How to do FFT of decimated digital signals from a ADC?
The FFT will not be any different for decimated data, but it will represent a lower bandwidth. The raw data from the ADC (or the ADC core if the decimation filter is integrated with the ADC) will represent a bandwidth of Fs/2 where Fs is the core sample rate. If you decimate by 2, then the decimated data will represent a Fs/4 bandwidth.
Here is a tutorial that you may find helpful:
Mixed Signal and DSP Design Techniques | Analog Devices
Section 5 includes FFTs.
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