Hi Ali. I imagined two cases given that your question is a bit ambiguous. First, in the case you know the original signal X, two measures could give you an idea of the decomposition level of a signal x extracted from X : (1) signal length, and more general (2) frequency spectrum. Second, if you are given a signal, let's say z, and the question: What level of decomposition is z?, The answer would be none. It is not decomposed as far as you can tell because the question does not states if z was obtained from a big Z. However, if you know the nature of the phenomena that generated z, then (2) will give you the answer again. For example, if z was generated by measuring muscle electrical activity, called EMG: Electromyography, it is commonly sampled at 1 kHz. Then if the spectrum of z is confined inside a bandwidth of ~125 Hz then you could say it was decomposed twice: (level zero bandwidth: 500 Hz, level 1: 250 Hz, level 2: 125 Hz...).
Hi Ali, I sugest you choose decomposition level according to the composition and characteristics of the signal you studied.
Decomposition level can be identified by looking at the frequency spectrum .Wavelet decomposition for instance is like a filter bank applied to your signal in which each level will represent a corresponding frequency.
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