I have data whose latter half are all-zero. For example,
data=[a, b, c, d, 0, 0, 0, 0], and
front_half=[a, b, c, d]. Is there any way to obtain FFT(data), by some compute-efficient transform on the FFT(front_half)?
I made some work on the equations. The even items in FFT(data) are just equal with FFT(front_half). But the odd items in FFT(data) seems twisted with dot-multiply with a time-domain weight vector, which looks hard to be calculated from the FFT(front_half).