le
发帖数: 190 | 1 why it has a white spectrum from DC to fs/2? | c**e
发帖数: 5555 | 2 there're presumptions for this conclusion. find a book about ADC and it
should be talked in the first chapter. | le
发帖数: 190 | 3 就是看不懂才到这里来问的
【在 c**e 的大作中提到】
: there're presumptions for this conclusion. find a book about ADC and it
: should be talked in the first chapter.
| f**h
发帖数: 1149 | 4 先通过滤波器了
【在 le 的大作中提到】
: 就是看不懂才到这里来问的
| f*********t
发帖数: 37 | 5 Sometimes we assume the input of A/D is a white signal and has uniform disitribution between [-max +max]. This is just an assumption. According to this assumption, the quantization noise for each sample will be independent to each other with the same distribtion. Power spectrum of i.i.d random process is white.
【在 le 的大作中提到】
: why it has a white spectrum from DC to fs/2?
| f*********t
发帖数: 37 | 6 Not sure if it is related with 滤波器.
Because if the input of A/D is a sine wave, then the quantization noise won'
t be white no matter what filter you use.
【在 f**h 的大作中提到】
: 先通过滤波器了
| le
发帖数: 190 | 7 I understand it's white. The input signal doesn't necessarily need to be
random, it just need to be busy.
I just don't see why its spectrum is from DC to fs/2. Of course, it cannot
be infinity, otherwise the PSD has to be zero.
disitribution between [-max +max]. This is just an assumption. According to
this assumption, the quantization noise for each sample will be independent
to each other with the same distribtion. Power spectrum of i.i.d random
process is white.
【在 f*********t 的大作中提到】
: Sometimes we assume the input of A/D is a white signal and has uniform disitribution between [-max +max]. This is just an assumption. According to this assumption, the quantization noise for each sample will be independent to each other with the same distribtion. Power spectrum of i.i.d random process is white.
| h********t
发帖数: 555 | 8 you are right. in reality, most noise energy is below fs/2, but there are
still some noise energy beyond fs/2. from design aspect, it is a good
assumption that all noise energy is below fs/2,so that you can be prepared
for the worst case. for high resolution A-D converters, the noise
performance actually is limited by thermal noise, not Q-noise.
to
independent
【在 le 的大作中提到】
: I understand it's white. The input signal doesn't necessarily need to be
: random, it just need to be busy.
: I just don't see why its spectrum is from DC to fs/2. Of course, it cannot
: be infinity, otherwise the PSD has to be zero.
:
: disitribution between [-max +max]. This is just an assumption. According to
: this assumption, the quantization noise for each sample will be independent
: to each other with the same distribtion. Power spectrum of i.i.d random
: process is white.
| f*********t
发帖数: 37 | 9 Spectrum is from DC to fs/2. This is because after signal sampled at
sampling rate of fs at time domain, the power spectrum on frequency domain
will be pereiodically extended with period to be fs. This means the power
spectrum of the sampled signal is from [-fs/2 fs/2] is the same as [(n-1)*fs/2 (
n+1)fs/2]. Usually for descrete signal we only use the power spectrum in one
period.
Also for real baseband signal, after sampled, the spectrum will be symetric
to DC. so the spectrum [-fs/2 Dc] is the
【在 le 的大作中提到】
: I understand it's white. The input signal doesn't necessarily need to be
: random, it just need to be busy.
: I just don't see why its spectrum is from DC to fs/2. Of course, it cannot
: be infinity, otherwise the PSD has to be zero.
:
: disitribution between [-max +max]. This is just an assumption. According to
: this assumption, the quantization noise for each sample will be independent
: to each other with the same distribtion. Power spectrum of i.i.d random
: process is white.
| c**e
发帖数: 5555 | 10 首先，白噪声是一种假设，当输入信号的变化足够快能keep ADC busy，并且和
sampling frequency是不相关的时候，可以认为量化噪声是平摊到nyquist带宽内的，
这样对分析设计有好处。
如果你问的是为什么有限带宽，sampling后的信号是离散的，带宽自然是有限，可以参
考信号系统知识和nyquist采样的定义。超过fs/2的能量被混叠回DC到fs/2的带内，类
似bouncing between DC and fs/2。 | | | f*********t
发帖数: 37 | 11 This is correct, hehe a concise explaination :)
【在 c**e 的大作中提到】
: 首先，白噪声是一种假设，当输入信号的变化足够快能keep ADC busy，并且和
: sampling frequency是不相关的时候，可以认为量化噪声是平摊到nyquist带宽内的，
: 这样对分析设计有好处。
: 如果你问的是为什么有限带宽，sampling后的信号是离散的，带宽自然是有限，可以参
: 考信号系统知识和nyquist采样的定义。超过fs/2的能量被混叠回DC到fs/2的带内，类
: 似bouncing between DC and fs/2。
| h********t
发帖数: 555 | 12 The original question is why quantization noise is band-limited to fs/2. what you claimed is that the power spectrum of the sampled signal from [-fs/2 fs/2] is the same as [(n-1)*fs/2 (n+1)fs/2]. In real world, that will not happen, because that could only happen if you could build an impulse sampling circuit. however, in real world, you just can not implement a impulse sampling circuit. you will have to either use sample and hold or sample and track circuit. in that case, the power spectrum of
【在 f*********t 的大作中提到】
: Spectrum is from DC to fs/2. This is because after signal sampled at
: sampling rate of fs at time domain, the power spectrum on frequency domain
: will be pereiodically extended with period to be fs. This means the power
: spectrum of the sampled signal is from [-fs/2 fs/2] is the same as [(n-1)*fs/2 (
: n+1)fs/2]. Usually for descrete signal we only use the power spectrum in one
: period.
: Also for real baseband signal, after sampled, the spectrum will be symetric
: to DC. so the spectrum [-fs/2 Dc] is the
| le
发帖数: 190 | 13 If we treat the sampled data as discrete time sequence, can we assume we
have an impulse sampling circuit?
what you claimed is that the spectrum of the sampled data with impulse
sampling is band limited. That is not relevant to the original question. In
real world, even the spectrum of the sampled data is not band-limited to fs/
2 either, because you just can not implement a impulse sampling circuit. you
will have to either use sample and hold or sample and track circuit. in
that case, spectru
【在 h********t 的大作中提到】
: The original question is why quantization noise is band-limited to fs/2. what you claimed is that the power spectrum of the sampled signal from [-fs/2 fs/2] is the same as [(n-1)*fs/2 (n+1)fs/2]. In real world, that will not happen, because that could only happen if you could build an impulse sampling circuit. however, in real world, you just can not implement a impulse sampling circuit. you will have to either use sample and hold or sample and track circuit. in that case, the power spectrum of
| h********t
发帖数: 555 | 14 it doesn't matter how you sample the data, the quantization noise is
still not band limited, because quantization will introduce high frequency components.the quantization noise spectrum is not relevant to the sampled data spectrum.
In
fs/
you
2.
quantization
【在 le 的大作中提到】
: If we treat the sampled data as discrete time sequence, can we assume we
: have an impulse sampling circuit?
:
: what you claimed is that the spectrum of the sampled data with impulse
: sampling is band limited. That is not relevant to the original question. In
: real world, even the spectrum of the sampled data is not band-limited to fs/
: 2 either, because you just can not implement a impulse sampling circuit. you
: will have to either use sample and hold or sample and track circuit. in
: that case, spectru
| h********t
发帖数: 555 | 15 The original question is why quantization noise is band limited to fs/2.what
you claimed is that the spectrum of the sampled data is band limited to fs/
2. From design aspect,as an approximation, we may assume that is true, but
strictly speaking, neither of them is really band limited to fs/2.
with ideal impulse sampling, for the sampled data, the high frequency
spectrum of the original signal will be aliased back to lower frequency,
but the lower frequency components will get high frequency
【在 c**e 的大作中提到】
: 首先，白噪声是一种假设，当输入信号的变化足够快能keep ADC busy，并且和
: sampling frequency是不相关的时候，可以认为量化噪声是平摊到nyquist带宽内的，
: 这样对分析设计有好处。
: 如果你问的是为什么有限带宽，sampling后的信号是离散的，带宽自然是有限，可以参
: 考信号系统知识和nyquist采样的定义。超过fs/2的能量被混叠回DC到fs/2的带内，类
: 似bouncing between DC and fs/2。
| f*********t
发帖数: 37 | 16 Well, I was talking about perfect sampling. I guess the original question
was about perfect sampling. This is just my guess because this is an
assumption in many DSP books when no specific sampling methods are specified
.
After sampling, continuous signals are sampled to discrete signal. Discrete
signal has periodic power spectrum. Based on this, we usually only consider
the power spectrum of baseband discrete signal winthin one period which is [
-fs/2 fs/2]. So not only for noise but also for a
【在 h********t 的大作中提到】
: The original question is why quantization noise is band limited to fs/2.what
: you claimed is that the spectrum of the sampled data is band limited to fs/
: 2. From design aspect,as an approximation, we may assume that is true, but
: strictly speaking, neither of them is really band limited to fs/2.
: with ideal impulse sampling, for the sampled data, the high frequency
: spectrum of the original signal will be aliased back to lower frequency,
: but the lower frequency components will get high frequency
| f*********t
发帖数: 37 | 17 hehe please give me a matlab code of FFT of any signal (I mean ANY) at
sampling rate, say, 1MHz. Let me see how do you get the spectrum components
out of 1MHz.
BTW, don't ask question such as 'do you really understand what is XXX?'.
This won't make you more convincing and will make
communication harder.
do
signal is discrete in aptitude, but still continuous in time.
.
【在 h********t 的大作中提到】
: The original question is why quantization noise is band limited to fs/2.what
: you claimed is that the spectrum of the sampled data is band limited to fs/
: 2. From design aspect,as an approximation, we may assume that is true, but
: strictly speaking, neither of them is really band limited to fs/2.
: with ideal impulse sampling, for the sampled data, the high frequency
: spectrum of the original signal will be aliased back to lower frequency,
: but the lower frequency components will get high frequency
| h********t
发帖数: 555 | 18 That is right. I do feel it is very diciffult to comnunicate with you.You need understand that the operation of quantization is different from sampling, and the sampling rate of FFT simulation is different from the sampling rate of the data converter under test. If you are interested in how to run FFT to see quantization noise spectrum beyond the data converter sampling rate fs, you can read the book of CMOS Mixed- Signal Circuit Design by Jake Baker. Simulation file and output spetrum are all t
【在 f*********t 的大作中提到】
: hehe please give me a matlab code of FFT of any signal (I mean ANY) at
: sampling rate, say, 1MHz. Let me see how do you get the spectrum components
: out of 1MHz.
: BTW, don't ask question such as 'do you really understand what is XXX?'.
: This won't make you more convincing and will make
: communication harder.
:
: do
: signal is discrete in aptitude, but still continuous in time.
: .
| le
发帖数: 190 | 19 No, quantization error happens after sampling. You cannot use sampling
theory to explain its spectrum distribution.
specified
Discrete
consider
[
other
【在 f*********t 的大作中提到】
: Well, I was talking about perfect sampling. I guess the original question
: was about perfect sampling. This is just my guess because this is an
: assumption in many DSP books when no specific sampling methods are specified
: .
: After sampling, continuous signals are sampled to discrete signal. Discrete
: signal has periodic power spectrum. Based on this, we usually only consider
: the power spectrum of baseband discrete signal winthin one period which is [
: -fs/2 fs/2]. So not only for noise but also for a
| f*********t
发帖数: 37 | 20 yeah its like
y(t) ---> y(n*Ts)+Q(n*Ts) and Q(n*Ts) is the quatization noise.
【在 le 的大作中提到】
: No, quantization error happens after sampling. You cannot use sampling
: theory to explain its spectrum distribution.
:
: specified
: Discrete
: consider
: [
: other
| f*********t
发帖数: 37 | 21 Well if 'the sampling rate of FFT test is different from the sampling rate
of the data converter under test', then it makes sense to me.
I am not a circuit design or mixed signal guy. At the input of DSP or
digital ASIC, everything are discrete at sampling rate. Acutally sometimes
they are just some data sitting in memory :). I was talking about the
quantization noise at this point. I think this is also the quantization
noise defined in may DSP books like the one wrote by Proakis. I modeled
thos
【在 h********t 的大作中提到】
: That is right. I do feel it is very diciffult to comnunicate with you.You need understand that the operation of quantization is different from sampling, and the sampling rate of FFT simulation is different from the sampling rate of the data converter under test. If you are interested in how to run FFT to see quantization noise spectrum beyond the data converter sampling rate fs, you can read the book of CMOS Mixed- Signal Circuit Design by Jake Baker. Simulation file and output spetrum are all t
| T******n
发帖数: 3180 | 22 你们一个在讲AD
另一个在讲DA
差不多就是这样
【在 f*********t 的大作中提到】
: Well if 'the sampling rate of FFT test is different from the sampling rate
: of the data converter under test', then it makes sense to me.
: I am not a circuit design or mixed signal guy. At the input of DSP or
: digital ASIC, everything are discrete at sampling rate. Acutally sometimes
: they are just some data sitting in memory :). I was talking about the
: quantization noise at this point. I think this is also the quantization
: noise defined in may DSP books like the one wrote by Proakis. I modeled
: thos
|
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