How do I approximate 300MHz sampled digital data using 301MHz sampled digital data?

The issue is as follows : 

Single-bit digital output data (from an oversampled sigma-delta ADC whose
sampling CK frequency is 301MHz) have to be approximated to the desired
data.

Here the desired data means digital data that are sampled at 300MHz.

And this approximation is to be carried out without a 300MHz clock.
Namely, 301MHz sampled single-bit data is to be approximated to 300MHz
sampled data without using a 300MHz (resampling) clock.

I'm considering using some linear/quadratic/cubic interpolation method for
the approximation of data.

Is it possible to do this?
How can I solve this issue?

Also I'd like to know a solution above in case that all the 301MHz's above
are replaced to 209MHz's.

Regards, 
fjwoemcu

fjwoemcu wrote:
> The issue is as follows :
>
> Single-bit digital output data (from an oversampled sigma-delta ADC whose
> sampling CK frequency is 301MHz) have to be approximated to the desired
> data.
>
> Here the desired data means digital data that are sampled at 300MHz.
>
> And this approximation is to be carried out without a 300MHz clock.
> Namely, 301MHz sampled single-bit data is to be approximated to 300MHz
> sampled data without using a 300MHz (resampling) clock.
>
> I'm considering using some linear/quadratic/cubic interpolation method for
> the approximation of data.
>
> Is it possible to do this?
> How can I solve this issue?
>
> Also I'd like to know a solution above in case that all the 301MHz's above
> are replaced to 209MHz's.
>
> Regards,
> fjwoemcu

The method you are considering will work just fine if the data is
oversampled, which it sounds like it is.

John

fjwoemcu wrote:

> The issue is as follows : 
> 
> Single-bit digital output data (from an oversampled sigma-delta ADC whose
> sampling CK frequency is 301MHz) have to be approximated to the desired
> data.
> 
> Here the desired data means digital data that are sampled at 300MHz.
> 
> And this approximation is to be carried out without a 300MHz clock.
> Namely, 301MHz sampled single-bit data is to be approximated to 300MHz
> sampled data without using a 300MHz (resampling) clock.
> 
> I'm considering using some linear/quadratic/cubic interpolation method for
> the approximation of data.
> 
> Is it possible to do this?

Yes. You can do it this way. However since your data is sampled to one 
bit and highly oversampled, all you have to do to change the sample rate 
is repeat or drop one sample per 300 samples.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Vladimir Vassilevsky wrote:
> fjwoemcu wrote:
>
> > The issue is as follows :
> >
> > Single-bit digital output data (from an oversampled sigma-delta ADC whose
> > sampling CK frequency is 301MHz) have to be approximated to the desired
> > data.
> >
> > Here the desired data means digital data that are sampled at 300MHz.
> >
> > And this approximation is to be carried out without a 300MHz clock.
> > Namely, 301MHz sampled single-bit data is to be approximated to 300MHz
> > sampled data without using a 300MHz (resampling) clock.
> >
> > I'm considering using some linear/quadratic/cubic interpolation method for
> > the approximation of data.
> >
> > Is it possible to do this?
>
> Yes. You can do it this way. However since your data is sampled to one
> bit and highly oversampled, all you have to do to change the sample rate
> is repeat or drop one sample per 300 samples.
>
> Vladimir Vassilevsky
>
> DSP and Mixed Signal Design Consultant
>
> http://www.abvolt.com

I've heard this called "drop sample interpolation". I think you will
want to drop one in 301. 

John

>
>
>fjwoemcu wrote:
>
>> The issue is as follows : 
>> 
>> Single-bit digital output data (from an oversampled sigma-delta ADC
whose
>> sampling CK frequency is 301MHz) have to be approximated to the
desired
>> data.
>> 
>> Here the desired data means digital data that are sampled at 300MHz.
>> 
>> And this approximation is to be carried out without a 300MHz clock.
>> Namely, 301MHz sampled single-bit data is to be approximated to 300MHz
>> sampled data without using a 300MHz (resampling) clock.
>> 
>> I'm considering using some linear/quadratic/cubic interpolation method
for
>> the approximation of data.
>> 
>> Is it possible to do this?
>
>Yes. You can do it this way. However since your data is sampled to one 
>bit and highly oversampled, all you have to do to change the sample rate

>is repeat or drop one sample per 300 samples.
>
>Vladimir Vassilevsky
>
>DSP and Mixed Signal Design Consultant
>
>http://www.abvolt.com
>

Thanks for your advice. I thought the answer was not that easy. 
Is there any information loss (or error) when dropping 1 sample out of 301
samples?
And don't I have to use any interpolation method(linear, quadratic, ...)?
(I don't have to use linear or quadratic interpolation for data
approximation because the input is one bit?)
What if I have to approximate 301+1/3MHz(=301.333...MHz) sampled data to
300MHz sampled data?

Expecting replies.
Regards, 
fjwoemcu.

>
>Vladimir Vassilevsky wrote:
>> fjwoemcu wrote:
>>
>> > The issue is as follows :
>> >
>> > Single-bit digital output data (from an oversampled sigma-delta ADC
whose
>> > sampling CK frequency is 301MHz) have to be approximated to the
desired
>> > data.
>> >
>> > Here the desired data means digital data that are sampled at 300MHz.
>> >
>> > And this approximation is to be carried out without a 300MHz clock.
>> > Namely, 301MHz sampled single-bit data is to be approximated to
300MHz
>> > sampled data without using a 300MHz (resampling) clock.
>> >
>> > I'm considering using some linear/quadratic/cubic interpolation
method for
>> > the approximation of data.
>> >
>> > Is it possible to do this?
>>
>> Yes. You can do it this way. However since your data is sampled to one
>> bit and highly oversampled, all you have to do to change the sample
rate
>> is repeat or drop one sample per 300 samples.
>>
>> Vladimir Vassilevsky
>>
>> DSP and Mixed Signal Design Consultant
>>
>> http://www.abvolt.com
>
>I've heard this called "drop sample interpolation". I think you will
>want to drop one in 301. 
>
>John
>

Thank you, sir.
But isn't there any information loss during sample drop?
And don't I have to use any interpolation(linear, quadratic, cubic, ...)
for data approximation?
What if I have to approximate 300MHz sampled data using
300+2/3MHz(=300.666...MHz) single-bit digital data?
Don't I have to acquire a multi-bit output data from the single-bit
digital input data?
Expecting replies.
Regards, 
fjwoemcu.

fjwoemcu wrote:
> >
> >
> >fjwoemcu wrote:
> >
> >> The issue is as follows :
> >>
> >> Single-bit digital output data (from an oversampled sigma-delta ADC
> whose
> >> sampling CK frequency is 301MHz) have to be approximated to the
> desired
> >> data.
> >>
> >> Here the desired data means digital data that are sampled at 300MHz.
> >>
> >> And this approximation is to be carried out without a 300MHz clock.
> >> Namely, 301MHz sampled single-bit data is to be approximated to 300MHz
> >> sampled data without using a 300MHz (resampling) clock.
> >>
> >> I'm considering using some linear/quadratic/cubic interpolation method
> for
> >> the approximation of data.
> >>
> >> Is it possible to do this?
> >
> >Yes. You can do it this way. However since your data is sampled to one
> >bit and highly oversampled, all you have to do to change the sample rate
>
> >is repeat or drop one sample per 300 samples.
> >
> >Vladimir Vassilevsky
> >
> >DSP and Mixed Signal Design Consultant
> >
> >http://www.abvolt.com
> >
>
> Thanks for your advice. I thought the answer was not that easy.
> Is there any information loss (or error) when dropping 1 sample out of 301
> samples?
> And don't I have to use any interpolation method(linear, quadratic, ...)?
> (I don't have to use linear or quadratic interpolation for data
> approximation because the input is one bit?)
> What if I have to approximate 301+1/3MHz(=301.333...MHz) sampled data to
> 300MHz sampled data?
>
> Expecting replies.
> Regards,
> fjwoemcu.

The point is that if you are oversampled to begin with then the samples
don't change much from one to the next, so the noise could be
tolerable. If your data has any DC runs in it then that would be the
place to drop a sample.

For the case you gave consider 301.333... = 904/3 and 300 = 900/3. You
need to drop 4 in every 904 samples.

John

fjwoemcu wrote:
>>

>>>And this approximation is to be carried out without a 300MHz clock.
>>>Namely, 301MHz sampled single-bit data is to be approximated to 300MHz
>>>sampled data without using a 300MHz (resampling) clock.
>>>
>>>I'm considering using some linear/quadratic/cubic interpolation method
> 
>>
>> However since your data is sampled to one 
>>bit and highly oversampled, all you have to do to change the sample rate
> 
> 
>>is repeat or drop one sample per 300 samples.
>>
> 
> 
> Thanks for your advice. I thought the answer was not that easy. 
> Is there any information loss (or error) when dropping 1 sample out of 301
> samples?

The error due to that will be about (Fsignal/Fsamplerate)*(1/301).


> And don't I have to use any interpolation method(linear, quadratic, ...)?
> (I don't have to use linear or quadratic interpolation for data
> approximation because the input is one bit?)

It is likely that the error will be buried into the quantization noise, 
so you don't have to bother.

> What if I have to approximate 301+1/3MHz(=301.333...MHz) sampled data to
> 300MHz sampled data?

Same idea. Drop one sample per 226 samples.


Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

>
>
>fjwoemcu wrote:
>>>
>
>>>>And this approximation is to be carried out without a 300MHz clock.
>>>>Namely, 301MHz sampled single-bit data is to be approximated to
300MHz
>>>>sampled data without using a 300MHz (resampling) clock.
>>>>
>>>>I'm considering using some linear/quadratic/cubic interpolation
method
>> 
>>>
>>> However since your data is sampled to one 
>>>bit and highly oversampled, all you have to do to change the sample
rate
>> 
>> 
>>>is repeat or drop one sample per 300 samples.
>>>
>> 
>> 
>> Thanks for your advice. I thought the answer was not that easy. 
>> Is there any information loss (or error) when dropping 1 sample out of
301
>> samples?
>
>The error due to that will be about (Fsignal/Fsamplerate)*(1/301).
>
>
>> And don't I have to use any interpolation method(linear, quadratic,
...)?
>> (I don't have to use linear or quadratic interpolation for data
>> approximation because the input is one bit?)
>
>It is likely that the error will be buried into the quantization noise, 
>so you don't have to bother.
>
>> What if I have to approximate 301+1/3MHz(=301.333...MHz) sampled data
to
>> 300MHz sampled data?
>
>Same idea. Drop one sample per 226 samples.
>
>
>Vladimir Vassilevsky
>
>DSP and Mixed Signal Design Consultant
>
>http://www.abvolt.com

Thank you, John and Vladimir.
What references may I read to get basic and quantitative explanation on
'drop sample interpolation error' and performance compared to
linear/quadratic interpolation?
(I already searched IEEE Explore for drop, sample, interpolation... but
couldn't find some kind papers on this topic.)
Regards, 
fjwoemcu.

fjwoemcu wrote:
> >
> >
> >fjwoemcu wrote:
> >>>
> >
> >>>>And this approximation is to be carried out without a 300MHz clock.
> >>>>Namely, 301MHz sampled single-bit data is to be approximated to
> 300MHz
> >>>>sampled data without using a 300MHz (resampling) clock.
> >>>>
> >>>>I'm considering using some linear/quadratic/cubic interpolation
> method
> >>
> >>>
> >>> However since your data is sampled to one
> >>>bit and highly oversampled, all you have to do to change the sample
> rate
> >>
> >>
> >>>is repeat or drop one sample per 300 samples.
> >>>
> >>
> >>
> >> Thanks for your advice. I thought the answer was not that easy.
> >> Is there any information loss (or error) when dropping 1 sample out of
> 301
> >> samples?
> >
> >The error due to that will be about (Fsignal/Fsamplerate)*(1/301).
> >
> >
> >> And don't I have to use any interpolation method(linear, quadratic,
> ...)?
> >> (I don't have to use linear or quadratic interpolation for data
> >> approximation because the input is one bit?)
> >
> >It is likely that the error will be buried into the quantization noise,
> >so you don't have to bother.
> >
> >> What if I have to approximate 301+1/3MHz(=301.333...MHz) sampled data
> to
> >> 300MHz sampled data?
> >
> >Same idea. Drop one sample per 226 samples.
> >
> >
> >Vladimir Vassilevsky
> >
> >DSP and Mixed Signal Design Consultant
> >
> >http://www.abvolt.com
>
> Thank you, John and Vladimir.
> What references may I read to get basic and quantitative explanation on
> 'drop sample interpolation error' and performance compared to
> linear/quadratic interpolation?
> (I already searched IEEE Explore for drop, sample, interpolation... but
> couldn't find some kind papers on this topic.)
> Regards,
> fjwoemcu.

IEEE Xplore is a piece of s**t. Try google or google scholar. 

John