I think you are not aswering his question (but maybe I am wrong).
If you want a Fourier transform with less frequencies than temporal samples you can perform a fft to get a result of same length like this :
9 2 7 6 1 8 (amplitude) 0 2 4 6 8 10 (frequency) Then transform it like this : 11 13 9 (amplitude) (integrate the amplitudes) 1 5 9 (frequency) (according to your frequencies) This is a trivial example...I hope it's clear enougth...
