A noob learns FFT

The event centers on a first-time user grappling with FFT output in R. The raw FFT returns complex numbers scaled by the sample count, requiring division by the number of samples to retrieve the original signal amplitude. This scaling is not always documented in introductory material, so engineers must remember to normalize the output before interpreting magnitudes. The example shows that even a pure sine wave produces non-zero values at both positive and negative frequencies, a detail often glossed over in theoretical explanations.

Spectral leakage emerges when the signal is truncated mid-cycle. The FFT assumes the input is periodic, so abrupt endings create discontinuities that spread energy across adjacent frequencies. While the original signal remains reconstructable, the spectrum becomes harder to read. Windowing functions like Hann or Hamming taper the signal edges, reducing leakage at the cost of slightly widening the main spectral peak. Engineers must choose between leakage suppression and frequency resolution based on their application needs.

Negative frequencies in FFT output are a mathematical artifact of representing real-valued signals in the complex domain. The example demonstrates that a 5 Hz sine wave appears as two symmetric peaks at +5 Hz and -5 Hz, each with half the original amplitude. For real-world analysis, these mirrored components are typically summed to recover the full amplitude. This step is essential when plotting or interpreting spectra, as ignoring negative frequencies leads to incorrect amplitude readings.

Noise and composite signals further complicate FFT interpretation. Even with added noise, the FFT correctly identifies the dominant frequency, though the noise floor raises the baseline across all bins. When multiple sine waves are present, the FFT resolves them as distinct peaks, provided their frequencies are sufficiently separated. However, closely spaced frequencies may merge due to spectral leakage or windowing effects, requiring careful selection of sample length and window type to maintain resolution.