Discrete Fourier Transform
For N samples, X[k] = Σ x[n] e^{-i2πkn/N} projects the signal onto N complex sinusoids whose frequencies are the Nth roots of unity; it is exactly a multiplication by an N×N matrix of powers of e^{-i2π/N}, and it implicitly treats the N samples as one period of a periodic signal.
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For N samples, X[k] = Σ x[n] e^{-i2πkn/N} projects the signal onto N complex sinusoids whose frequencies are the Nth roots of unity; it is exactly a multiplication by an N×N matrix of powers of e^{-i2π/N}, and it implicitly treats the N samples as one period of a periodic signal.
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