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The Discrete Fourier Transform

Bridging the Gap

The Discrete Fourier Transform (DFT) is an essential building block of Digital Signal Processing (DSP). It allows you to elegantly decompose digital signals into their fundamental frequencies, revealing characteristics that can't be observed in the time domain.

Understanding how the DFT works and how it's computed is an important step to using it in practice, but the DFT on paper can look quite different from the DFT in action.

Translating the DFT from theory to practice has many pitfalls with ambiguous solutions, especially when processing audio. Much of the DFT's elegance must be compromised in practice, and it's not entirely obvious how or why.

This talk aims to bridge the gap between theory and practice by exploring the inner-workings of the DFT and using it to perform EQ-related effects on an audio stream.

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