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Spectral analysis Kenneth D. Harris 18/2/15
Continuous processes A continuous process defines a probability distribution over the space of possible signals Sample space = all possible LFP signals Probability density 0.000343534976
Multivariate Gaussian distribution
Stationary Gaussian process
Types of covariance matrix
Which are stationary?
Power spectrum estimation error
Power spectrum estimation
Tapering Fourier transform assumes a periodic signal Periodic signal is discontinuous => too much high-frequency power
Welch’s method Average the squared FFT over multiple windows Simplest method, use when you have a long signal
Welch’s method results (100 windows)
Averaging in time and frequency Shorter windows => more windows Less noisy Less frequency resolution Averaging over multiple windows is equivalent to averaging over neighboring frequencies
Multi-taper method Only one window, but average over different taper shapes Use when you have short signals Taper shapes chosen to have fixed bandwidth
Multitaper method (1 window)
Hippocampus LFP power spectra Typical “1/f” shape Oscillations seen as modulations around this Usually small, broad peaks CA1 pyramidal layer Buzsaki et al, Neuroscience 2003
Connexin-36 knockout Buhl et al, J Neurosci 2003
Stimulus changes power spectrum in V1 High-frequency broadband power usually correlates with firing rate Is this a gamma oscillation? Henrie and Shapley J Neurophys 2005
Attention changes power spectrum in V1 Chalk et al, Neuron 2010
Noise in Radiographic Imaging
Change-Point Detection Techniques for Piecewise Locally Stationary Time Series Michael Last National Institute of Statistical Sciences Talk for Midyear.
Gravitational Wave Astronomy Dr. Giles Hammond Institute for Gravitational Research SUPA, University of Glasgow Universität Jena, August 2010.
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Adaptive Hough transform for the search of periodic sources P. Astone, S. Frasca, C. Palomba Universita` di Roma “La Sapienza” and INFN Roma Talk outline.
Fourier series With coefficients:. Complex Fourier series Fourier transform (transforms series from time to frequency domain) Discrete Fourier transform.
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Local Field Potentials, Spikes and Modeling Strategies for Both Robert Haslinger Dept. of Brain and Cog. Sciences: MIT Martinos Center for Biomedical Imaging:
Environmental Data Analysis with MatLab Lecture 12: Power Spectral Density.
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DEVON BRYANT CS 525 SEMESTER PROJECT Audio Signal MIDI Transcription.
The Fourier transform. Properties of Fourier transforms Convolution Scaling Translation.
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