Signal Distortion
Fourier transforms measured against the original signal bandwidth reveal errors that occur when high frequency components are removed during sampling. Encountering spectral truncation artifacts can lead to incorrect peaks in digital signal processing or infrared spectroscopy. These errors appear as oscillations near sharp transitions in the data and are known as the Gibbs phenomenon.
The effect is most pronounced when the measurement window does not capture the full decay of the signal.
Sampling Error
Encountering these oscillations can obscure real features in the spectrum or create false readings of the signal amplitude. The problem arises from the assumption that the signal is periodic and continuous outside of the recorded time window.
These Oscillations
These errors are mitigated by applying windowing functions like Hanning or Hamming to the raw data before the transform. This process smooths the edges of the window and reduces the magnitude of the false peaks.
Artifact Mitigation
Careful selection of the sampling frequency and the window length ensures that the important features of the signal are preserved. If the sampling is too slow, the high frequency information is lost and the resulting spectrum is distorted. Reliable analysis depends on the suppression of these mathematical errors.
