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In this course, you will :
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Intermediate to advanced MATLAB programming proficiency. This is *the only course* that develops intermediate and advanced programming skills.
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Obtain real-world application experience that that researchers and industry professionals use MATLAB for, including signal processing, matrix decompositions, spectral analysis, linear and nonlinear model-fitting, and statistics.
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Gain skills to solve challenging problems in MATLAB, as opposed to memorizing syntax rules.
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Data science projects and problem-solving in MATLAB
Syllabus :
1. Vectors and Variables
- Create Vectors and Matrices
- Unsolved: Valid and Invalid Matrices
- Working with Text (Characters and Strings)
- HTML Table from MATLAB Code
- Round pi to N significant Digits
- File/folder Information Using Structures
2. Command Statements
- Create a Hilbert Matrix Using for-loops.
- Unsolved: Compare two while Loops
- Create an Upper-Triangular Matrix
- Random Count-Down Timer (Poisson-like)
- Display the day of 1 January
3. Import and Export Data
- Save and Load Multiple Files
- Import Formatted Text Data
- Import Excel-format Data
4. Translate Formulas into Code
- Trig Functions and Gaussians
- Laplace and log-normal Distributions
- Complex Numbers and Euler's Formula
- Piecewise Functions
- Piecewise Function in one line of Code
- Unsolved: Sigmoid and Error Function
- Circular p-value and its Approximation
5. Descriptive Statistics
- Compute Measures of Central Tendency
- Compute Variance and Standard Deviation
- Unsolved: Sort Data up and down
- Data Transformations (log, sqrt, rank)
6. 2D Plotting
- Lines
- Bars and errorbars
- Dots
- Multidimensional Data with Colored Scatter
- Unsolved: imagesc vs. pcolor
- Histograms
- Uncertainty in Future Money (using patch)
- Blend Pictures Using Transparency
- Vertically Stacking Data Series
- Distance Matrix from Generated Points
- Gabor Patch Marginal Histograms
- List of other image-processing videos in this course
7. 3D Plotting
- Sphere in a Cube
- Colorful Cube (a.k.a. the happy Borg ship)
- Expanding Wavelets with Surfaces
- Textured Gaussian Surfaces
- A Ball in 3D Color Space
- Plane in R3 Spanned by Two Vectors
- The Prickly Gabor Patch
8. Segmentation
- Threshold-based Time Series Segmentation
- Derivative-based Time Series Segmentation
- Intensity-based Image Segmentation
- Identify Neurons in a Mouse Brain Slice
9. Data Animations
- Random Floating Ball
- The Square Chases the Mouse
- The Magically Materializing Peaks
- Smooth Sailing: The Movie
- Real-time Audio Spectrum from Mic
- Möbius Transformation
- UFO on a Sandcastle
10. Graphical User Interfaces
- Dialog Box for User Input
- Interface to Select a File
- Input and Message Boxes
- GUI to Create Random Landscapes
- GUIDE to Sigmoid Parameter Space
11. Functions and Anonymous Functions
- Same-length Differentiation
- Damped Oscillator
- Unsolved: Damped Arcsine
- Find and Extract a Function Core
- Smooth Plotting Function with Options
12. Find, Min, Max
- Find Point Closest to Specified Value
- Unsolved: Manual Peak-Picking
- Find Negative Extrema in a 2D Function
- Unsolved: Find Ridges of a 2D Surface
- Find Local Maxima
- Replace Image Pixels in an Intensity Range
- Find Signal Clipping Points
13. Calculus and Differential Equations
- Plotting Symbolic Functions
- Function Limits
- Function Derivatives
- Function Integration
- Solving Differential Equations
14. Cleaning Univariate Time Series
- Running Mean Flter
- Threshold Median Filter
- Unsolved: all-points Median Filter
- Interpolate Missing Time Points
- Spectral Mixing Interpolation
- Polynomial Fitting to Remove Drifts
- Unsolved: Polynomial Fitting to Isolate Drifts
- Unsolved: Local Maxima in Noisy Data
15. Cleaning Multivariate Time Series
- Three Ways to make a Covariance Matrix
- Reject Data Based on Extreme Covariance
- Effects of Averaging on Covariance Matrices
- Simulate Tri-Component Time-Space Data
- Unsolved: Tri-component Data without Loops
- Spatial Smoothing on a Grid of Channels.
- Spatial Sharpening via Laplacian
16. Time Series Analysis
- Convolution
- High-pass Filter using FIR Filter
- Narrow-band Filter via Frequency-Domain Gaussian
- Causal vs. Zero-Phase-Shift Filter
- Line Noise Notch Filter
- Compute Envelope Over Peaky, Noisy Signal
- Frequency-domain Mean Filter
- Create a "chirp" (FM Signal)
- Detrended Fluctuation Analysis
17. Spectral Analysis
- Create Multispectral Time Series
- Power Spectrum from FFT and Welch's Method
- Spectrogram of Bird Call
- Phase-scramble Narrowband Time Series
- Hilbert Transform
- Oscillations in Human Brain Recordings
- Time Frequency Analysis via Wavelet Convolution
18 Matrix Analysis
- Four Ways to Compute the Dot Product
- Unsolved: Plot Vectors and Compute Lengths
- Hermitian vs. Regular Transpose
- Create a Symmetric Matrix: Additive
- Create a Square Symmetric Matrix: Multiplicative
- MxM Matrix with Rank M-1
- MxN Matrix with Rank r via SVD
- Create a Random Hankel Matrix
- Unsolved: Element-wise Hankel Matrix with Mod Function
- Unsolved: Create a Toeplitz Matrix
- Eigenvectors of a Hankel Matrix
- Compute a Unit Vector in some Direction
- Orthogonalize a Pair of Vectors
- Gram-Schmidt Algorithm
- Matrix Inverse via QR Decomposition
- Visualize the Quadratic form of a 2x2 Matrix
- Eigenvectors and Quadratic Form
- PCA of Low-Rank Space-Time Data
- Covariance Shrinkage Regularization in PCA
19. Circular Distributions and Analyses
- Draw a Vector in Polar Plane
- Circular Histogram
- Compute and Plot Mean Vector Length
- Phase Difference Between Two Distributions
20. Fractal Time Series and Images
- The Sierpinksi Triangle
- Unsolved: Sierpinksi Triangle as Dense Matrix
- Brownian Motion
- Cantor Set and Devil's Staircase
- Unsolved: Initialize the Cantor Set
- Mandelbrot Set
- Weierstrass Function
- Fractal Circles and Bubbles
21. Nonparametric Statistics
- Wilcoxon Rank Test
- 2D Space of Wilcoxon Effect Sizes
- KL Divergence of Two Distributions
- 2D Space of KL Divergences
- Permutation Testing
- Bootstrapping for Confidence Intervals
- Unsolved: Bootstrapping Medians
22. Nonlinear Model Fitting
- Find a Function Minimum
- Fit a Gaussian to a Distribution
- Two-piece Linear Regression
- Fit a Sine Wave
- Fit a Circle to a Noisy Ring
