[Eeglablist] scaling factors when using wavelet transform?

[Paul Kieffaber]

Good morning list.

I am using a plain "vanilla" wavelet (morlet) transform to generate some 
time-frequency plots and have a question for the list about the 
amplitude units that are returned. All I have done at this point is to 
implement the transform as described in Herrmann et al., 2004a 
<http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VNP-4MFCWC4-1&_user=650606&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000035099&_version=1&_urlVersion=0&_userid=650606&md5=3677b462874a0dd17bef64c5ee59d929#bbib21> 
C.S. Herrmann, M. Grigutsch and N.A. Busch, EEG oscillations and wavelet 
analysis. In: T.C. Handy, Editor, /Event-related potentials – a methods 
handbook/, MIT Press (2004), pp. 229–259.

Using the wavelet-scaling factor, [sqrt(2/pi) / sigma_t], the units of 
amplitude match the units of the input signal. That is, if I submit a 
vector composed of the combination of a 10Hz sine wave with amplitude 5 
and a 20Hz sine wave with amplitude 15, the wavelet transform produces a 
time-frequency representation of the signal with peaks at frequencies of 
10 and 20 Hz and peak amplitudes at ~5 and ~15 respectively.

The question I have is about the units that are returned when the 
wavelets are instead scaled by [1/(sqrt(sigma_t*sqrt(pi))] to have unit 
energy. In this case, the time-frequency representation is qualitatively 
the same, but I am unclear about the interpretation of the units.

Thanks in advance,

Paul Kieffaber