FFT of white noise with different sampling rate

Question

I have a question on how I should interpret the white noise power level (noise floor) obtain from FFT for different hardware sampling rates. I realized if I sample the same noise at different rates (100 MHz, 10 MHz), even though I have down-converted (FIRfilter and decimate) them to the same, lower rate (1 MHz), I will obtain a different noise level if I FFT the data.

For example, with 1 sec worth of data, I obtain 100 million points sampled at 100 MHz. By down-converting it to 1 MHz and doing FFT, I obtain a noise floor of -80 dBm. If now I reduce my hardware sampling rate to 10 MHz and down-convert it to 1 MHz, the FFT result will give me -70 dBm of noise floor which is higher than when I sampled at 100 MHz.

May I know what the cause is?

My initial guess was the broad-band noise caused aliasing and they added up. Does it mean I should always filter out physically the noise above double my sampling frequency?

Answer 1

The variance of sampled white noise that is filtered by a brick-wall lowpass filter is reduced by a factor equal to the ratio of the filter cutoff frequency to 1/2 the sample-rate. You start off with the same variance for the 100mhz and 10mhz cases, but the reduction factors are different due to the different sample-rates. Or to put it another way, the 100mhz-sampled signal has less power/Hz than the 10mhz sampled signal, so when you compare them over the same bandwidth, the filtered 100mhz signal has less power.