CH 13: Complex Morlet Wavelets and Extracting Power and Phase

This chapter discusses Complex Morlet Wavlets, how they extend on Morlet Wavelets from last chapter to extract phase and power information, and mechanisms of imaginary numbers to accomplish this. Also covers some practical advise on using them.

13.1 The Wavelet Complex

Complex Morlet Wavelets are needed to to extract power and phase information from EEG data. They are called complex because they involve complex numbers (IE they use imaginary numbers). This means the complex wavelet occupies 3 dimensions (real numbers, imaginary numbers, and time). 

Think of this as a corkscrew going through time (with the x and y plane the corkscrew rotates on being the real and imaginary axis). 

Before this point, with non-complex Morlet wavelets, we did not see the imaginary axis due simpler equations used, but also since we only showed 2D views for the data. Arguably you can do those projects of this 3D spiral onto 2D planes as well.

13.2 Imagining the Imaginary

Imaginary numbers are denoted with i (or sometimes j ), and represent the square root of negative one. They are often scaled by a scalar (For example: 3i ). When combined with a non-imaginary number (they cannot be added directly), we end up with a 2 number expression, such as 6 + 3i . This expression is known as a complex number.

Be sure to practice and understand the concept of imaginary numbers before going further, otherwise you WILL get lost!