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FFT interpolation: background How does it work? Given a number of samples, how can it be possible to interpolate the “in-between” with perfect accuracy?
The answer is:
- FFT rewrites the signal as a sum of “parts” (superposition)
- Each “part” is a sequence of points following a sine / cosine curve of different frequency
- Once FFT has calculated the amplitude of each “part”, it can be easily evaluated at any point in time, since it is a simple sine / cosine function
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Figure 1 shows an example for the “parts” used by a real-valued 8-point Fourier transform (red points), and the underlying sine / cosine wave (blue curves).
Figure 3: All possible sine / cosine waves in a real-valued 8-point FFT |  
Once the amplitude and phase of each component is known, the continuous-time signal can be calculated by evaluating the Fourier sum. |
© Markus Nentwig 2007-2008
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mnentwig@elisanet.fi
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