The major goal of presentation is to illustrate some of the more important applications of the wavelet analysis to financial data set. The focus is set on identification and description of hidden patterns.

Views: 3274
Data Science Society

This is a ~3-minute video highlight produced by undergraduate students Charlie Tian and Christina Coley regarding their research topic during the 2017 AMALTHEA REU Program at Florida Institute of Technology in Melbourne, FL. They were mentored by doctoral student Kaylen Bryan and professor Dr. Adrian Peter (Engineering Systems Department). More details about their project can be found at http://www.amalthea-reu.org.

Views: 3913
The AMALTHEA REU Program

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: 167927
MATLAB

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: 7637
Mike X Cohen

COURSE WEBPAGE: Inferring Structure of Complex Systems
https://faculty.washington.edu/kutz/am563/am563.html
This lecture introduces the wavelet decomposition of a signal. The time-frequency decomposition is a generalization of the Gabor transform and allows for a intuitive decomposition of time series data at different frequencies.

Views: 9927
Nathan Kutz

In this talk, Danny Yuan explains intuitively fast Fourier transformation and recurrent neural network. He explores how the concepts play critical roles in time series forecasting. Learn what the tools are, the key concepts associated with them, and why they are useful in time series forecasting.
Danny Yuan is a software engineer in Uber. He’s currently working on streaming systems for Uber’s marketplace platform.
This video was recorded at QCon.ai 2018: https://bit.ly/2piRtLl
For more awesome presentations on innovator and early adopter topics, check InfoQ’s selection of talks from conferences worldwide http://bit.ly/2tm9loz
Join a community of over 250 K senior developers by signing up for InfoQ’s weekly Newsletter: https://bit.ly/2wwKVzu

Views: 30526
InfoQ

Authors:
Jingyuan Wang (Beihang University); Ze Wang (Beihang University); Jianfeng Li (Beihang University); Junjie Wu (Beihang University)
More on http://www.kdd.org/kdd2018/

Views: 235
KDD2018 video

Vanishing moments, heisenberg uncertainty explained

Views: 98279
Simon Xu

Views: 24679
Science Port

PyData New York City 2017
Time series data is ubiquitous, and time series modeling techniques are data scientists’ essential tools. This presentation compares Vector Autoregressive (VAR) model, which is one of the most important class of multivariate time series statistical models, and neural network-based techniques, which has received a lot of attention in the data science community in the past few years.

Views: 27487
PyData

Lecture with Ole Christensen. Kapitler: 00:00 - Repetition ; 06:00 - The Key Step (Prop 8.2.6); 29:00 - Construction Of The Wavelet (Thrm 8.2.7); 36:00 - More On The Wavelet (Prop. 8.2.8); 45:00 - Conciderations Concerning Applications;

Views: 25842
DTUdk

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: 5257
Mike X Cohen

Lecture 12 (Wim van Drongelen)
Wavelet Analysis (CH 15 and 16)
Book: Signal Processing for Neuroscientists by Wim van Drongelen
Course: Modeling and Signal Analysis for Neuroscientists

Views: 11842
epilepsylab uchicago

To download the TSAF GUI, please click here:
http://www.mathworks.com/matlabcentral/fileexchange/54276-time-series-analysis-and-forecast
Please check out www.sphackswithiman.com for more tutorials.

Views: 4914
iman

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: 8313
Mike X Cohen

•Try Wavelet Toolbox: https://goo.gl/m0ms9d
•Ready to Buy: https://goo.gl/sMfoDr
The video focuses on two important wav
Get an overview of how to use MATLAB®to obtain a sharper time-frequency analysis of a signal with the continuous wavelet transform. This video uses an example seismic signal to highlight the frequency localization capabilities of the continuous wavelet transform.
Video Transcript
In this video, we will see a practical application of the wavelet concepts we learned earlier. I will illustrate how to obtain a good time-frequency analysis of a signal using the Continuous Wavelet Transform. To begin, let us load an earthquake signal in MATLAB. This signal is sampled at 1 Hz for a duration of 51 minutes. You can view the signal using the plot command. Looking at the time domain representation of the signal, we see two distinct regions. The first seismic activity occurs around the 30 minute mark. This lasts for a very short duration. The second seismic activity occurs sometime around 34 minutes and is relatively longer. You can see how it is difficult to separate the noise from the seismic signals just by looking at the time-domain representation. Many naturally occurring signals have similar characteristics. They are composed of slowly varying components interspersed with abrupt changes and are often buried in noise. Wavelets are very useful in analyzing these kinds of signals. We will see how a bit later. But first, let us see what happens when we use the short time Fourier transform to produce a time-frequency visualization. We pass in the signal and the sampling frequency as input arguments to the function spectrogram. Looking at the output, you can see that the two instances of seismic activity we just saw are now indistinguishable.
All we see is a signal whose frequency is spread around 0.05 Hz but is not very well localized. Let us see what happens when we try to localize the events by reducing the window size used in the spectrogram. By reducing the size of the window, we see some bright spots around 30 and 33 mins, but the two events are not well separated. The frequency and time uncertainty of the events is still very high. Reducing the window size was not very helpful. We need to somehow localize the frequency information of these two events. Now let us repeat the analysis - this time using wavelets. We will use the CWT function in MATLAB to compute the Continuous Wavelet Transform. This will help obtain a joint time frequency analysis of the earthquake data. The CWT function supports these analytic key wavelets. If you don’t specify which wavelet you want to use, the CWT uses morse wavelets by default. When no output parameters are specified, the function, CWT produces a joint time -frequency visualization of the input signal. The minimum and maximum scales for analysis are determined automatically by the CWT function based on the wavelet's energy spread. The magnitude of the wavelet coefficients returned by the function are color coded. The white dashed lines denote the cone of influence. Within this region, the wavelet coefficient estimates are reliable.
Looking at the plot, we can see the two regions produced by the earthquake. The first seismic activity is clearly separated from the second. Both these events seem to be well localized in time and frequency. For a richer time-frequency analysis, you can choose to vary the wavelet scales over which you want to carry out the analysis. You can do this by using different parameters. For this example, we will set the number of octaves to 10 and the number of voices per octave to 32. The function returns the wavelet coefficients and the equivalent frequencies as outputs. We can plot the coefficients a as function of time and frequency plot, using the surface command. Looking at this plot, it is clear that the frequency of the seismic event ranges from 0.03 Hz to 0.06 Hz. We can also reconstruct the time-domain representation of this seismic event from the wavelet coefficients using the function icwt. We pass in the wavelet coefficients and the frequency vector, which is the output of the CWT function. We also pass the frequency range of the signal that we want to extract. In this case, we’re inputting 0.03 to 0.06. The output is a time-domain representation of the seismic signal of interest. This way, you can use wavelets for performing joint time-frequency analysis.

Views: 46705
MATLAB

See what's new in the latest release of MATLAB and Simulink: https://goo.gl/3MdQK1
Download a trial: https://goo.gl/PSa78r
A key challenge with the growing volume of measured data in the energy sector is the preparation of the data for analysis. This challenge comes from data being stored in multiple locations, in multiple formats, and with multiple sampling rates. This presentation considers the collection of time-series data sets from multiple sources including Excel files, SQL databases, and data historians. Techniques for preprocessing the data sets are shown, including synchronizing the data sets to a common time reference, assessing data quality, and dealing with bad data. We then show how subsets of the data can be extracted to simplify further analysis.
About the Presenter: Abhaya is an Application Engineer at MathWorks Australia where he applies methods from the fields of mathematical and physical modelling, optimisation, signal processing, statistics and data analysis across a range of industries. Abhaya holds a Ph.D. and a B.E. (Software Engineering) both from the University of Sydney, Australia. In his research he focused on array signal processing for audio and acoustics and he designed, developed and built a dual concentric spherical microphone array for broadband sound field recording and beam forming.

Views: 48193
MATLAB

Explore the workings of wavelet transforms in detail.
•Try Wavelet Toolbox: https://goo.gl/m0ms9d
•Ready to Buy: https://goo.gl/sMfoDr
You will also learn important applications of using wavelet transforms with MATLAB®.
Video Transcript:
In the previous session, we discussed wavelet concepts like scaling and shifting. We will now look at two types of wavelet transforms: the Continuous Wavelet Transform and the Discrete Wavelet Transform. Key applications of the continuous wavelet analysis are: time frequency analysis, and filtering of time localized frequency components. The key application for Discrete Wavelet Analysis are denoising and compression of signals and images. As I mentioned in the previous session, these two transforms differ based on how they discretize the scale and the translation parameters. We will discuss these techniques as they apply in the 1-D scenario. Let’s take a closer look at the continuous wavelet transform – or CWT.
You can use this transform to obtain a simultaneous time frequency analysis of a signal. Analytic wavelets are best suited for time frequency analysis as these wavelets do not have negative frequency components. This list includes some analytic wavelets that are suitable for continuous wavelet analysis. The output of CWT are coefficients, which are a function of scale or frequency and time. Let’s now discuss the process of constructing different wavelet scales. Recall from our previous video that, when you scale a wavelet by a factor of 2, it results in reducing the equivalent frequency by an octave. With the CWT, you have the added flexibility to analyze the signal at intermediary scales within each octave. This allows for fine scale analysis. This parameter is referred as the number of scales per octave (Nv). The higher the number of scales per octave, the finer the scale discretization.
Typical values for this parameter are 10, 12, 16, and 32. The scales are multiplied with the sampling interval of the signal to obtain a physical significance. Here is an example of scales for a bump wavelet with 32 scales per octave. The signal is sampled every 7 micro seconds. This is the corresponding plot with the equivalent frequency for the scales. Notice that the actual scale values are exponential. Now, each scaled wavelet is shifted in time along the entire length of the signal and compared with the original signal. You can repeat this process for all the scales, resulting in coefficients that are a function of the wavelet’s scale and shift parameter. To put it in perspective, a signal with 1000 samples analyzed with 20 scales results in 20,000 coefficients.
In this way, you can better characterize oscillatory behavior in signals with the Continuous wavelet transform. The discrete wavelet transform or DWT is ideal for denoising and compressing signals and images, as it helps represent many naturally occurring signals and images with fewer coefficients. This enables a sparser representation. The base scale in DWT is set to 2. You can obtain different scales by raising this base scale to integer values represented in this way. The translation occurs at integer multiples represented in this equation. This process is often referred to as a dyadic scaling and shifting.
This kind of sampling eliminates redundancy in coefficients. The output of the transform yields the same number of coefficients as the length of the input signal. Therefore, it requires less memory. The discrete wavelet transform process is equivalent to comparing a signal with discrete multirate filter banks. Conceptually, here is how it works: Given a signal - S, - the signal is first filtered with special lowpass and high pass filter to yield lowpass and highpass sub-bands.
We can - refer to these as A1 and D1. Half of the samples are discarded after filtering as per the Nyquist criterion. The filters typically have a small number of coefficients and result in good computational performance. These filters also have the ability to reconstruct the sub bands, while cancelling any aliasing that occurs due to downsampling. For the next level of decomposition, the lowpass subband (A1) is iteratively filtered by the same technique to yield narrower subbands - A2 and D2 and so on. The length of the coefficients in each sub band is half of the number of coefficients in the preceding stage. With this technique, you can capture the signal of interest with a few large magnitude DWT coefficients, while the noise in the signal results in smaller DWT coefficients. This way, the DWT helps analyze signals at progressively narrower subbands at different resolutions. It also helps denoise and compress signals.

Views: 91609
MATLAB

Lecture with Ole Christensen. Kapitler: 00:00 - Introduction; 02:45 - Paley-Wiener Space; 06:30 - The Sinc-Function; 08:30 - Shannon Sampling Theorem; 24:00 - Applications; 33:45 - Convolution;

Views: 20864
DTUdk

Sequence classification tasks can be solved in a number of ways, including both traditional ML and deep learning methods. Catch Lauren Tran’s talk at the Women in Machine Learning and Data Science meetup as she discusses the general LSTM, CNN, and SVM algorithms, how they work, and how they are applied in sequence labeling tasks with time series data. She'll walk through a practical application of applying these algorithms and techniques to financial transaction data to detect signs of financial distress and predict insolvency.

Views: 3452
Microsoft Developer

Lecture Series on Digital Voice and Picture Communication by Prof.S. Sengupta, Department of Electronics and Electrical Communication Engg ,IIT Kharagpur . For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 108867
nptelhrd

Very briefly we talk about the Theory of Wavelet Transform and code its implementation using Matlab. The code is available at www.thelearningsquare.in

Views: 104508
rashi agrawal

A short tutorial on using DWT and wavelet packet on 1D and 2D data in Matlab, denoising and compression of signals, signal pre-processing

Views: 15542
Furcifer

COURSE WEBPAGE: Inferring Structure of Complex Systems
https://faculty.washington.edu/kutz/am563/am563.html
This lecture gives a formal introduction into multi-resolution analysis (MRA) which can be accomplished with a wavelet basis. The method is able to decompose signals into different time-space scale features in a principled way.

Views: 1700
Nathan Kutz

MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013
View the complete course: http://ocw.mit.edu/18-S096F13
Instructor: Peter Kempthorne
This is the first of three lectures introducing the topic of time series analysis, describing stochastic processes by applying regression and stationarity models.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Views: 172033
MIT OpenCourseWare

Advanced Digital Signal Processing-Wavelets and multirate by Prof.v.M.Gadre,Department of Electrical Engineering,IIT Bombay. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 7764
nptelhrd

Time Series with R - Introduction and Decomposition

Views: 8348
Dragonfly Statistics

The Image Analysis Class 2013 by Prof. Fred Hamprecht. It took place at the HCI / Heidelberg University during the summer term of 2013.
Part 03 -- The Wavelet Transform
- Discrete Wavelet Transform
- Haar Wavelets, Daubechies Wavelets 00:36:08
- 2D Wavelet transform of images and application in image compression 01:01:21

Views: 63119
UniHeidelberg

Instituto de Geofísica
Dr. Willie Soon
*Charla en Idioma Inglés*
12 de Marzo de 2014

Views: 392
Instituto Geofísica

We may say that signals as random entities.
* Fourier transformation is suitable for the stationary signal. Whereas,
Wavelet transformation is suitable for the stationary and non-stationary signal.
* Fourier transform convert signal from time domain to frequency domain signal. It provides two-dimensional information about any signal that what different frequency component present in a signal and what are their respective amplitudes.
Wavelet transform gives a complete three-dimensional information about any signal that is what different frequency components are present in any signal and what are their respective amplitudes and at time axis where these different frequency components exist.
* Fourier transformation has zero-time resolution and very high-frequency resolution.
Wavelet transformation has high time resolution and high-frequency resolution, as well as time and frequency resolution, changed.
#StudyHour
===========================================
Watch "Optimization Techniques" on YouTube
https://www.youtube.com/playlist?list=PLvfKBrFuxD065AT7q1Z0rDAj9kBnPnL0l
===========================================
🙏 LIKE || COMMENT || SUBSCRIBE || SHARE 🙏
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Watch "Queuing Theory" on YouTube
https://www.youtube.com/playlist?list=PLvfKBrFuxD04697xAZ_9J30KPhhM-W2B9
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🙏 THANK YOU FOR WATCHING 🙏

Views: 645
SukantaNayak edu

PyCon Canada 2015: https://2015.pycon.ca/en/schedule/50/
Talk Description:
The main subject of this talk is how Python can be used as an alternative to the more commonly used high-level languages used in the scientific data analysis industry.
This talk will focus on PyRF, an open-source library developed by ThinkRF, and how it has been used to provide the same functionality in terms of instrumentation control, data acquisition, digital signal processing, automated testing, production testing, as well as application development.

Views: 26980
PyCon Canada

Time-frequency analysis of magnetoencephalography (MEG) data with wavelet (Morlet). The method can transform time domain data to time-frequency representation in real-time, accumulation, and sequential format. Intuitive GUI is provided to the entire process.

Views: 217
Jing Xiang

Wavelet Coherence
The continuous wavelet transform (CWT) allows you to analyze the temporal
evolution of the frequency content of a given signal or time series. The
application of the CWT to two time series and the cross examination of
the two decompositions can reveal localized similarities in time and
scale. Areas in the time-frequency plane where two time series exhibit
common power or consistent phase behavior indicate a relationship between
the signals.

Views: 3003
pgembeddedsystems matlabprojects

Advanced Digital Signal Processing-Wavelets and multirate by Prof.v.M.Gadre,Department of Electrical Engineering,IIT Bombay. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 8196
nptelhrd

A first lesson on using fwt on time series data. We create pseudo time series data (poisson, gaussian, and brownian) using GNU Octave, display the results using gnuplot, and then demonstrate a couple of methods to extract wavelet coefficients using fwt. More complicated examples to follow.

Views: 1671
Glen MacLachlan

Digital Image Processing Using MATLAB
https://amzn.to/2oH4Xkd
A Guide To Matlab: For Beginners And Experienced Users
https://amzn.to/2CmdUJr
MATLAB and its Applications in Engineering
https://amzn.to/2MQi294
Understanding MATLAB: A Textbook for Beginners
https://amzn.to/2NfjNMv
Essential MATLAB for Engineers and Scientists
https://amzn.to/2LXFfB9
MATLAB: An Introduction with Applications
https://amzn.to/2M0FxqS
Matlab Essentials for Problem Solving
https://amzn.to/2ML8iNs
Matrix and Linear Algebra Aided with MATLAB
https://amzn.to/2wLIIhb
Getting Started with MATLAB: A Quick Introduction for Scientists & Engineers
https://amzn.to/2M0ahrS
Modeling and Simulation using MATLAB - Simulink
https://amzn.to/2LYx8nY
-------------------------------------
search and find the relevant notes at-https://viden.io/

Views: 9418
LearnEveryone

Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis!
The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied mathematicians commonly call time-frequency analysis; in different settings, this approach also goes by the name micro-local analysis. The goal is to decompose signals, functions and operators in ways that preserve, isolate or emphasize local features in both time (or space) and frequency (or momentum). Decompositions of this type can be viewed as analogous to standard music notation, which tells the musician which notes (= frequency information) to play when (= localization in time).
Tools used for time-frequency localization include, for instance, the so-called short-time Fourier transform as well as wavelets and curvelets; both tools have applications that range widely, and that include, to name a few, semiclassical approximations and estimates in quantum mechanics, image compression, new tools for art conservators, and filters used for gravitational wave detection. We will also discuss the important role of sparsity, a central concept not only in signal analysis (compressed sensing) but also in inverse problems and large-scale computation.

Views: 2743
Institut des Hautes Études Scientifiques (IHÉS)

Lecture Series on Digital Voice and Picture Communication by Prof.S. Sengupta, Department of Electronics and Electrical Communication Engg ,IIT Kharagpur . For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 82571
nptelhrd

Lecture with Ole Christensen. Kapitler: 00:00 - Wavelets; 03:00 - Preliminaries; 10:30 - Def.: Wavelet; 23:00 - Multiresolution Analysis; 32:00 - Lemma 8.2.2;

Views: 7065
DTUdk

This playlist/video has been uploaded for Marketing purposes and contains only selective videos.
For the entire video course and code, visit [http://bit.ly/2xQrLB8].
This video shows how to do time series decomposition in R.
• Discuss an example of time series data
• Show how to do log transformation of data
• Show how to do decomposition of additive time series
For the latest Big Data and Business Intelligence video tutorials, please visit
http://bit.ly/1HCjJik
Find us on Facebook -- http://www.facebook.com/Packtvideo
Follow us on Twitter - http://www.twitter.com/packtvideo

Views: 4098
Packt Video

Views: 426
brink

Wavelet Scalogram Using 1D Wavelet Analysis
This 1D Wavelet Analysis shows how to obtain spectral information of a signal using
continuous wavelet transform analysis.

Views: 3981
pgembeddedsystems matlabprojects

Lecture 13 (Wim van Drongelen)
Wavelet Analysis, Nonlinear Systems (CH 16, 17, ch 2, and Powerpoint Slides)
Book: Signal Processing for Neuroscientists by Wim van Drongelen
Course: Modeling and Signal Analysis for Neuroscientists

Views: 1813
epilepsylab uchicago

This video outlines the steps involved in denoising a signal with the discrete wavelet transform using MATLAB®.
•Try Wavelet Toolbox: https://goo.gl/m0ms9d
•Ready to Buy: https://goo.gl/sMfoDr
Learn how this denoising technique compares with other denoising techniques.
Video Transcript:
In this video, we will discuss how to use MATLAB to denoise a signal using the discrete wavelet transform. Let us load a signal and plot it in MATLAB. There are two signals here. The first is the original, signal and the second one is the original signal with some noise added to it. Our goal here is to denoise the noisy signal using the discrete wavelet transform technique.
Soon you will see how easy it is to do this in MATLAB. Here is an overview of the steps involved in wavelet denoising: 1. Your first step is to obtain the approximation and detail coefficients. Do this by performing a multilevel wavelet decomposition. Recall that the discrete wavelet transform splits up a signal into a low pass subband (also called the “approximation level”) and high pass subband (also called the “detail level”). You can decompose the approximation sub band at multiple levels or scales for a fine scale analysis. 2. The second step is to analyze the details and identify a suitable thresholding technique. I will cover this later in the video. 3. The third step is to threshold the detail coefficients and reconstruct the signal Let us first perform a multilevel wavelet decomposition using the function wavedec. We will use a sym6 wavelet and decompose the noisy signal down to 5 levels. The function outputs the fifth level approximation coefficients along with the detail coefficients from levels 1 through 5. The first level details coefficients captures the high frequencies of the signal.
Most of the high- frequency content is comprised of the noise present in the signal. However, part of the high frequency is made up of abrupt changes in the signal. There are times when these abrupt changes carry meaning, and you would want to retain this information while removing the noise. Let us take a closer look at the details sub band. To extract the coefficients, you can use the detcoef function and plot the coefficients for each level. I am using a helper function to extract and plot the coefficients. What you are seeing here is the original signal along with the details plotted for levels 1 through 45. Notice that the activity reduces drastically as the scale or /level increases. So, we will focus on the level 1 details and ignore the rest for now. Our aim here is to retain these sharp changes while getting rid of the noise. One way to do this is by scaling the detail coefficients by a threshold. There are four main techniques available in MATLAB to help you compute a threshold. for the purpose of denoising The universal threshold is the simplest to compute and is computed using this formula.
Manually computing the threshold for the other three denoising techniques is not as straightforward. Instead, you can use MATLAB for this, so that you can focus on using the threshold value without worrying about how it is computed. There are two ways of applying the threshold. There are two thresholding operations, Soft thresholding and hard thresholding. In both cases, the coefficients with magnitude less than the threshold are set to zero. The difference between these two thresholding operations lies in how they deal with coefficients that are greater in magnitude than the threshold. In the case of soft thresholding, the coefficients greater in magnitude than the threshold are shrunk towards zero by subtracting the threshold value from the coefficient value, whereas in hard thresholding, the coefficients greater in magnitude than the threshold are left unchanged. Coming back to our example, let us denoise our noisy signal using sure shrink with the soft thresholding technique. Soft thresholding is a good starting point if you are not sure which technique to choose.
The entire process of thresholding the coefficients and reconstructing the signal from the new coefficients can be done using a single function as shown here. The first parameter, f, is the noisy signal, the second parameter specifies the thresholding technique - in this case, sure shrink. 's' denotes soft thresholding, and the parameter 'sln' indicates threshold rescaling using a single estimate of noise based on first level coefficients. Level indicates the wavelet decomposition level and the last parameter specifies the wavelet, which is sym6 in this case. The function wden performs a multilevel decomposition of the input signal, computes and applies the threshold to the detail coefficients, reconstructs the signal with the new detail coefficients, and provides it as an output. Let us now use the plot command to compare the noisy signal with the denoised signal - which was the output of the previous step.

Views: 71635
MATLAB

PyData Amsterdam 2017
Deep learning is a state of the art method for many tasks, such as image classification and object detection. For researchers that have time series data, but are not an expert on deep learning, the barrier can be high to start using deep learning. We developed mcfly, an open source python library, to help machine learning novices explore the value of deep learning for time series data.
In this talk, we will explore how machine learning novices can be aided in the use of deep learning for time series classification.
In a variety of scientific fields researchers face the challenge of time series classification. For example, to classify activity types from wrist-worn accelerometer data or to classify epilepsy from electroencephalogram (EEG) data. For researchers who are new to the field of deep learning, the barrier can be high to start using deep learning. In contrast to computer vision use cases, where there are tools such as caffe that provide pre-defined models to apply on new data, it takes some knowledge to choose an architecture and hyperparameters for the model when working with time series data.
We developed mcfly, an open source python library to make time series classification with deep learning easy. It is a wrapper around Keras, a popular python library for deep learning. Mcfly provides a set of suitable architectures to start with, and performs a search over possible hyper-parameters to propose a most suitable model for the classification task provided. We will demonstrate mcfly with excerpts from (multi-channel) time series data from movement sensors that are associated with a class label, namely activity type (sleeping, walking, climbing stairs). In our example, mcfly will be used to train a deep learning model to label new data.

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PyData

PyData London 2015
The tutorial covers standard Python and Open Source tools (pandas, matplotlib, seaborn, R/ggplot, etc.) and recent innovations (TsTables, bcolz, blaze, plot.ly) for financial time series analysis and visualization. In addition, approaches are illustrated for high performance I/O of high frequency financial data. It briefly sheds light on the visualization of real-time/streaming financial data.
Slides available here: https://github.com/yhilpisch/pydlon15

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PyData