# [Eeglablist] Wavelet comparisons

Arnaud Delorme arno at salk.edu
Mon Feb 14 18:43:30 PST 2005

```>
> In an ECoG experiment, I want to calculate frequency power changes in
> induced activity.  I have applied the continuous wavelet transform
> (CWT) and now I want to use a measure of 'change' from the baseline
> (that is, prior to the event).  Three issues arise:
>
> 1) How to calculate the "baseline" wavelet coefficient: I could take a
> 100msec window prior to the event and calculate an average baseline
> coefficient.  Is this 'mathematically' valid?  It works ok for
> frequency power data, but coefficient data are another story.

Wavelet can be processed the same as FFT data. Convoluting complex
wavelets with continuous data is similar to applying a windowed FFT
(they both return complex numbers at each time-frequency points). The
main difference with wavelets is that the number of cycles (~
oscillations) remains the same at all frequencies (with FFT since the
window size is the same at all frequencies, there are many more cycles
at high frequencies than at low frequencies). With wavelets and FFT, the
strategy to compute amplitude and power is the same: for amplitude, you
take the absolute value of the complex number at each time-frequency
point. Power is the square of the amplitude. Power in dB is 10*Log10(Power).

> 2) How to calculate the "change": I could simply take the adjusted
> difference in the coefficient between each timepoint and the
> baseline.  But is this valid?

Yes, you may subtract the dB power during the baseline (or divide by the
absolute power during baseline which is the same).

> 3) How to produce an "average change" waveform: Is this possible by
> simply averaging coefficient waveforms for all trials?

Yes, and normalizing. The timef() function will do all that for you.
Equations are described in the EEGLAB reference paper

http://feedback.ebay.com/ws/eBayISAPI.dll?ResolveDispute&DisputeId=49514302

> My intuition says that wavelet data are to be treated differently that
> plain frequency power data.

No, they can be treated similarly as explained above.

Hope this help.

Arno

```