# FFT of white noise with different sampling rate

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?

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.

• Thanks for the idea, this is also how I was understanding it, where they have the same variance at different bandwidth means different noise power density to begin with. If this is the case, which one of them gives the correct power/Hz? Or it is simply I will have more noise with lower hardware sampling frequency? Thanks. Commented Oct 23, 2019 at 13:47