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1-D Discrete Fourier Transforms

DFT Analysis equation: X[k]=n=0N1x[n]e2πjknN,0kN1X[k] = \sum_{n=0}^{N-1}x[n] e^{-2\pi j \frac{kn}{N}} , 0\leq k\leq N-1

DFT Synthesis equation: x[n]=1Nk=0N1X[k]e2πjknN,0nN1x[n] =\frac{1}{N} \sum_{k=0}^{N-1}X[k] e^{2\pi j \frac{kn}{N}} , 0\leq n\leq N-1

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Updated 2026-05-17

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Python Programming Language

Data Science