Fourier transform: Difference between revisions
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Recall that Euler's formula states: <math>e^{ix} = cos(x) + i \sin(x)</math>. | Recall that Euler's formula states: <math>e^{ix} = cos(x) + i \sin(x)</math>. | ||
Hence, <math>e^{-i2 \pi \xi x} = cos(2 \pi \xi x) + i \sin(2 \pi \xi x)</math> | Hence, <math>e^{-i2 \pi \xi x} = cos(-2 \pi \xi x) + i \sin(-2 \pi \xi x)</math> | ||
In other words, the Fourier transform is the integral (i.e. alignment) of signal times some sine and cosine waves. | In other words, the Fourier transform is the integral (i.e. alignment) of signal times some sine and cosine waves. | ||