Downsampling/Decimation - When is well done? I am working on decimation of signal, and I want to know which is the best way to understand if the downsampling is well done or not. At the moment I am comparing the FFT of the source signal and the downsampled signal and I observed a downward shift of it (I think it is due to the lesser quantity of samples), I had also a look into the time behavior. Do you have other advices/suggestions?

EDIT

From the comments/answers:


one method to understand if the downsampling process is well done is by comparing the FFT of the decimated signal and the original signal. The original signal must be attenuated by the decimation factor as suggested in the answer from @user2934229. Otherwise the signals can be normalized by the length of the signal (not suggested in my case because the signal is too long);
Ignoring your original question, and referring to your comment:


  I am observing the FFT of the downsampled signal presents an attenuation. I don't understand why.


The output of FFT (or DFT in general) isn't normalized - it is relative to the signal length (the total amount of samples being transformed). When decimating a signal (say, by a factor of M), you end up with a signal with 1/M length the original signal's length.

So, because DFT/FFT results are relative to signal length, a decimated signal with a 1/M length would have DFT/FFT components "attenuated" by a factor of M as well, even if the original signal was properly downsampled (i.e. bandlimited before being decimated).

To properly compare between the DFT of different signals, you should divide the output of DFT by the length of the transformed signal, to normalize the transform.