Fourier Analysis Courses and Certifications

Banach Center

Sharp Restriction Theory - Part 1

Explore advanced concepts in sharp restriction theory, focusing on key principles and applications in mathematical analysis.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

Ryan O'Donnell

Fourier Analysis of Boolean Functions - Lecture 8a of CS Theory Toolkit

Explore Fourier analysis of Boolean functions, focusing on real-valued functions and their Fourier transforms in this graduate-level theoretical computer science lecture.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Ryan O'Donnell

Ryan O'Donnell Tutorial on Hardness of Approximation - Part 3

Explore advanced concepts in approximation algorithms, focusing on Max 3-Lin, Fourier analysis, and edge weights in optimization problems.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Hans Feichtinger- Fourier Analysis via the Banach Gelfand Triple

Explore Gabor analysis foundations using MATLAB, focusing on finite Abelian groups and matrix analysis methods. Learn to apply abstract harmonic analysis concepts to signal processing problems.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Ciprian Demeter - Restriction of Exponential Sums to Hypersurfaces

Explore exponential sums on hypersurfaces, focusing on sharp moment inequalities and scale-independent results. Gain insights into critical exponents and Hardy-Littlewood lemmas.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Endpoint Fourier Restriction and Unrectifiability

Explore endpoint Fourier restriction and its connection to measure unrectifiability in R^d, featuring a dichotomy between absolute continuity and 1-pure unrectifiability.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Betsy Stovall- Fourier Restriction to the Sphere Is Extremizable More Often Than Not

Explore Fourier restriction to the sphere, focusing on extremizers and their prevalence. Delve into proofs, key limits, and spatial decomposition in this mathematical analysis.

• YouTube
• 1 hour
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Terence Tao- The Circle Method from the Perspective of Higher Order Fourier Analysis

Explore higher order Fourier analysis and its application to the circle method, offering new perspectives on multilinear averages and complex mathematical problems.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Jonathan Hickman: The Helical Maximal Function

Explore the helical maximal function in R3, its Lp boundedness, and related Fourier analytic tools. Gain insights into space curves and geometric measure theory.

• YouTube
• 51 minutes
• On-Demand
• Free Video

International Mathematical Union

Weighted Fourier Extension Estimates and Applications

Explore weighted Fourier extension estimates and their applications in PDEs and geometric measure theory, covering topics like Fourier restriction, SME, and Falconer's distance set problem.

• YouTube
• 43 minutes
• On-Demand
• Free Video

Graph Theory and Additive Combinatorics

Explore classical and modern developments in graph theory and additive combinatorics, connecting the two subjects and introducing current research topics and open problems.

• MIT OpenCourseWare
• On-Demand
• Free Online Course

Digital Signal Processing 1: Basic Concepts and Algorithms

599 ratings at Coursera

Digital Signal Processing is the branch of engineering that, in the space of just a few decades, has enabled unprecedented levels of interpersonal communication and of on-demand entertainment.

• Coursera
• 1 day 4 hours 44 minutes
• On-Demand
• Free Online Course (Audit)

Digital Signal Processing 2: Filtering

182 ratings at Coursera

Explore digital filtering techniques, from basic concepts to advanced filter design and adaptive processing, enhancing your signal processing toolkit for real-world applications.

• Coursera
• 18 hours 24 minutes
• On-Demand
• Free Online Course (Audit)

Digital Signal Processing 3: Analog vs Digital

83 ratings at Coursera

Explore analog-to-digital conversion, sampling, interpolation, and aliasing in signal processing. Learn practical applications and techniques for handling discrete-time signals.

• Coursera
• 15 hours 55 minutes
• On-Demand
• Free Online Course (Audit)

Digital Signal Processing 4: Applications

71 ratings at Coursera

Explore image processing, JPEG compression, digital communications, ADSL, and real-time audio processing on microcontrollers. Gain practical DSP skills through hands-on examples and demonstrations.

• Coursera
• 14 hours 7 minutes
• On-Demand
• Free Online Course (Audit)