Howtosignalprocessing
- What does DFT do to a signal?
- What happens if we apply DFT twice to a signal?
- What is the drawback of DFT?
- What is the computational complexity of DFT?
What does DFT do to a signal?
The Discrete Fourier Transform (DFT) is of paramount importance in all areas of digital signal processing. It is used to derive a frequency-domain (spectral) representation of the signal.
What happens if we apply DFT twice to a signal?
Applying the DFT twice results in a scaled, time reversed version of the original series. The transform of a constant function is a DC value only.
What is the drawback of DFT?
In the Fourier analysis of mixed-structure signals, the disadvantages of DFT are most significantly manifested. These disadvantages are picket-fence, leakage, aliasing effects and amplitude modulation spectrum.
What is the computational complexity of DFT?
As multiplicative constants don't matter since we are making a "proportional to" evaluation, we find the DFT is an O(N2) computational procedure. This notation is read "order N-squared". Thus, if we double the length of the data, we would expect that the computation time to approximately quadruple.
