Timeline for How does downsampling decrease the noise power?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2023 at 19:40 | comment | added | David | If the quantization noise is white, then the quantization noise power will be spread across the entire frequency sampling bandwidth i.e. $F_s$. By filtering out half the frequency band, the noise power will be reduced by a factor of 2 - since we assumed it was spread equally across $F_s$. If there is no power loss in the signal due to the filtering, then you will see a 3dB gain in the SNR. | |
| Aug 22, 2023 at 14:34 | comment | added | Ash | See this post deriving a constant PSD for downsampling (without filtering) a wide-sense stationary signal. | |
| Aug 22, 2023 at 14:28 | comment | added | Vic | @David, when I searched for the answer for my questions, I have also learnt that the quantization noise decreased by 3 dB by doubling the ADC sampling frequency. But is the SNR improvement from downsampling and filtering operation due to less thermal noise power or less quantization noise power or both? | |
| Aug 22, 2023 at 14:21 | comment | added | Vic | @DamienBradley ,thanks. another question is : is the fitlering that TimWescott mentioned in his comments required for this 3 dB noise reduction? Tim mentions that without filtering, the noise power stays the same. my understanding is: the PSD is the same before and after downsampling, and the frequency band has decreased with the downsampling, so even without filtering, the power should still be decreased with the downsampling; but to avoid aliasing and get the SNR improvement, the anti-aliasing filtering is required. | |
| Aug 22, 2023 at 14:13 | vote | accept | Vic | ||
| Aug 21, 2023 at 19:32 | comment | added | David | The basic idea and the math is correct but you don't need the Gaussian assumption. In practice it's a little more complicated. ADC quantization noise is usually not white. At high SNR, the quantization noise tends to be correlated, so you tend not to see the 3 dB improvement. At lower SNRs, the white noise begins to dominate and you'll begin to approach 3dB improvement. | |
| Aug 21, 2023 at 18:23 | history | edited | Jdip | CC BY-SA 4.0 | added 12 characters in body |
| Aug 21, 2023 at 16:01 | history | answered | DamienBradley | CC BY-SA 4.0 |