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1-D discrete Fourier transforms

DFT Analysis equation

X[k]=n=0N1x[n]e2πjknN,0kN1 X[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,0nN1 x[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 2021-08-17

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Python Programming Language

Data Science