When calculating the FT of a signal, and the FT of that same signal but after having applied zero-padding to it, should't the amplitudes of the FT of the zero-padded signal decrease with respect to the FT amplitudes of the original signal?
1) Since the FT of the zero-padded signal has more frequency bins (since we have interpolated the spectrum), my intuition tells me that the amplitude of the frequency bins of this FT should be lower.
However, when I calculate the FT of the two signals (I use the fft function available in Scipy for Python), I get the same amplitudes for their spectra. I was not expecting this behaviour.
2) If I add the normalization term when calculating the FT (Scipy FFT does not include this), i.e. $FT = fft(signal) / length(signal)$, then I get different amplitudes for the two FT, which again, was not what I was expecting. Specifically, the zero-padded signal FT amplitudes decrease with respect to the non zero-padded, and the more zero-padding I add, the more the amplitudes of the FT decrease.
I am a bit confused with whether these results are supossed to be like that, or if I have done something wrong in my calculations.