Pustam | पुस्तम | পুস্তম🇳🇵The Fourier transform (FT), explained in one sentence: 🔗 https://blog.revolutionanalytics.com/2014/01/the-fourier-transform-explained-in-one-sentence.html
\[\boxed{\hat{f}(\xi)=\displaystyle\int_{-\infty}^\infty e^{-i2\pi\xi t}f(t)\ \mathrm{d}t}\]
Discrete Fourier transform (DFT):
\[\displaystyle x_n = \sum_{k=0}^{N-1} X_k \cdot e^{-i2\pi \tfrac{n}{N}k}\]
Inverse transform:
\[\displaystyle X_k = \frac{1}{N} \sum_{n=0}^{N-1} x_n \cdot e^{i2\pi \tfrac{n}{N} k}\]
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The Fourier Transform, explained in one sentence
If, like me, you struggled to understand the Fourier Transformation when you first learned about it, this succinct one-sentence colour-coded explanation from Stuart Riffle probably comes several years too late: Stuart provides a more detailed explanation here. This is the formula for the Discrete Fourier Transform, which converts sampled signals (like a digital sound recording) into the frequency domain (what tones are represented in the sound, and at what energies?). It's the mathematical engine behind a lot of the technology you use today, including mp3 files, file compression, and even how your old AM radio stays in tune. The daunting...