FFT of a stretched vector Lets say I have a small size vector x=[a b c d]. Now I stretch this vector 3 times and I got x3=[a a a b b b c c c d d d]. What would be the relation between fft(x) and fft(x3)?
Conceptually you should split this into two steps

Up-sample by a factor of 3, i.e. x = [a 0 0 b 0 0 ...]. This results in a 3 times periodic repetition of the spectrum.
Convolve with a rectangular pulse of length three, i.e. h = [1 1 1]. This crates time stretched sequence you want. Convolution in time is multiplication in frequency, your three copies of the original spectrum get multiplied with a $sinc$ function.