Enhancing resolution of an oversampled signal

Hi,
I have an oversampled 1kHz sine signal with a sampling frequency of 
62.5MHz and vertical resolution of 8bit.
I take FFT (in matlab) to determine the signal's phase.
What I need is phase accuracy. Do you think it is better to enhance
vertical resolution to a greater number of bits? How to do this? Moving
average filter? Or it is better to take the FFT of the signal as it is?

Thank you so much,
Matteo.

Ettos wrote:

> I have an oversampled 1kHz sine signal with a sampling frequency of 
> 62.5MHz and vertical resolution of 8bit.

Wow.

> I take FFT (in matlab) 

62.5 MHz in Matlab?

to determine the signal's phase.

Phase with respect to what?

> What I need is phase accuracy.

What is the accuracy requirement?

> Do you think it is better to enhance
> vertical resolution to a greater number of bits?

Better for what?

> How to do this? Moving
> average filter? Or it is better to take the FFT of the signal as it is?

Get a clue.

> Thank you so much,
> Matteo.

Stupident.

On 1/28/2012 9:54 AM, Ettos wrote:
> Hi,
> I have an oversampled 1kHz sine signal with a sampling frequency of
> 62.5MHz and vertical resolution of 8bit.
> I take FFT (in matlab) to determine the signal's phase.
> What I need is phase accuracy. Do you think it is better to enhance
> vertical resolution to a greater number of bits? How to do this? Moving
> average filter? Or it is better to take the FFT of the signal as it is?
>
> Thank you so much,
> Matteo.

Vladimir already gave you all the answer that your question permits, but 
it seems likely to me that you don't know enough to understand it. Here 
are a few facts that might find useful:

1. The signal's actual frequency matters.
2. Phase has meaning only with respect to a reference.
3. Phase has well defined meaning only for pure sinusoids.
4. All the information is already in the samples. Accuracy depends on
    how they are processed.
5. FFT is not necessarily the most accurate way to measure relative
    phase.

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

On 28/01/2012 16.43, Jerry Avins wrote:
> Vladimir already gave you all the answer that your question permits, but
> it seems likely to me that you don't know enough to understand it. Here
> are a few facts that might find useful:
>
> 1. The signal's actual frequency matters.
> 2. Phase has meaning only with respect to a reference.
> 3. Phase has well defined meaning only for pure sinusoids.
> 4. All the information is already in the samples. Accuracy depends on
>      how they are processed.
> 5. FFT is not necessarily the most accurate way to measure relative
>      phase.

I'll try to be more precise.
I'm trying do determine the phase shift between two sine waves (actual 
frequency is 1kHz) sampled at 62.5MHz and 8 bit.
I calculated the phase shift between the fundamentals of the two signals 
using FFT. Is there a more accurate way to measure the phase shift in 
this particular situation (oversampled signal and poor vertical resolution)?

Thank you.

On 1/28/2012 6:56 PM, Ettos wrote:
> On 28/01/2012 16.43, Jerry Avins wrote:
>> Vladimir already gave you all the answer that your question permits, but
>> it seems likely to me that you don't know enough to understand it. Here
>> are a few facts that might find useful:
>>
>> 1. The signal's actual frequency matters.
>> 2. Phase has meaning only with respect to a reference.
>> 3. Phase has well defined meaning only for pure sinusoids.
>> 4. All the information is already in the samples. Accuracy depends on
>> how they are processed.
>> 5. FFT is not necessarily the most accurate way to measure relative
>> phase.
>
> I'll try to be more precise.
> I'm trying do determine the phase shift between two sine waves (actual
> frequency is 1kHz) sampled at 62.5MHz and 8 bit.
> I calculated the phase shift between the fundamentals of the two signals
> using FFT. Is there a more accurate way to measure the phase shift in
> this particular situation (oversampled signal and poor vertical
> resolution)?

There is no hope unless the sampling clocks of the two signals are 
synchronized. Are they?

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

Ettos <matmail_NOSPAM_@europe.com> wrote:

(snip)
> I'll try to be more precise.
> I'm trying do determine the phase shift between two sine waves (actual 
> frequency is 1kHz) sampled at 62.5MHz and 8 bit.
> I calculated the phase shift between the fundamentals of the two signals 
> using FFT. Is there a more accurate way to measure the phase shift in 
> this particular situation (oversampled signal and poor vertical resolution)?

Well, another way is to watch for the zero crossing, possibly after a
filter if there is too much noise. You didn't say how close it needs
to be, or much else about the source.

With 62500 samples per cycle, if you know which sample it crossed
zero on, then you have a 1 in 62500 phase accuracy. Doesn't sound
bad to me. Then you count the samples between when one crosses and
when the other crosses, divide by 62500. (Adjust depending on phase
units.)

-- glen

Jerry Avins <jya@ieee.org> wrote:

(snip)
>> I'll try to be more precise.
>> I'm trying do determine the phase shift between two sine waves (actual
>> frequency is 1kHz) sampled at 62.5MHz and 8 bit.

(snip)
> There is no hope unless the sampling clocks of the two signals are 
> synchronized. Are they?

Hmm, is it required? I suppose for FFT it would be.

If you do it by zero crossing, though, maybe it isn't required.
Count how many clocks between when they cross, count the period for
each (hope it isn't too different), and divide. 

-- glen

On Jan 28, 6:37 pm, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
> Jerry Avins <j...@ieee.org> wrote:

> ...
> > There is no hope unless the sampling clocks of the two signals are
> > synchronized. Are they?
>
> Hmm, is it required? I suppose for FFT it would be.

Clock synchronization would be required for the phase ("shift')
comparison regardless of algorithm.

If instrumentation performing  the DFT were used, it would be
desirable to select a bandwidth such that the signal is at 20 to 40%
of Fs to allow the anti-aliasing filter to limit the noise bandwidth.
Such instrumentation usually provides better than 8 bit quantization,
too.

Dale B. Dalrymple

On 29/01/2012 3.16, glen herrmannsfeldt wrote:

> Well, another way is to watch for the zero crossing, possibly after a
> filter if there is too much noise. You didn't say how close it needs
> to be, or much else about the source.
>
> With 62500 samples per cycle, if you know which sample it crossed
> zero on, then you have a 1 in 62500 phase accuracy. Doesn't sound
> bad to me. Then you count the samples between when one crosses and
> when the other crosses, divide by 62500. (Adjust depending on phase
> units.)

Other details: I acquire signals with a digital oscilloscope (Tektronix 
DPO2014), so the signals are clock synchronized.
In my measurement system I'm bound to acquire only one cycle of the sine 
wave so I've got only 62500 samples (I'm doing spectroscopy measurements 
on soil samples). For the noise, I apply a digital low pass filter 
implemented on the oscilloscope.
Sometimes happens that one of the sine wave I record is distorted, so I 
must look for the phase shift between the fundamentals of the two 
signals. Do you think the zero-crossing method is good even in this 
situation?

Thanks to all.

Ettos <matmail_NOSPAM_@europe.com> wrote:

(snip on zero cross detection)

> Other details: I acquire signals with a digital oscilloscope (Tektronix 
> DPO2014), so the signals are clock synchronized.
> In my measurement system I'm bound to acquire only one cycle of the sine 
> wave so I've got only 62500 samples (I'm doing spectroscopy measurements 
> on soil samples). For the noise, I apply a digital low pass filter 
> implemented on the oscilloscope.

In that case, my next suggestion is non-linear least squares fit
to a sinusoid. 

In the analog days, this was done with a lock-in amplifier, 
usually synchronous to the signal source. Averaged over many cycles,
the output I and Q, or atan2(Q,I) would be used.

Are the two signals the input and output, or two outputs?

> Sometimes happens that one of the sine wave I record is distorted, so I 
> must look for the phase shift between the fundamentals of the two 
> signals. Do you think the zero-crossing method is good even in this 
> situation?

It depends on the distortion. Some will move the zero crossing,
others won't. It would seem to me that the distortion would be something
you would want to measure and characterize, but maybe not.

-- glen