What is meant by bandwidth here?

Question

Regarding the following text:

Dynamic Range is defined as ratio between the smallest and the largest signals that can be measured by the system.

Smallest signal is usually the RMS Noise which is the root-mean-square value of the signal measured with no applied signal. The measured RMS Noise level will depend on the bandwidth it is measured over. Each time bandwidth is doubled, recorded noise increases by 1.41 or 3dB.

For the part "Each time bandwidth is doubled"; what is meant by bandwidth here? Bandwidth of what? Do they mean the sampling frequency of the ADC?

So if our noise signal's FFT yields the noise signal's max frequency is 1kHz i.e signal bandwidth is 1kHz. And if the ADC samples this signal with 10kHz. Is the bandwidth meant in the paragraph bandwidth of the noise or the ADC sampling frequency?

Answer 1

If you filter the signal over a certain bandwidth the noise power is proportional to the bandwidth. They are assuming white noise (constant power spectral density). So the noise power between 0Hz and 1MHz is the same as the noise power between 1MHz and 2MHz and half that between 1MHz and 3MHz.

In a sampled data your analog anti-aliasing filter may be designed to block signals that approach fs/2 or less, or you might be undersampling. If you are undersampling you likely have an anti-aliasing filter that is a bandpass filter, to the same effect, the noise power is proportional to the bandwidth of the analog filter.

Real noise power usually includes a 1/f component, may not be all that constant with frequency, and always declines at high frequencies (or the power would be infinite).