PDA

View Full Version : A/D periodic


gilbert
11-22-2003, 10:59 AM
hi,

i have a question for A/D cycle.

The question will be state as below.

if we use sample rate with 2khz to sample 1khz signal , we can get 2 points in one period

but if we use 2khz sample rate to sample 1.1khz signal, how can we calculate the periodic after sampling.?


Tks

Jerry Avins
11-22-2003, 02:19 PM
gilbert wrote:

> hi,
>
> i have a question for A/D cycle.
>
> The question will be state as below.
>
> if we use sample rate with 2khz to sample 1khz signal , we can get 2
> points in one period
>
> but if we use 2khz sample rate to sample 1.1khz signal, how can we
> calculate the periodic after sampling.?
>
>
> Tks

Samples are valid only when the sampling rate exceeds twice the
highest frequency in the signal. Note well: not greater than or equal
to twice; absolutely greater than twice. The amplitude of your 1 KHz
signal is indeterminate. The samples of your 1.1 KHz signal are
indistinguishable from samples of a 0.9 KHz signal. That is called
"aliasing".

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

Jerry Avins
11-22-2003, 03:50 PM
Please keep newsgroup messages in the newsgroup.

The best way to determine the frequency of the waveform represented by
the samples depends on the nature of the signal. If the noise is small
and harmonics are few and weak, inspection is often good enough. For
waveforms rich in detail, Fourier analysis is usually needed. The usual
way to do that is with an FFT.

Of course, all measured frequencies are relative to the sampling
frequency, 11/50 in the case you pose.

Jerry
--
I would not bet against the possibility of time travel. My opponent
might be from the future and know the answer. .. Stephen Hawking
¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â ¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â ¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â¡Â
chao wrote:

> hi, jerry
>
> Thanks for your reply
>
> if i use 5khz sample rate to sample 1.1 khz signal.
> How can i calculate the periodic after sampling?
>
> Tks
>
>>Samples are valid only when the sampling rate exceeds twice the
>>highest frequency in the signal. Note well: not greater than or equal
>>to twice; absolutely greater than twice. The amplitude of your 1 KHz
>>signal is indeterminate. The samples of your 1.1 KHz signal are
>>indistinguishable from samples of a 0.9 KHz signal. That is called
>>"aliasing".
...

Vladimir Vassilevsky
11-23-2003, 01:15 AM
Jerry Avins wrote:
>
> Samples are valid only when the sampling rate exceeds twice the
> highest frequency in the signal.

Common misconception. Use "bandwidth" instead of "frequency".

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Jerry Avins
11-23-2003, 02:50 AM
Vladimir Vassilevsky wrote:
>
> Jerry Avins wrote:
>
>>Samples are valid only when the sampling rate exceeds twice the
>>highest frequency in the signal.
>
>
> Common misconception. Use "bandwidth" instead of "frequency".
>
> Vladimir Vassilevsky
>
> DSP and Mixed Signal Design Consultant
>
> http://www.abvolt.com

Start slowly. He wanted to know how to interpret the 1.,0 and 1.1 KHz
sampled at 2 Khz. Sub band sampling is a little too deep right now.

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

Fred Marshall
11-23-2003, 09:42 PM
"Jerry Avins" <[email protected]> wrote in message
news:[email protected]...
> Vladimir Vassilevsky wrote:
> >
> > Jerry Avins wrote:
> >
> >>Samples are valid only when the sampling rate exceeds twice the
> >>highest frequency in the signal.
> >
> >
> > Common misconception. Use "bandwidth" instead of "frequency".
> >
> > Vladimir Vassilevsky
> >
> > DSP and Mixed Signal Design Consultant
> >
> > http://www.abvolt.com
>
> Start slowly. He wanted to know how to interpret the 1.,0 and 1.1 KHz
> sampled at 2 Khz. Sub band sampling is a little too deep right now.
>

I agree with Jerry that we should keep it simple. And, I agree with
Vladimir. My reasoning is below. This came up a few months ago when one of
our stalwarts seemed to insist that a particular waveform was bandlimited
(it wasn't).

Start with your favorite sinusoid: f(t) = sin(2*pi*f1*t); -inf <= t <= +inf
Here, there is a single frequency and the waveform is bandlimited.

Now, time limit f(t): multiply by g(t)=1.0, -0.5 <= t <= +0.5; g(t)=0,
|t|>0.5
Resulting in:
f'(t)=sin(2*pi*f1*t), -0.5 <= t <= +0.5; f'(t)=0, |t|>0.5

Because of the notation above for f'(t), it may appear that "there is only
one frequency" and it may be OK to say that there is only one frequency if
the comment is suitably qualified. However, the bandwidth is infinite. So,
some band limitation is necessary if suitable sampling / reconstruction is
going to be possible. The band limitation that's suitable will depend on
the width of g(t), the temporal epoch or length of the sequence of samples.

In order to accomplish this, you are going to have to lowpass filter the
gated signal - which will modify the temporal samples at least at the edges.
I can imagine that it's sometimes OK to do this filtering after sampling and
sometimes not. I'll leave that discussion up to others.

I realize that gilbert asked about what *could* be continuous sampling - in
which case this all might be moot. However, he also asked about
"calculating the periodic" [sic] and that implies a temporal epoch - the
time over which this measurement is going to happen - or the integration
time or...... So, a part of the answer to gilbert is:

**Make sure that the length of the time sample is long compared to
1/((fs/2) - f1). Otherwise, there may be more frequency aliasing (and
error) than you can tolerate.**

Interesting isn't it? The closer the frequency of the sinusoid is to fs/2,
the longer one has to sample to avoid aliasing. I haven't thought much
further about it. It's simply saying that the sinc or Dirichlet width
around the frequency spike (due to finite temporal epoch) should not be such
that it is very large at fs/2. The closer f1 is to fs/2, the narrower the
sinc needs to be. The same applies for overlap around f=0, so fs/4
conceptually allows the shortest epoch it appears - for the same degree of
error. Of course, the error varies up and down as the frequency is changed
and the tails of the sinc add or subtract from one another. So the actual
frequency and the length of the epoch (period of the sinc) interact in
generating the error.

Fred