CCD shift enhanced resolution

[John Sheehy]

I don't follow. By a swept sinusoid I guess you mean an FMCW signal
with a linear (usually triangle) modulation?

No, I'm just talking about a sine wave that slowly increases or decreases in frequency.

A unity amplitude sine wave at Fs/4, sampled at t=0 will have the
folling repetative pattern: 0, 1, 0, -1, so you will have fullscale
outputs.

What guarantees that synchronization? How do you know it won't be .707, .707, -.707, -.707 ?

At some frequency during a slow sweep, this is going to happen.

--
John

 

[alanr0]

I have never heard of this, could you provide a reference?

It probably doesn't happen much in sampling acoustic sounds, but if
you create a slow sine-wave sweep through the sampling range, the
volume drops out at frequencies like the ones I mentioned, because
at certain frequencies only low values will be sampled. Think of
it this way; if the sweep is slow enough, at some frequency, the
samples are going to occur at equally-spaced excursions both
postive and negative, with a very low signal resulting, for fs/4.

This is true, at least, for mathematically generated sweeps.
Perhaps sampled ones don't have the opportunity to be articulate
enough to record full modulation at these frequencies.

I don't follow. By a swept sinusoid I guess you mean an FMCW signal
with a linear (usually triangle) modulation? Perhaps the modulating
waveform, such as a triangle, is causing your signal to go over
the nyquist frequency and that you therefore see amplitude
modulation.

A unity amplitude sine wave at Fs/4, sampled at t=0 will have the
folling repetative pattern: 0, 1, 0, -1, so you will have fullscale
outputs.

But if you sample 1/8 period later, the output is 0.707, 0.707, -0.707 -0.707. This may not give a full scale (+1 -1) excursion after low pass filtering (interpolation). Depending on the filter implementation, it may not have the same amplitude as the sequence sampled from t=0. However, I would not call either a 'very low signal at fs/4'.

The sampling theorem implies that sampling a band-limited signal at greater** than twice the maximum signal frequency gives sufficient information to re-construct the original input. http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem

It does not guarantee that a particular implementation will accurately reproduce an input.

--
Alan Robinson

 

[Laurens]

Uk implementation dependent but AFAIK it's quite possible to build reconstruction filters that exhibit less than 0.1dB ripple at fs/4.

Laurens

I have never heard of this, could you provide a reference?

It probably doesn't happen much in sampling acoustic sounds, but if
you create a slow sine-wave sweep through the sampling range, the
volume drops out at frequencies like the ones I mentioned, because
at certain frequencies only low values will be sampled. Think of
it this way; if the sweep is slow enough, at some frequency, the
samples are going to occur at equally-spaced excursions both
postive and negative, with a very low signal resulting, for fs/4.

This is true, at least, for mathematically generated sweeps.
Perhaps sampled ones don't have the opportunity to be articulate
enough to record full modulation at these frequencies.

I don't follow. By a swept sinusoid I guess you mean an FMCW signal
with a linear (usually triangle) modulation? Perhaps the modulating
waveform, such as a triangle, is causing your signal to go over
the nyquist frequency and that you therefore see amplitude
modulation.

A unity amplitude sine wave at Fs/4, sampled at t=0 will have the
folling repetative pattern: 0, 1, 0, -1, so you will have fullscale
outputs.

But if you sample 1/8 period later, the output is 0.707, 0.707,
-0.707 -0.707. This may not give a full scale (+1 -1) excursion
after low pass filtering (interpolation). Depending on the filter
implementation, it may not have the same amplitude as the sequence
sampled from t=0. However, I would not call either a 'very low
signal at fs/4'.

No, but a sinusoid is the only signal that would satisfy that amplitude/time set and be within the sampling limits. Mathematically a recontruction filter could give arbitrary precision, in any case > 99% amplitude. Physical implementation at fs/4 is probably limited to, 95-99%, pretty close to full scale The discussion is moving pretty far away from teh original thread though, where everyone agrees that with current AA LPF there is not much to be gained by shifting your sensor.

The sampling theorem implies that sampling a band-limited signal at
greater** than twice the maximum signal frequency gives
sufficient information to re-construct the original input.
http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem
It does not guarantee that a particular implementation will
accurately reproduce an input.

--
Alan Robinson

 

[Laurens]

Uk implementation dependent but AFAIK it's quite possible to
build reconstruction filters that exhibit less than 0.1dB ripple at
fs/4.

Laurens

ignore the bit above in my original reply, I got distracted and started a-
fresh