Master the Fourier transform and its applications from Udemy

What's inside

Syllabus

See a few example applications of the Fourier transform for time series and images.

Learn how to follow along the course in code.

Using Udemy like a pro

Learn about this course and a nontechnical introduction to the Fourier transform

Course materials (reader, MATLAB code, Python code)

A nontechnical introduction of the interpretations and two major goals of the Fourier transform.

Learn the main concepts underlying the Fourier transform (sine waves, complex numbers, dot products)

Course materials (reader, MATLAB code, Python code, exercises)

Complex numbers aren't so complicated once you get used to them.

xkcd explanation of why we need complex numbers

One of the most important equations in human civilization, not to mention the Fourier transform!

Hint: Three parameters to rule them all!

The dot product is a fundamental building-block computation underlying most of signal processing.

What happens when a complex number walks into a dot product? Watch and find out!

Put the pieces together to understand how the Fourier transform works, and how it is implemented in MATLAB and Python!

If you think the Fourier transform is really weird and complicated, this video will prove you wrong.

Learn how to get meaningful frequencies from the output of the Fourier transform.

Converting indices to frequencies: part 2

Shortcut: Converting indices to frequencies

The answer to a common question about the Fourier transform.

Learn how to interpret and work with "negative frequencies."

The units that fft outputs are "wrong"; learn how to fix them!

Learn how to interpret the phase values of the Fourier coefficients.

The two ways to average Fourier coefficients together can give very different results!

The 0-frequency corresponds to the average signal value.

See the difference between amplitude and power, and why I always use amplitude when I teach.

Hopefully some clarifications of confusing terminology used in the Fourier transform.

Learn how to invert the Fourier transform to get from the frequency domain to the time domain.

What goes up, must come down...

See an application of the inverse Fourier transform in signal processing.

The loop-based Fourier transform discussed so far is slooooooow! Here you will learn lightning-fast Fourier transform with the FFT.

Don't let the Fourier transform slow you down; use the fast Fourier transform!

What goes up, must come down (fast!).

A few explanations for why the Fourier transform is so perfect.

Avoid loops at all costs!

Learn about how sampling and zero-padding affect the results of the forward and inverse Fourier transform.

How many and which frequencies do you get from the Fourier transform? It depends...

Create more frequencies by adding nothing.

See how zero-padding is sinc-interpolation

See how two signal properties affect frequency resolution.

Course tangent: self-accountability in online learning

Learn when and why the power spectrum can give results that are difficult to interpret.

The Nyquist frequency is the speed limit of the Fourier transform!

Learn the definition (and ambiguities) of signal non-stationarities.

Non-stationarities can make the results of the Fourier transform difficult to interpret.

See several solutions for dealing with non-stationarities in signals.

One of the primary methods for spectral analysis of nonstationary signals.

An alternative way of thinking about frequency leads to a different way of characterizing time series data.

Bored with 1D signals? Then learn about the Fourier transform of images!

Explanation of the 2D FFT used for image processing.

Now that you know the theory and implementation of the Fourier transform, it's time to see it in action!

Using spectral analysis to reveal walking dynamics.

There is electricity in your brain, and it's doing the wave.

The FFT is used in signal processing to speed up convolution.

Application of the FFT for narrowband filtering.

Application of the FFT for image processing.

Another application of the 2D FFT in image processing (filtering).

The question is when are people interested in the Fourier transform!

Bonus section

Bonus lecture

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Master the Fourier transform and its applications with these activities:

Review Complex Numbers

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Solidify your understanding of complex numbers, a fundamental concept for grasping the Fourier transform.

Browse courses on Complex Numbers

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Review the definition of imaginary numbers and complex numbers.
Practice arithmetic operations with complex numbers.
Understand the geometric representation of complex numbers on the complex plane.

Read 'The Scientist and Engineer's Guide to Digital Signal Processing'

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Supplement your learning with a practical guide to digital signal processing, focusing on the Fourier transform.

View Digital Signal Processing: A Practical Guide... on Amazon

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Read the relevant chapters on the Fourier transform and its applications.
Work through the examples and exercises provided in the book.
Compare the book's explanations with the course materials.

Read 'Understanding Digital Signal Processing'

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Gain a deeper understanding of the Fourier transform through a comprehensive DSP textbook.

View Digital Signal Processing: A Practical Guide... on Amazon

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Read the chapters related to the Fourier transform and spectral analysis.
Work through the examples and exercises provided in the book.
Relate the concepts in the book to the course materials.

Four other activities

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Follow Online FFT Tutorials

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Enhance your understanding of the Fast Fourier Transform (FFT) by following online tutorials that demonstrate its implementation and applications.

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Search for online tutorials on FFT implementation in MATLAB or Python.
Follow the tutorials step-by-step, implementing the code examples.
Experiment with different parameters and signals to see how they affect the results.

Implement FFT in MATLAB/Python

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Reinforce your understanding of the FFT algorithm by implementing it from scratch in MATLAB or Python.

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Implement a basic FFT algorithm using the Cooley-Tukey method.
Compare your implementation's performance with the built-in FFT functions.
Experiment with different signal types and lengths.

Create a Fourier Transform Visualization

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Solidify your understanding by creating a visualization that demonstrates how the Fourier transform decomposes a signal into its frequency components.

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Choose a signal to analyze (e.g., audio, image).
Implement the Fourier transform on the signal.
Create a visualization showing the signal in both the time and frequency domains.
Add interactive elements to explore different parameters.

Audio Equalizer Project

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Apply your knowledge of the Fourier transform to build a practical audio equalizer application.

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Design the architecture of the audio equalizer.
Implement the Fourier transform and inverse Fourier transform for audio processing.
Create filters to adjust different frequency bands.
Integrate the filters into the audio processing pipeline.
Test and refine the equalizer's performance.

Career center

Learners who complete Master the Fourier transform and its applications will develop knowledge and skills that may be useful to these careers:

Signal Processing Engineer

A signal processing engineer analyzes, designs, and develops signal processing systems. This course provides students with the theoretical and computational bases of the Fourier transform, making it invaluable for aspiring signal processing engineers. The course emphasizes how the Fourier transform is used in modern applications, focusing on digital signal processing. Learning about spectral resolution, normalization, and filtering helps a signal processing engineer develop practical skills. With its focus on implementations using MATLAB and Python code, this course prepares students for real-world engineering challenges. Students interested in becoming a signal processing engineer would benefit from the course's advanced topics and hands-on exercises.

See salaries and explore the career path for Signal Processing Engineer

Image Processing Specialist

An image processing specialist enhances and manipulates digital images. This course helps build a foundation in the Fourier transform, crucial for image processing applications. With a focus on both the theoretical underpinnings and practical implementations, this course offers a comprehensive understanding of how the Fourier transform works in image filtering and analysis. The course includes MATLAB and Python code, which allows image processing specialists to learn by doing and adapt the code to various projects. Someone who wants to become an image processing specialist would find the course's coverage of the two dimensional Fourier transform particularly useful.

See salaries and explore the career path for Image Processing Specialist

Data Scientist

A successful data scientist relies on a deep understanding of data analysis techniques. This course introduces the theoretical and computational bases of the Fourier transform, with a strong focus on modern applications in data analysis. Learning the Fourier transform helps a data scientist discover hidden patterns and extract meaningful insights from complex datasets. The course includes MATLAB and Python code and exercises, that allow data scientists to implement the techniques and reinforce their learning. The ability to implement the Fourier transform on computers, as taught in this course, is especially valuable for a data scientist.

See salaries and explore the career path for Data Scientist

Research Scientist

Research scientists design and conduct experiments. This course helps build a foundation in data analysis and signal processing, which may be useful for research involving time series or image data. The course covers both basic and advanced topics related to the Fourier transform, including its applications in signal processing and image filtering. The course's hands-on exercises and MATLAB and Python code can help research scientists implement and adapt these techniques in their own research projects. Students who wish to become research scientists can learn about the Fourier transform to aid them in their research.

See salaries and explore the career path for Research Scientist

Quantitative Analyst

Quantitative analysts use mathematical and statistical methods to solve financial problems. This course emphasizes the theoretical and computational bases of the Fourier transform. This focus may allow quantitative analysts to analyze time-series data and identify trends. The course includes MATLAB and Python code for implementing the Fourier transform, which is useful for quantitative analysts. Aspiring quantitative analysts would benefit from the practical coding experience and the understanding of advanced topics.

See salaries and explore the career path for Quantitative Analyst

Machine Learning Engineer

Machine learning engineers design and develop machine learning models. This course can help build a foundation in feature extraction and signal processing, which are essential for many machine learning applications. The course covers the theoretical and computational bases of the Fourier transform, in modern applications in signal processing, data analysis, and image filtering. Hands-on exercises and MATLAB and Python code are great tools for machine learning engineers to implement and test these techniques. The practical skills taught in this course may benefit those interested in becoming machine learning engineers.

See salaries and explore the career path for Machine Learning Engineer

Acoustic Engineer

Acoustic engineers analyze and design systems to control sound and vibration. This course offers a strong foundation in signal processing, including the Fourier transform. The course's MATLAB and Python examples will be useful for acoustic engineers who need to implement their own signal processing tools. The course's treatment of non-stationarities can benefit someone who wants to become an acoustic engineer, as real-world sound signals are often non-stationary.

See salaries and explore the career path for Acoustic Engineer

Geophysicist

Geophysicists study the physical properties and processes of the Earth. This course emphasizes frequency analysis, which is heavily used in geophysics for analyzing seismic and other geophysical data. With MATLAB and Python examples included in the course, geophysicists can implement the techniques in real-world data analysis. Aspiring geophysicists benefit from exploring advanced topics such as spectral resolution, normalization, and filtering.

See salaries and explore the career path for Geophysicist

Biomedical Engineer

Biomedical engineers apply engineering principles to solve medical and biological problems. This course can help biomedical engineers analyze biosignals, such as EEG or ECG data. The course includes advanced topics, such as dealing with non-stationarities, that are relevant to the analysis of biological signals. The inclusion of MATLAB and Python code in the course gives biomedical engineers hands-on experience implementing the Fourier transform. This course may be useful for anyone who wants to become a biomedical engineer analyzing complex biological signals.

See salaries and explore the career path for Biomedical Engineer

Robotics Engineer

Robotics engineers design, build, and program robots. This course can help robotics engineers process sensor data, such as from cameras or accelerometers. The course provides a solid foundation in the Fourier transform, and includes MATLAB and Python code for implementation. Students who wish to become robotics engineers may find the image processing component of the course helpful for applications involving computer vision.

See salaries and explore the career path for Robotics Engineer

Financial Analyst

Financial analysts provide guidance to businesses and individuals making investment decisions. This course may be useful for financial analysts who need to analyze time-series data, such as stock prices. The course includes MATLAB and Python examples, which help financial analysts to apply the techniques in real-world scenarios. Students who want to become financial analysts may find the course helps them analyze financial data.

See salaries and explore the career path for Financial Analyst

Software Developer

Software developers design, write, and test code. This course may be useful for software developers working on signal processing or image processing applications. The course includes extensive MATLAB and Python code, which can help software developers implement the Fourier transform in their projects. The course's coverage of both the theoretical and practical aspects of the Fourier transform helps someone who wants to become a software developer build a useful system.

See salaries and explore the career path for Software Developer

Data Analyst

Data analysts interpret data and turn it into information which can offer ways to improve a business. The course may be useful for data analysts who need to perform frequency analysis on datasets. Data analysts who are looking to learn MATLAB or Python programming would find this course helpful. This course may particularly help data analysts who want to improve their skills in data analysis.

See salaries and explore the career path for Data Analyst

Statistician

Statisticians collect, analyze, and interpret numerical data. This course may be useful for statisticians working with time series data. While focused on computation, the course covers theoretical aspects of the Fourier transform. Those who are interested in becoming statisticians may find that the course is useful for understanding methods of statistical analysis.

See salaries and explore the career path for Statistician

Mathematician

Mathematicians apply mathematical theories and techniques to solve practical problems. This course may be useful for mathematicians interested in the computational aspects of the Fourier transform. Mathematicians should note that the course emphasizes applications and implementations rather than pure mathematical theory. Mathematicians may still find this course helpful for complementing their theoretical knowledge.

See salaries and explore the career path for Mathematician

Master the Fourier transform and its applications

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