Master the Fourier transform and its applications

Learn the Fourier transform in MATLAB and Python, and its applications in digital signal processing and image processing

4.81 (2212 reviews)
Udemy
platform
English
language
Other
category
instructor
16,027
students
7 hours
content
Feb 2024
last update
$94.99
regular price

What you will learn

Learn about one of the single most important equations in all of modern technology and therefore human civilization.

The fundamental concepts underlying the Fourier transform

Sine waves, complex numbers, dot products, sampling theorem, aliasing, and more!

Interpret the results of the Fourier transform

Apply the Fourier transform in MATLAB and Python!

Use the fast Fourier transform in signal processing applications

Improve your MATLAB and/or Python programming skills

Know the limitations of interpreting the Fourier transform.

Description

The Fourier transform is one of the most important operations in signal processing and modern technology, and therefore in modern human civilization. But how does it work, and why does it work?


What you will learn in this course:

You will learn the theoretical and computational bases of the Fourier transform, with a strong focus on how the Fourier transform is used in modern applications in signal processing, data analysis, and image filtering. The course covers not only the basics, but also advanced topics including effects of non-stationarities, spectral resolution, normalization, filtering. All videos come with MATLAB and Python code for you to learn from and adapt!

This course is focused on implementations of the Fourier transform on computers, and applications in digital signal processing (1D) and image processing (2D). I don't go into detail about setting up and solving integration problems to obtain analytical solutions. Thus, this course is more on the computer science/data science/engineering side of things, rather than on the pure mathematics/differential equations/infinite series side.


This course is for you if you are an aspiring or established:

  • Data scientist

  • Statistician

  • Computer scientist (MATLAB and/or Python)

  • Signal processing or image processing expert (or aspiring!)

  • Biologist

  • Engineer

  • Student

  • Curious independent learner!


What you get in this course:

  • >6 hours of video lectures that include explanations, pictures, and diagrams

  • pdf readers with important notes and explanations

  • Many exercises and their solutions! (Note: exercises are in the pdf readers)

  • MATLAB code, Python code, and sample datasets for applications

With >3000 lines of MATLAB and Python code, this course is also a great way to improve your programming skills, particularly in the context of signal processing and image processing.


Why I am qualified to teach this course:

I have been using the Fourier transform extensively in my research and teaching (primarily in MATLAB) for nearly two decades. I have written several textbooks about data analysis, programming, and statistics, that rely extensively on the Fourier transform. Most importantly: I have taught the Fourier transform to bachelor's students, PhD students, professors, and professionals, and I have taught to people from many backgrounds, including biology, psychology, physics, mathematics, and engineering.


So what are you waiting for??

Watch the course introductory video to learn more about the contents of this course and about my teaching style. And scroll down to see what other students think of this course and of my teaching style.

I hope to see you soon in the course!

Mike


Content

Introduction to the Fourier transform

Course materials (reader, MATLAB code, Python code)
Nontechnical description of Fourier transform
Examples of Fourier transform applications
MATLAB, Octave, Python, or just watch
Leaving reviews, course coupons

Foundations of the Fourier transform

Course materials (reader, MATLAB code, Python code, exercises)
Complex numbers
xkcd explanation of why we need complex numbers
Euler's formula e^ik
Sine waves and complex sine waves
Dot product
Complex dot product

The discrete Fourier transform

Course materials (reader, MATLAB code, Python code, exercises)
How the discrete Fourier transform works
Converting indices to frequencies
Normalized time vector
Positive and negative frequencies
Accurate scaling of Fourier coefficients
Interpreting phase values
Averaging Fourier coefficients
The DC (zero frequency) component
Amplitude spectrum vs. power spectrum
A note about terminology of Fourier features

The discrete inverse Fourier transform

Course materials (reader, MATLAB code, Python code, exercises)
How and why it works
Inverse Fourier transform for bandstop filtering

The fast Fourier transform

Course materials (reader, MATLAB code, Python code, exercises)
How it works, speed tests
The fast inverse Fourier transform
The perfection of the Fourier transform
Using the fft on matrices

Frequency resolution and zero padding

Course materials (reader, MATLAB code, Python code, exercises)
Sampling and frequency resolution
Time-domain zero padding
Frequency-domain zero padding
Sampling rate vs. signal length

Aliasing, stationarity, and violations

Course materials (reader, MATLAB code, Python code, exercises)
Aliasing
Signal stationarity and non-stationarities
Effects of non-stationarities on the power spectrum
Solution to understanding nonstationary time series
Windowing and Welch's method
Instantaneous frequency

2D Fourier transform

Course materials (reader, MATLAB code, Python code, exercises)
How the 2D FFT works

Applications of the Fourier transform

Course materials (reader, MATLAB code, Python code, exercises)
Rhythmicity in walking (gait)
Rhythmicity in electrical brain waves
Time series convolution
Narrowband temporal filtering
2D image filtering
Image narrowband filtering
Real data from trends.google.com!

Bonus section

Bonus lecture

Screenshots

Master the Fourier transform and its applications - Screenshot_01Master the Fourier transform and its applications - Screenshot_02Master the Fourier transform and its applications - Screenshot_03Master the Fourier transform and its applications - Screenshot_04

Reviews

Jasper
October 26, 2023
I really did not understand anything in this course. I really dislike the use of matlab aswell. Most people don't have access to matlab just use python. I really liked the linear algebra course of this teacher but this one is just not really understandable to me.
Philipp
October 2, 2023
This is a really good course. The author clearly describes the theoretical background. Seeing the principles applied using MATLAB code is also helpful. The only thing I would have liked is a more in-depth explanation of the fast fourier algorithm (I am not afraid of matrix decomposition methods ;-)
Mateusz
September 14, 2023
Insight into topics, way of teaching, accountability. Courses only for those serious - and if so then - You'll leave 5/5*.
Adam
September 13, 2023
I really enjoyed this course. I have already taken a class on Fourier Transforms in University and must say that it has given me some additional insights as well as helped me implement some of the theoretical concepts I have already learnt in Matlab. For instance, the most interesting insight, in my eyes, has been that it is possible to view a single non-stationary in the frequency domain as the 'cause' of a 'ringing' sine wave in the time domain. I removed half a star because the 2D FT section could be explained a bit better (perhaps making a dedicated course on the analysis of 2D FT instead of covering it superficially could solve this issue?). So in short, highly recommended for those seeking additional insights into FT as well as learning how the theory gets implemented in Matlab.
Karen
August 15, 2023
As a visual learner, I really appreciate how the provided codes frequently included simulations of the processes! This is already my second course, and I'm loving how each lesson can be applied in various areas, especially in neuroscience. The lessons have been incredibly helpful. Thank you!
Or
August 4, 2023
Excellent course! I have completed 4 of Mike's courses, and I have come to the conclusion that his courses are of the highest quality compared to the other teachers. This course is fascinating and very valuable. Thank you!
Randall
July 25, 2023
I have studied electronics and radar systems, in the radar systems we used fast fourier to better distinguish the target, for instance in rain. I like to understand the working. How does it work in modern hearing adds.
Amr
July 5, 2023
Mr. Cohen leaves every topic that he addresses fully and yet succintly explained. I think this course is perfect as an introduction to Fourier Transform. I would have liked more in-depth treatment of 2D FT and IFT, but I am happy with what i got. Highly recommended.
Hailu
July 2, 2023
Very clear explanations of terminologies such as DC, negative & positive frequencies, amplitude, and power for signals.
Daniel
May 30, 2023
Love it. My goal taking this course is to get into DSP as a software dev and had good use already correcting an old project in C where I tried to use 3rd party FFT lib and now I know what I did wrong the first time (normalisation etc.) Looking forward to last half and the DSP course.
Geoff
April 14, 2023
Its fine business. Nevertheless, I am interested in understanding how to make DSP for audio effects. I suppose this is going to take longer than expected.
Mladen
April 11, 2023
A nice applied approach to teaching Fourier transform. Instructor is knowledgeable about the subject. Lectures are short and clear. I would recommend learners to take some extra time with the computational exercises in order to get more out of the class.
Dimitrios
March 22, 2023
I started with the signal processing course but I felt like I need some refreshing on the Fourier Transform. So I ended up on this course. After this course I noticed It was not a refresher. This course helped me to understand the Fourier Transform even better than I had probably during my time as a student. Clear and precise explanation in combination with nice visual examples. Can´t wait to continue now with the signal processing course :)
Amar
January 1, 2023
I recently completed a course on Fourier transform and I have to say, the instructor did an excellent job explaining the concept from a basic loop method all the way to advanced techniques using functions and programming in MATLAB. The course was full of examples and the instructor really took the time to explain the nuances and important considerations when using the Fast Fourier Transform (FFT). Overall, it was a very good course and I highly recommend it to anyone looking to learn more about Fourier transform.
Akhila
December 30, 2022
Was an Amazing Course. Years of struggling to develop an understanding of FFT and Fourier transform concepts were accomplished with the instructor's excellent explanation and by providing examples to visualize.

Coupons

DateDiscountStatus
12/22/202130% OFF
expired
3/5/202230% OFF
expired
11/12/202230% OFF
expired

Charts

Price

Master the Fourier transform and its applications - Price chart

Rating

Master the Fourier transform and its applications - Ratings chart

Enrollment distribution

Master the Fourier transform and its applications - Distribution chart

Related Topics

1441216
udemy ID
11/21/2017
course created date
7/12/2019
course indexed date
Bot
course submited by