or observe, or "remember") a portion of the signal which can be considered as stationary. Recently, new methods arose and became popular (EMD, SSA). These methods are algorithms (EMD) or empirical approaches (SSA) and although they are powerful tools, they do not have still a robust mathematical/theoretical framework.
Said this, I do not find any reason to not use wavelet or other methods with stationary time series, but I also do not find any reason to prefer these methods, in general more complicated to tune/adapt to the particular application, rather than FT, which has excellent properties in the ideal case and a lot of add-ons and improvements (theoretically proven) to deal with its most common drawbacks.
Hi,
I do not know, which nature are your signals!? and their sources. So, you can apply the mentioned method (stationary signals)...But you can use the simplest one FT.
Hi Hassan,
You will certainly find very useful information in Akay's book from IEEE press. This one has been my reference book for time-frequency transforms.
Also Bronzino's The Biomedical Engineering Handbook Section VI (Biomedical Signal Analysis, Chapters 57, 58 and 59) has a large collection of Time Frequency transforms, including a chapter dedicated to Wavelet transforms.
References are:
i) Akay, Metin (Editor). Time Frequency and Wavelets in Biomedical Signal Processing. IEEE Press, 1998. ISBN 0-7803-1147-7
ii) Bronzino,Joseph D. (Editor). The Biomedical Engineering Handbook. Section VI, pp 886-916. CRC Press / IEEE Press, 1995. ISBN 0-8493-8346-3
Best regards,
Peace and blessings!
Dear Hassan
There is no problem in using EMD with stationary signals. On the contrary, it may happen you obtain some components you were expecting to exist. To examplify. I used it with tidal signals and the two main components (earth and Moon) appeared separated. Go ahead. If you need an algorithm, let me know - [email protected]
In my opinion by applying basic common sense: any method that is suitable for non-stationary signals, can be applied to stationary signals as well. But the other way round is not possible. E.g. EMD/EEMD is data driven method, so doesn't matter whether your data is stationary or non-stationary, it is applicable to any data. Hope this helps a bit. Thanks
In my opinion it can be applied to both Stationary as well as non stationary data sets. But it is well suited for non stationary and non linear data.
Here is the link of my article ,Hope is helpful :
Article SVM Multi-Classification of Induction Machine's bearings def...
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