Fourier transform

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keywords:

[a mathematical transform that decomposes functions]

[functions depending on frequency]

[a complex-valued function of frequency]

[Fourier series]

[complicated but periodic functions]

[complicated periodic functions]

[the properties of sine and cosine]

[trigonometric sine function]

[trigonometric cosine function]

[recover the amplitude of each wave]

[linearity]

[time-scaling]

[time scaling]

[conjugation]

[invertibility]

[periodicity]