Hi,
Benefits:
* for single frequency a DFT is more useful than an FFT.
* Usual FFT algorithms are optimized for 2^n samples per window. A DFT can work with any window size.
Example (one of my applications):
Precise phase shift calculation between V and I of a mains application.
Mains frequency --> singe frequency
Phase shift = phase(V) - phase(I)
Another example:
Let´s say you work on an line application, where a phase control operates nearby. Causing spikes at certain phase angles.
Now let´s assume you do a 64 point FFT over 80ms at 50Hz mains frequency.
Starting at 0° the sample points are: 0°, 22.5°, 45°, 67.5°, 90°, 112°, 135°, 157,5°, 180°, 202,5°, 225°, 247,5°, 270°, 292,5°, 315°, 337,5°, ....4 full waves repeating the same phase angles..
Indeed this just gives about the same information of a 16 point FFT, averaged over 4 calculations.
Now let´s assume the "spikes" are at 45° then they will also be at 180°+45° = 225°. In worst case 8 out of the 64 samples are corrupted.
Now imagine you run a DFT over 63 points at the same 80ms.
You get informations of 63 different points of the waveform. In worst case only one sample is corrupted by the spikes. Error-spreading
Klaus