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Wavelet transformation

Wavelet transformation. Emrah Duzel Institute of Cognitive Neuroscience UCL. Why analyse neural oscillations?. Temporal code of information processing (versus rate code) Functional coupling Interareal synchrony Local field potentials and their correlation with fMRI

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Wavelet transformation

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  1. Wavelet transformation Emrah Duzel Institute of Cognitive Neuroscience UCL

  2. Why analyse neural oscillations? • Temporal code of information processing (versus rate code) • Functional coupling • Interareal synchrony • Local field potentials and their correlation with fMRI • Functional specificity of oscillations

  3. Makeig et al., 2004 Large scale neural dynamics of higher cognitive processes: At least three types of stimulus-responses • Evoked response:the addition of response amplitude to the ongoing brain activity in a time-locked manner. • Schah et al., 2004, Cereb Cortex • Phase resetting response:the resetting of ongoing oscillatory brain activity without concomitant changes in response amplitude. • Penny, Kiebel, Kilner, Rugg, 2002, Trends in Cog Sci. / Makeig et al., 2002, Science • Induced response:the addition of response amplitude that is not time-locked to stimulus onset. • Tallon-Baudry and Bertrand, 1998, Trends in Cog Sci.

  4. 1 0 Phase resetting 8 trials Phase-resetting of a 10 Hz oscillation ERP power Penny, Kiebel, Kilner, Rugg, 2002, Trends in Cog Sci. / Makeig et al., 2002, Science / Klimesh et al., 2001, Cog Brain Res. / Burgess and Gruzelier, 2000, Psychophys. Measure of phase alignment

  5. Single subject analyses of M400 old/new effects Clear evidence of evoked responses in some subjects

  6. Overview • Basics of digital signal processing • Sampling theory • Fourier Transforms • Discrete Fourier Transforms • Wavelet Analysis • Applications and online demonstrations

  7. Digital signal processing • Decompose a signal into simple additive components • Process these components in a useful manner • Synthesize them into a final result

  8. Sampling theory • Nyquist theorem • Sample rate • Nyquist frequency • Aliasing • With each signal there are 4 critical parameters: • Highest frequency in the signal (determined by low-pass filter) • Twice this frequency • Sampling rate • SR / 2 (nyquist frequency/rate)

  9. Sampling theoryNyquist theorem: a signal can be properly sampeld only if it does not contain frequencies above ½ sampling frequency • Aliasing: if a signal contains frequencies above the Nyquist frequency. • Loss of information • Introduces wrong information (waves take on different ‚identities‘ • Loss of phase information (phase shift)

  10. Single-epoch wavelet transforms Spectral analysis x Wavelet averaging

  11. Wavelettransformation ERP + Phase

  12. Different morlet wavelets Better time resolution Good compromise Better freq. resolution

  13. Time-frequency resolution of a standard Morlet-wavelet

  14. Time-frequency resolution of a standard Morlet-wavelet

  15. Time-frequency resolution of a standard Morlet-wavelet

  16. convolution

  17. Matlab demo • Create an artificial signal composed of several frequencies of varying time/amplitude modulation • continuous delta [2Hz] • continuous alpha [10 Hz] • continuous beta [20Hz] • theta-burst [5Hz, +200 ms] • gamma_burst [40 Hz, -200] • gamma_burst [67 Hz, -100] • gamma_burst [67 Hz, +200] • Create a wavelet • Convolve wavelets and signal • highlight the issue of amplitude normalization • highlight limits of time/frequency resolution • Plot a time/frequency spectrogramm • Illustrate phase resetting 67hz 40hz beta alpha theta delta -500 +500

  18. Matlab demo • Create an artificial signal composed of a linear combination of several sinusoids with different frequencies and time/amplitude modulations angular frequency A*sin(2 pi ω t) • where • ω is the angular frequency or angular speed (measured in radians per second), • T is the period (measured in seconds), • f is the frequency (measured in hertz) • e.g. if T = 50 ms = 0.05 sec • then f = 1/0.05 = 20 Hz delta=sin(2*pi*1/500*(t)) t=-500:500

  19. Matlab demo • Create a wavelet wavelet_beta=sin(2*pi*t/50).*exp(-(t/50/strecth).^2)

  20. Complex numbers In polar notation each point zis determined by an angle φand a distance r In a Cartesian coordinate system each point z is determined by two axes central point is ‘pole’ r trigonometric form exponential form Euler’s formula r is called the absolute value or modulus of z

  21. Frequency resolution Time resolution

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