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How to inspect time-frequency results
 
20:16
If you are unsure of how to look at time-frequency results, this video has the 5-step plan that you need! It also discusses whether time-frequency features can be interpreted as "oscillations." For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 5831 Mike X Cohen
Broad overview of EEG data analysis analysis
 
29:02
This lecture is a very broad introduction to the most commonly used data analyses in cognitive electrophysiology. There is no math, no Matlab, and no data to download. For more information about MATLAB programming: https://www.udemy.com/matlab-programming-mxc/?couponCode=MXC-MATLAB10 For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 8127 Mike X Cohen
Morlet wavelets in time and in frequency
 
14:36
Convolution requires two time series: The data and the kernel. The data is what you already have (EEG/MEG/LFP/etc); here you will learn about the most awesomest kernel for time-frequency decomposition of neural time series data: The Morlet wavelet. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/morlet/morletWavelet.m For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 5030 Mike X Cohen
Multitaper
 
19:47
The final time-frequency analysis method shown here is the multitaper method. It is an extention of the STFFT that can be useful in low-SNR situations. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/multitaper/multitaper.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1066 Mike X Cohen
Fourier transform frequencies and zero-padding
 
38:46
The final thing to know about the Fourier transform is how to convert unit-indices to frequencies in Hz. You will also learn about frequency resolution and how to increase resolution by zero-padding. Patrick McGoohan makes another guest appearance. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/frequencies/frequencies.m A full-length course on the Fourier transform using MATLAB and Python programming can be found here: https://www.udemy.com/fourier-transform-mxc/?couponCode=MXC-FOURIER10 For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 2525 Mike X Cohen
Sine waves in time and in frequency
 
17:24
This video provides a deeper introduction to sine waves. This lecture plus the next lecture (dot-product) are essential for understanding how the Fourier transform works. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/sinewave/sinewave.m For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 2673 Mike X Cohen
Matthieu Kowalski: Time-frequency frames and applications to audio analysis - Part 2
 
01:14:29
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area Time-frequency (or Gabor) frames are constructed from time- and frequency shifts of one (or several) basic analysis window and thus carry a very particular structure. On the other hand, due to their close relation to standard signal processing tools such as the short-time Fourier transform, but also local cosine bases or lapped transforms, in the past years time-frequency frames have increasingly been applied to solve problems in audio signal processing. In this course, we will introduce the basic concepts of time-frequency frames, keeping their connection to audio applications as a guide-line. We will show how standard mathematical tools such as the Walnut representations can be used to obtain convenient reconstruction methods and also generalizations such the non-stationary Gabor transform. Applications such as the realization of an invertible constant-Q transform will be presented. Finally, we will introduce the basic notions of transform domain modelling, in particular those based on sparsity and structured sparsity, and their applications to denoising, multilayer decomposition and declipping. (Slides in attachment). Recording during the thematic meeting: "Computational harmonic analysis - with applications to signal and image processing" the October 22, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
Total vs. phase-locked vs. non-phase-locked power
 
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Time-frequency power can be decomposed into phase-locked and non-phase-locked components. This is a methodological distinction that helps understand which time-frequency power features are also phase-locked. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/nonphaselocked/nonphaselocked.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 863 Mike X Cohen
Accurately recovering data units in FFT and convolution
 
22:20
This lecture shows how to recover the original units in the data after computing the FFT or wavelet convolution. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/units/units.m For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 363 Mike X Cohen
Instantaneous frequency (frequency sliding)
 
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Although most time-frequency analysis methods assume frequency stationarity, there are several ways to measure the time-varying changes in dominant frequency within a restricted range (e.g., within the alpha band). Instantaneous frequency ("frequency sliding") is one of those methods. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/freqslide/freqslide.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1223 Mike X Cohen
Intro to connectivity, volume conduction, and time- vs. trial-based connectivity
 
19:20
This lecturelet will introduce you to four considerations to keep in mind when performing or evaluating functional connectivity analyses with EEG/LFP data. For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1008 Mike X Cohen
Linear vs. logarithmic time-frequency plots
 
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This video has a quick discussion on whether you should use logarithmically or linearly spaced time-frequency plots. It also contains a few hints and tricks about using imagesc and contourf functions. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/loglinTF/loglinTF.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 387 Mike X Cohen
Filter, epoch, baseline subtraction, referencing
 
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This lecture provides a brief overview of EEG preprocessing steps. For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 3220 Mike X Cohen
The Hilbert transform
 
09:46
In this video you will learn about the Hilbert transform, which can be used to compute the "analytic signal" (a complex time series from which instantaneous power and phase angles can be extracted). This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/hilbert/hilbertX.m mikexcohen.com/lecturelets/sampleEEGdata.mat For more information about spectral analysis: https://www.udemy.com/fourier-transform-mxc/?couponCode=MXC-FOURIER10 For more information about MATLAB programming: https://www.udemy.com/matlab-programming-mxc/?couponCode=MXC-MATLAB10 For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 12744 Mike X Cohen
Convolution in the time domain
 
23:52
Now that you understand the Fourier transform, it's time to start learning about time-frequency analyses. Convolution is one of the best ways to extract time-frequency dynamics from a time series. Convolution can be conceptualized and implemented in the time domain or in the frequency domain. It is important to understand both conceptualizations. We start with the time domain implementation. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/convolutiontime/convolutionTime.m For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 4685 Mike X Cohen
Power-law scaling and the need for normalization
 
09:30
Time-frequency power decreases nonlinearly with increasing frequency. In this video you will learn about the problems in interpretation and statistics that this "power-law" creates, and in the next video you will learn a few ways to remedy the situation. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/powerlaw/powerLawTF.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1148 Mike X Cohen
Euler's formula and extracting power and phase
 
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Extracting time-frequency information from the result of complex Morlet wavelet convolution involves reinterpreting Euler's formula (eik), which allows you to extract three important pieces of information from the result of complex Morlet wavelet convolution (power, phase, and the band-pass filtered signal). This lecture is different from the one on complex Fourier coefficients, so don't skip this one! This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/eulersconvolution/eulers_and_convolution.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1601 Mike X Cohen
Short-time Fourier transform
 
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Here you will learn about the short-time Fourier transform (STFFT; the extra "F" is for "fast"), which is another method for time-frequency analysis. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/stfft/stfft.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat A full-length course on the Fourier transform using MATLAB and Python programming can be found here: https://www.udemy.com/fourier-transform-mxc/?couponCode=MXC-FOURIER10 For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 3037 Mike X Cohen
Introduction to time series analysis lecturelets
 
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A short introduction to these lectures, what you will get out of them, and how best to learn from them. And you'll see a picture of the disembodied voice behind all the lectures. For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 3878 Mike X Cohen
Introduction to statistics
 
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This lecturelet will introduce you to the series on statistical analyses of time-frequency data. For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 845 Mike X Cohen
Effects of signal nonstationarities on the Fourier power spectrum
 
09:29
This is part of an online course on foundations and applications of the Fourier transform. The course includes 4+ hours of video lectures, pdf readers, exercises, and solutions. Each of the video lectures comes with MATLAB code, Python code, and sample datasets for applications. With 3000+ lines of code, this course is also a great way to improve your programming skills. More info here: https://www.udemy.com/fourier-transform-mxc/?couponCode=MXC-FOURIER10
Views: 173 Mike X Cohen
The dot (a.k.a. inner) product
 
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The dot product is a simple but important algorithm for many signal processing applications, including the Fourier transform and convolution. In this video, you will learn how to compute the dot product, how to interpret the sign of a dot product, and two interpretations (algebraic and geometric) of the dot product. For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1316 Mike X Cohen
Frequency resolution of wavelet convolution
 
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This video explains how you can measure 2 Hz activity in 200 ms. It's a clarification of a question that I often get. For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1144 Mike X Cohen
Complex sine waves and interpreting Fourier coefficients
 
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Now that you know the basic mechanics underlying the Fourier transform, it's time to learn about complex numbers, complex sine waves, and how to extract power and phase information from a complex dot product. Don't worry, it's actually not so complex! This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/complexfourier/complexfourier.m A full-length course on the Fourier transform using MATLAB and Python programming can be found here: https://www.udemy.com/fourier-transform-mxc/?couponCode=MXC-FOURIER10 For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1725 Mike X Cohen
The discrete-time Fourier transform
 
30:57
The Fourier transform is arguably the most important algorithm in signal processing and communications technology (not to mention neural time series data analysis!). This video provides an in-depth, step-by-step explanation of how the Fourier transform works. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/fourier/fourier.m A full-length course on the Fourier transform using MATLAB and Python programming can be found here: https://www.udemy.com/fourier-transform-mxc/?couponCode=MXC-FOURIER10 For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 2539 Mike X Cohen
Convolution via frequency domain multiplication
 
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Is time-domain convolution too slow? (Yes it is.) Learn how to do lightning-fast convolution in the frequency domain. This will also help you understand that wavelet convolution is really just filtering. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/convfreqdom/convolutionAsFreqMult.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 3132 Mike X Cohen
Effects of Morlet wavelet parameters on results
 
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There is one important parameter of Morlet wavelets, which is the width of the Gaussian (a.k.a. the "number of cycles"). In this video we will explore this parameter and see what effects different parameter values have on the results. I will also provide some advice for when you should use which parameter settings, and how to interpret results of different settings. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/waveletparams/waveletparams.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 3138 Mike X Cohen
Adi cohen - class
 
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Adi cohen stupida
Views: 49 shira attiach
Stationarity and effects of violations
 
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In simplistic introductory tutorials on the Fourier transform, you see examples of perfectly stationary signals ("stationary" means the statistical properties such as mean, variance, etc., remain the same over time). But brain activity is far from stationary! In fact, it is fairly accurate to say that neuroscientists are specifically interested in the brain's non-stationarities (for example, after seeing a visual stimulus or when recalling a specific memory). In this video you will learn what happens in the frequency domain when the time-domain signal is non-stationary. And to quell suspense: The Fourier transform is always a perfect and useful reconstruction, even when the data violate stationarity. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/fftstationarity/fftstationarity.m For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 719 Mike X Cohen
The three most important equations in neural time series analyses
 
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There are three equations that form the mathematical backbone of nearly all time-frequency-based analyses. If you memorize these equations, and can learn to recognize them embedded inside code and long equations, you will find learning data analysis to be much more intuitive and tangible. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/trinity/threeImportantEquations.m For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1245 Mike X Cohen
Independent components analysis for removing artifacts
 
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This lecturelet will illustrate one method of identifying independent components for removal. For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 5112 Mike X Cohen
Band-pass filtering and the filter-Hilbert method
 
30:20
The Hilbert transform produces uninterpretable results on broadband data. You will need to narrow-band filter the signal first. This video shows one method of computing an FIR filter and applying it to EEG data. Together with the Hilbert transform, this gives us the filter-Hilbert method. This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/firfilter/firfilter.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 2710 Mike X Cohen
Zero-padding in the time domain
 
08:25
This is part of an online course on foundations and applications of the Fourier transform. The course includes 4+ hours of video lectures, pdf readers, exercises, and solutions. Each of the video lectures comes with MATLAB code, Python code, and sample datasets for applications. With 3000+ lines of code, this course is also a great way to improve your programming skills. More info here: https://www.udemy.com/fourier-transform-mxc/?couponCode=MXC-FOURIER10
Views: 399 Mike X Cohen
Inter-trial phase clustering
 
27:51
So far you've just been learning about how to deal with the power of the time-frequency results. This video will introduce you to working with phase values, which reflect the timing of the activity relative to the time=0 event (e.g., stimulus onset). This video uses the following MATLAB code: http://mikexcohen.com/lecturelets/itpc/itpc.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1134 Mike X Cohen
How to calculate Cohen d effect size
 
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Tutorial on how to calculate the Cohen d or effect size in for groups with different means. This test is used to compare two means. http://www.Youtube.Com/statisticsfun Like us on: http://www.facebook.com/PartyMoreStudyLess Created by David Longstreet, Professor of the Universe, MyBookSucks http://www.linkedin.com/in/davidlongstreet
Views: 93462 statisticsfun
Convolution with many trials
 
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So far, all of the analyses have used single-trial data. But most experiments involve many trials. In this video you will learn about performing wavelet convolution over many trials. You will also learn a few Matlab programming tricks that will help make your analysis faster and more elegant. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/manytrials/manyTrials.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1103 Mike X Cohen
Multiclass Epileptic Seizure classification using time frequency analysis of EEG signals
 
03:59
Seizure is a transient abnormal behavior of neurons within one or several neural networks, which limits the patients physical and mental activities. Since conventional time or frequency domain analysis is found inadequate to describe the characteristics of a non-stationary signal, such as electroencephalography (EEG), in this paper, we propose to transform the EEG data using twelve Cohen class kernel functions in order to facilitate the time-frequency analysis. The transformed data thus obtained is exploited to formulate a feature vector consists of modular energy and modular entropy that can better model the time-frequency behavior of the EEG data. The feature vector is fed to an Artificial Neural Network (ANN) classifier in order to classify epileptic seizure data originating from different parts and state of the brain. A number of simulations is carried out using a benchmark EEG dataset. It is shown that the proposed method is capable of producing greater accuracy in comparison to that obtained by using a state-of-the-art method of epileptic seizure classification using the same EEG dataset and classifier.
Views: 1153 VERILOG COURSE TEAM
Choosing a "baseline"
 
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Selecting an appropriate baseline period for normalization is not a trivial decision. Watch and learn! This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/whichbaseline/whichbaseline.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 860 Mike X Cohen
Post-analysis temporal downsampling
 
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Are your time-frequency results matrices too big? Watch this video to learn how to reduce the temporal resolution of your results to match their temporal precision, which can save lots of time and space. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/postanal_ds/postanalysis_ds.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 366 Mike X Cohen
Bei mir bist du schejn - frequency analysis
 
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This Video shows the song "Bei mir bist du schejn", as performed by the "Budapest Klezmer Band" together with its frequency spectrum. The original video can be found here: http://www.youtube.com/watch?v=ZUVEq6NC7mM If you ever wanted to know what your music really is, if you're interested in the perfect choreography of oszillations that makes you feel happy or sad, you might be interested in antonia: http://qt-apps.org/content/show.php/antonia?content=118179 (I hope you know http://qt-apps.org ?) antonia (A New TOol for maNIpulating Audiodata) is a program that enables you to manipulate audiodata in the time- as well as in the frequency-domain. Actually, it is not much more than a proof-of-concept, but at least it reveals some information about your music that you never might get otherwise. about the video: Time goes from left to right, frequency from bottom to top. The bar in the middle shows the actual position. The frequency-scale is neither linear nor logarithmic, but is the bark-scale, that is supposed to fit best with humans sense for tone-pitch. The scales on both sides give the tone a=440Hz and its upper and lower octaves. If lower tones look a little blurrier, this is due to a mathematical effect that is related to the uncertainty principle (but it is not a quantum mechanical effect). You simply can't calculate both the time and frequency of a tone with arbitrary high accuracy. Since (for this scale) frequency-resolution increases for lower frequencies, time-resolution has to decrease. http://en.wikipedia.org/wiki/Bark_scale http://en.wikipedia.org/wiki/Uncertainty_principle#Uncertainty_theorems_in_harmonic_analysis
Views: 304 hellnonamefree
Inverse Fourier transform
 
08:52
This is part of an online course on foundations and applications of the Fourier transform. The course includes 4+ hours of video lectures, pdf readers, exercises, and solutions. Each of the video lectures comes with MATLAB code, Python code, and sample datasets for applications. With 3000+ lines of code, this course is also a great way to improve your programming skills. More info here: https://www.udemy.com/fourier-transform-mxc/?couponCode=MXC-FOURIER10
Views: 1221 Mike X Cohen
Power-based connectivity analyses
 
19:26
This lecturelet will introduce you to two methods of estimating functional connectivity via time-frequency power. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/powerconn/powerconn.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 408 Mike X Cohen
Phase-based connectivity analyses
 
37:27
Phase-based connectivity methods are the most widely used for estimating frequency-band-specific functional connectivity. This video provides a discussion and illustration of two classes of phase-based connectivity methods (cluster-based and lag-based). This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/phaseconn/phase_connectivity.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 790 Mike X Cohen
Sub-Nyquist Sampling of Wideband Signals- Deborah Cohen - Technion
 
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Lecture presented on March 21, 2012 - Technion Faculty of Electrical Engineering Radio frequency (RF) technology enables the modulation of narrowband signals by high carrier frequencies. As a result, many important and emerging applications, such as cognitive radios, have to sense and sample wideband signals with extremely high Nyquist rates, leading to a large number of samples that need to be transmitted, stored and processed. Those required sampling rates may even exceed today's best analog-to-digital (ADCs) front-end bandwidths by orders of magnitude. Therefore we need to exploit the structure of the input signal in order to acquire it. Such wideband signals are typically sparse, that is, consist of a relatively small number of narrowband transmissions spread across a wide spectrum. We present a sampling system, the modulated wideband converter (MWC), that performs preprocessing on a sparse analog signal before sampling it at a low rate, namely twice the Landau rate. We then develop a digital architecture that reconstructs the analog signal, showing that we can recover the original signal from the sub-Nyquist samples.
Views: 2122 Technion
EEG data and indexing in Matlab
 
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This video describes how to identify time/frequency/electrode points in your data, as well as a few tips for Matlab programming and debugging. The video uses the following files (and also the topoplot function, which is free to download with the eeglab toolbox): http://mikexcohen.com/lecturelets/indexing/indexing.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat A full-length course on MATLAB programming and debugging can be found here: https://www.udemy.com/matlab-programming-mxc/?couponCode=MXC-MATLAB10 For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 4239 Mike X Cohen
Understanding Wavelets, Part 1: What Are Wavelets
 
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This introductory video covers what wavelets are and how you can use them to explore your data in MATLAB®. •Try Wavelet Toolbox: https://goo.gl/m0ms9d •Ready to Buy: https://goo.gl/sMfoDr The video focuses on two important wavelet transform concepts: scaling and shifting. The concepts can be applied to 2D data such as images. Video Transcript: Hello, everyone. In this introductory session, I will cover some basic wavelet concepts. I will be primarily using a 1-D example, but the same concepts can be applied to images, as well. First, let's review what a wavelet is. Real world data or signals frequently exhibit slowly changing trends or oscillations punctuated with transients. On the other hand, images have smooth regions interrupted by edges or abrupt changes in contrast. These abrupt changes are often the most interesting parts of the data, both perceptually and in terms of the information they provide. The Fourier transform is a powerful tool for data analysis. However, it does not represent abrupt changes efficiently. The reason for this is that the Fourier transform represents data as sum of sine waves, which are not localized in time or space. These sine waves oscillate forever. Therefore, to accurately analyze signals and images that have abrupt changes, we need to use a new class of functions that are well localized in time and frequency: This brings us to the topic of Wavelets. A wavelet is a rapidly decaying, wave-like oscillation that has zero mean. Unlike sinusoids, which extend to infinity, a wavelet exists for a finite duration. Wavelets come in different sizes and shapes. Here are some of the well-known ones. The availability of a wide range of wavelets is a key strength of wavelet analysis. To choose the right wavelet, you'll need to consider the application you'll use it for. We will discuss this in more detail in a subsequent session. For now, let's focus on two important wavelet transform concepts: scaling and shifting. Let' start with scaling. Say you have a signal PSI(t). Scaling refers to the process of stretching or shrinking the signal in time, which can be expressed using this equation [on screen]. S is the scaling factor, which is a positive value and corresponds to how much a signal is scaled in time. The scale factor is inversely proportional to frequency. For example, scaling a sine wave by 2 results in reducing its original frequency by half or by an octave. For a wavelet, there is a reciprocal relationship between scale and frequency with a constant of proportionality. This constant of proportionality is called the "center frequency" of the wavelet. This is because, unlike the sinewave, the wavelet has a band pass characteristic in the frequency domain. Mathematically, the equivalent frequency is defined using this equation [on screen], where Cf is center frequency of the wavelet, s is the wavelet scale, and delta t is the sampling interval. Therefore when you scale a wavelet by a factor of 2, it results in reducing the equivalent frequency by an octave. For instance, here is how a sym4 wavelet with center frequency 0.71 Hz corresponds to a sine wave of same frequency. A larger scale factor results in a stretched wavelet, which corresponds to a lower frequency. A smaller scale factor results in a shrunken wavelet, which corresponds to a high frequency. A stretched wavelet helps in capturing the slowly varying changes in a signal while a compressed wavelet helps in capturing abrupt changes. You can construct different scales that inversely correspond the equivalent frequencies, as mentioned earlier. Next, we'll discuss shifting. Shifting a wavelet simply means delaying or advancing the onset of the wavelet along the length of the signal. A shifted wavelet represented using this notation [on screen] means that the wavelet is shifted and centered at k. We need to shift the wavelet to align with the feature we are looking for in a signal.The two major transforms in wavelet analysis are Continuous and Discrete Wavelet Transforms. These transforms differ based on how the wavelets are scaled and shifted. More on this in the next session. But for now, you've got the basic concepts behind wavelets.
Views: 134257 MATLAB
Multiclass epileptic seizure classification using using DFT and FFT of EEG signals
 
07:22
Seizure is a transient abnormal behavior of neurons within one or several neural networks, which limits the patients physical and mental activities. Since conventional time or frequency domain analysis is found inadequate to describe the characteristics of a non-stationary signal, such as electroencephalography (EEG), in this paper, we propose to transform the EEG data using twelve Cohen class kernel functions in order to facilitate the time-frequency analysis. The transformed data thus obtained is exploited to formulate a feature vector consists of modular energy and modular entropy that can better model the time-frequency behavior of the EEG data. The feature vector is fed to an Artificial Neural Network (ANN) classifier in order to classify epileptic seizure data originating from different parts and state of the brain. A number of simulations is carried out using a benchmark EEG dataset. It is shown that the proposed method is capable of producing greater accuracy in comparison to that obtained by using a state-of-the-art method of epileptic seizure classification using the same EEG dataset and classifier.
Views: 1171 VERILOG COURSE TEAM
Overview of time-domain analyses
 
18:29
This video introduces the mathematics behind event-related potentials (averaging) and how to compute ERPs in Matlab. You'll also learn how ERPs were computed in the 1950's. This video uses the following MATLAB files: http://mikexcohen.com/lecturelets/timedomain/timedomain.m http://mikexcohen.com/lecturelets/sampleEEGdata.mat For more online courses about programming, data analysis, linear algebra, and statistics, see http://sincxpress.com/
Views: 1428 Mike X Cohen
Examples of Fourier transform applications
 
09:20
This is part of an online course on foundations and applications of the Fourier transform. The course includes 4+ hours of video lectures, pdf readers, exercises, and solutions. Each of the video lectures comes with MATLAB code, Python code, and sample datasets for applications. With 3000+ lines of code, this course is also a great way to improve your programming skills. More info here: https://www.udemy.com/fourier-transform-mxc/?couponCode=MXC-FOURIER10
Views: 836 Mike X Cohen