Appendix A
564
The result is a tremendous increase in processing speed compared
to DFT:
FFT vs. DFT
This advantage is the reason why FFT is preferred.
Neither DFT nor FFT convert a single data point into a single
frequency line.
NOTE Every Fourier transformation requires a complete set of samples. If
you move the measurement window by discarding the oldest sample
and capturing a new data point, you need to repeat the
transformation completely to obtain the updated spectrum.
FFT Characteristics
Frequency resolution From N sampled data points, we get N/2 equally spaced lines in
the frequency domain. If T is the width of the time record
(T = N × Tsampling), the spacing of the lines is 1/T.
Besides the achievable resolution, the FFT has another
characteristic which affects its use. This is called leakage.
Leakage The FFT algorithm is based on the assumption that the time
record is repeated throughout time; it assumes that the signal
under investigation is a periodic signal.
If the repetition of the time record does not represent the original
signal, we see a phenomenon called leakage.
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