# Aliasing question

Started by June 28, 2009
```Hi, I'm junior in the signal processing and I have a question. Can anybody
help to answer me? Suppose there's a analog signal bandwidth is B Hz and
with noise. There is no higher frequency componet outside the B Hz but the
noise. If I sample and quantize the analog signal by the sampling rate 2*B
Hz without aliasing filter. What does the noise happen in the digital
domain? Are they aliasing? how? I am just curious about the variation of
the noise floor and how it affect the in-band signal.

```
```lovejet wrote:
> Hi, I'm junior in the signal processing and I have a question. Can anybody
> help to answer me? Suppose there's a analog signal bandwidth is B Hz and
> with noise. There is no higher frequency componet outside the B Hz but the
> noise. If I sample and quantize the analog signal by the sampling rate 2*B
> Hz without aliasing filter. What does the noise happen in the digital
> domain? Are they aliasing? how? I am just curious about the variation of
> the noise floor and how it affect the in-band signal.

Out-of-band noise will alias into the band, degrading the SNR. Could you
imagine another outcome?

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```>Out-of-band noise will alias into the band, degrading the SNR. Could you

>imagine another outcome?
>
>Jerry
>--
>Engineering is the art of making what you want from things you can get.
>&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;
>

The in-band signal in the digital domain is repeated with 2*B Hz duration
that the aliasing occur. Does the in-band signal degraded by the 2nd, 3rd
... repeated spectum's out-of-band noise? If so, does it mean that the
in-band signal will finally sink into the noise floor and the SNR will be
0dB? If not, how does the aliased noise(2nd, 3rd and so on) stop to affect
the in-band signal? I'm so confused.
Grant
```
```On Thu, 02 Jul 2009 09:49:05 -0500, lovejet wrote:

> Hi, I'm junior in the signal processing and I have a question. Can
> anybody help to answer me? Suppose there's a analog signal bandwidth is
> B Hz and with noise. There is no higher frequency componet outside the B
> Hz but the noise. If I sample and quantize the analog signal by the
> sampling rate 2*B Hz without aliasing filter. What does the noise happen
> in the digital domain? Are they aliasing? how? I am just curious about
> the variation of the noise floor and how it affect the in-band signal.

>>Out-of-band noise will alias into the band, degrading the SNR. Could you
>
>>imagine another outcome?
>>
>>Jerry
>>--
>>Engineering is the art of making what you want from things you can get.
>>&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;
>>
>>
> The in-band signal in the digital domain is repeated with 2*B Hz
> duration that the aliasing occur. Does the in-band signal degraded by
> the 2nd, 3rd .. repeated spectum's out-of-band noise? If so, does it
> mean that the in-band signal will finally sink into the noise floor and
> the SNR will be 0dB? If not, how does the aliased noise(2nd, 3rd and so
> on) stop to affect the in-band signal? I'm so confused.
> Grant

When you sample finite-amplitude broadband noise it looks white after
sampling, but it'll still be of finite amplitude.  What happens is that
you get noise before sampling that you could filter out, but after
sampling it's all over your signal and you have no chance.

Consider that if you sampled by 10x over and filtered in the digital
domain the filtering would essentially be a weighted average of the
samples, with a 10/sqrt(10) advantage in SNR.

This may help:  http://www.wescottdesign.com/articles/Sampling/
sampling.html.

--
www.wescottdesign.com
```
```lovejet wrote:
>> Out-of-band noise will alias into the band, degrading the SNR. Could you
>> imagine another outcome?
>>
>> Jerry
>> --
>> Engineering is the art of making what you want from things you can get.
>>
>
> The in-band signal in the digital domain is repeated with 2*B Hz duration
> that the aliasing occur. Does the in-band signal degraded by the 2nd, 3rd
> .. repeated spectum's out-of-band noise? If so, does it mean that the
> in-band signal will finally sink into the noise floor and the SNR will be
> 0dB? If not, how does the aliased noise(2nd, 3rd and so on) stop to affect
> the in-band signal? I'm so confused.

Yes, you are. Baseband digital-to-analog conversion involves creating
analog pulses of values given by successive samples, then passing the
resulting stair-step signal through an analog low-pass filter to remove
frequencies above the sample rate (thus also removing the steps).

All of the aliases are in band after this process. I'm sure you
understand that that a 7 KHz sinusoid sampled at 8Ks/s appears in the
output as a 1 KHz alias. Noise components are no different.

Jerry
--
Engineering is the art of making what you want from things you can get.
```