Uploaded August 2020 | Updated September 2026, 3 weeks ago

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In my new tutorial, I explain how we can use complex numbers to define the Fourier transform in a compact and elegant way. I talk about the complex Fourier transform coefficients, and show how we can interpret the complex definition of the Fourier transform visually. I also introduce the inverse Fourier transform and provide a visual interpretation.

Slides:
github.com/musikalkemist/AudioSignalProcessingForML/blob/master/12-%20Defining%20the%20Fourier%20transform%20using%20complex%20numbers/Defining%20the%20Fourier%20Transform%20Using%20Complex%20Numbers.pdf

Code:
github.com/musikalkemist/AudioSignalProcessingForML/blob/master/12-%20Defining%20the%20Fourier%20transform%20using%20complex%20numbers/Defining%20the%20Fourier%20Transform%20Using%20%20Complex%20Numbers.ipynb

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