> Hi,
>
> How can I determine those ranges ?
>
> Thanks
>
> Hern�n S�nchez
>
>
> "Rick Lyons" <r.lyons@REMOVE.ieee.org> escribi� en el mensaje
> news:40190b23.59185953@news.west.earthlink.net...
>
>>Hi,
>> here are the frequency ranges (in kHz)
>>within which you can have your Fs sample rate:
>>
>>Fs_ranges =
>>
>> 150.0000 -to- 276.0000
>> 100.0000 -to- 138.0000
>> 75.0000 -to- 92.0000
>> 60.0000 -to- 69.0000
>> 50.0000 -to- 55.2000
>> 42.8571 -to- 46.0000
>> 37.5000 -to- 39.4286
>> 33.3333 -to- 34.5000
>> 30.0000 -to- 30.6667
>> 27.2727 -to- 27.6000
>> 25.0000 -to- 25.0909
>>
>>Zak is right, 48 kHz won't work.
>>
>>Good luck,
>>[-Rick-]
The only comprehensive discussion I've seen was in Rick's book
("Understanding Digital Signal Processing" by Richard G. Lyons, ISBN
0-201-63467-8, Section 2.3). A second edition is coming out soon.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by ●February 3, 20042004-02-03
Hi,
How can I determine those ranges ?
Thanks
Hern�n S�nchez
"Rick Lyons" <r.lyons@REMOVE.ieee.org> escribi� en el mensaje
news:40190b23.59185953@news.west.earthlink.net...
>
> Hi,
> here are the frequency ranges (in kHz)
> within which you can have your Fs sample rate:
>
> Fs_ranges =
>
> 150.0000 -to- 276.0000
> 100.0000 -to- 138.0000
> 75.0000 -to- 92.0000
> 60.0000 -to- 69.0000
> 50.0000 -to- 55.2000
> 42.8571 -to- 46.0000
> 37.5000 -to- 39.4286
> 33.3333 -to- 34.5000
> 30.0000 -to- 30.6667
> 27.2727 -to- 27.6000
> 25.0000 -to- 25.0909
>
> Zak is right, 48 kHz won't work.
>
> Good luck,
> [-Rick-]
>
Reply by Pawel●February 2, 20042004-02-02
Hello,
Thanks for all the remarks and the interesting discussion!
Pawel
Reply by Rick Lyons●February 1, 20042004-02-01
On Sat, 31 Jan 2004 23:16:08 -0800, "Mac" <foo@bar.net> wrote:
OK, ... I think I've got it.
Pawel apparently wanted his image to be centered
at Fs/4. His Fs was 192 kHz, so his Fs/4 was 48 kHz.
With help from MATLAB and several bottles of my
favorite alchoholic beverage from Holland,
I now think Pawel can get an image centered
at Fs/4 by choosing an Fs that satisfies:
Fs = 4Fc/m
where m is an odd integer, and Fc is Pawel's
144 kHz.
When m = 3, 7, 11, 15, etc.
spectral inversion will take place.
So Pawel's sample rate can be 192 kHz, 115.2 kHz,
82.28571 kHz, 64 kHz, 52.36364 kHz, 40.30792 kHz, etc.
[-Rick-]
Reply by Rick Lyons●February 1, 20042004-02-01
On Sat, 31 Jan 2004 23:16:08 -0800, "Mac" <foo@bar.net> wrote:
(snipped)
>Uh, equation (1) has a problem. If you solve it for Fi, the FC falls out.
Hi,
well, Eq, (1) is *already* solved in terms of Fi.
Here's Eq. (1) again:
Fi = Fs(1 + {Fc/Fs}) -Fc (1)
>Start by distributing the Fs back in. This gives you:
>Fi = (Fs + Fs{Fc/Fs}) - Fc
Yep, that's Eq. (1) all right.
>Which can be simplified to:
>
>Fi = Fs + Fc - Fc
>
>which is just:
>
>Fi = Fs
Oops, there's the problem Mac. The squiggly brackets
{x} mean the integer part of x. So {Fc/Fs} is *not*
equal to straight Fc/Fs. And Fs{Fc/Fs} is not equal
to Fc.
Now Jerry's idea of solving Eq. (1) for {Fc/Fs} first
seems like a good idea. Solving for {Fc/Fs}, we have:
Fi + Fc
{Fc/Fs} = ---------- -1. (2)
Fs
Which implies the ratio (Fi+Fc)/Fs must be
an integer because {Fc/Fs} is an integer.
Humm, ... mumble, grumble, mumble.
Thinking about integers, solving Eq. (1) for Fs
gives:
Fi + Fc
Fs = -------------- . (3)
{Fc/Fs} + 1
This means Fs is (Fi + Fc) divided by an integer.
However, the glitch is: Eq. (1) only applies, as
far as I know, when {2*Fc/Fs} is an odd integer.
Shoot! I have to think more about this.
It looks like bandpass sampling, for me, is like
a woman. As soon as you think you understand
something, you find out later that really you don't.
I'm gonna work on this during the Super Bowl.
Thanks guys,
[-Rick-]
Reply by Mac●February 1, 20042004-02-01
On Sat, 31 Jan 2004 12:26:05 +0000, Rick Lyons wrote:
> On 29 Jan 2004 11:33:44 -0800, pawel.kluczynski@comhem.se (Pawel)
> wrote:
>
> (snipped)
>>
>>Hello,
>>Thanks for the answers!
>>I did not say I wanted to sample at 48 kHz. I said I have a 144 KHz
>>analog signal that I want to alias to 48 kHz by sampling at Fs=192kHz.
>>Therefore I was looking for an audio 192 kHz ADC for the application.
>>The problem is that they ones I could find have too small analog
>>passband so the udersampling trick would not work.
>>
>>Regards,
>>
>>Pawel
>
> Hi,
> I was thinkin' some more about your question,
> and darn it, you make me ask a question.
>
> If we define:
>
> Fc = carrier freq (Pavel's 144 kHz)
> Fs = sample rate (Pavel's 198 kHz)
> Fi = the positive center freq of the aliased
> spectral replication nearest to zero Hz.
>
> In Pavel's case:
>
> Fi = Fs(1 + {Fc/Fs}) -Fc (1)
>
> where {Fc/Fs} means the integer part of Fc/Fs.
>
> Using that Eq. (1), Pavel's Fi (in kHz) is:
>
> Fi = 192(1 + 0) -144 = 48
>
> which is what he said.
>
> So now here's my question: At the risk of lookin'
> like (as Fred Sanford would say) a big dummy,
> is there a way to solve the above Eq. (1) for Fs
> in terms of Fc and Fi?
>
> For some reason (maybe Alzheimers) I can't
> figure out how to handle that {Fc/Fs} operation
> in algebra.
>
> Thanks,
> [-Rick-]
Uh, equation (1) has a problem. If you solve it for Fi, the FC falls out.
Start by distributing the Fs back in. This gives you:
Fi = (Fs + Fs{Fc/Fs}) - Fc
Which can be simplified to:
Fi = Fs + Fc - Fc
which is just:
Fi = Fs
Or am I missing something?
Mac
Reply by Rick Lyons●January 31, 20042004-01-31
On Sat, 31 Jan 2004 12:26:05 GMT, r.lyons@_BOGUS_ieee.org (Rick Lyons)
wrote:
It should be
Fs = sample rate (Pavel's 192 kHz)
Pawel, please pardon me for spelling your
name wrong. :-(
[-Rick-]
>
>
Reply by Jerry Avins●January 31, 20042004-01-31
Rick Lyons wrote:
> On 29 Jan 2004 11:33:44 -0800, pawel.kluczynski@comhem.se (Pawel)
> wrote:
>
> (snipped)
>
>>Hello,
>>Thanks for the answers!
>>I did not say I wanted to sample at 48 kHz. I said I have a 144 KHz
>>analog signal that I want to alias to 48 kHz by sampling at Fs=192kHz.
>>Therefore I was looking for an audio 192 kHz ADC for the application.
>>The problem is that they ones I could find have too small analog
>>passband so the udersampling trick would not work.
>>
>>Regards,
>>
>>Pawel
>
>
> Hi,
> I was thinkin' some more about your question,
> and darn it, you make me ask a question.
>
> If we define:
>
> Fc = carrier freq (Pavel's 144 kHz)
> Fs = sample rate (Pavel's 198 kHz)
> Fi = the positive center freq of the aliased
> spectral replication nearest to zero Hz.
>
> In Pavel's case:
>
> Fi = Fs(1 + {Fc/Fs}) -Fc (1)
>
> where {Fc/Fs} means the integer part of Fc/Fs.
>
> Using that Eq. (1), Pavel's Fi (in kHz) is:
>
> Fi = 192(1 + 0) -144 = 48
>
> which is what he said.
>
> So now here's my question: At the risk of lookin'
> like (as Fred Sanford would say) a big dummy,
> is there a way to solve the above Eq. (1) for Fs
> in terms of Fc and Fi?
>
> For some reason (maybe Alzheimers) I can't
> figure out how to handle that {Fc/Fs} operation
> in algebra.
>
> Thanks,
> [-Rick-]
A big dummy doesn't know. A big idiot thinks he does but doesn't. I'll
risk being branded with the latter title.
Solve for {Fc/Fs} first. Then, given the known Fc, see what range of Fs
makes that possible. I've introduced another variable, {Fc/Fs}, so it
may take some trial and error anyway, but at least it's directed.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Rick Lyons●January 31, 20042004-01-31
On 29 Jan 2004 11:33:44 -0800, pawel.kluczynski@comhem.se (Pawel)
wrote:
(snipped)
>
>Hello,
>Thanks for the answers!
>I did not say I wanted to sample at 48 kHz. I said I have a 144 KHz
>analog signal that I want to alias to 48 kHz by sampling at Fs=192kHz.
>Therefore I was looking for an audio 192 kHz ADC for the application.
>The problem is that they ones I could find have too small analog
>passband so the udersampling trick would not work.
>
>Regards,
>
>Pawel
Hi,
I was thinkin' some more about your question,
and darn it, you make me ask a question.
If we define:
Fc = carrier freq (Pavel's 144 kHz)
Fs = sample rate (Pavel's 198 kHz)
Fi = the positive center freq of the aliased
spectral replication nearest to zero Hz.
In Pavel's case:
Fi = Fs(1 + {Fc/Fs}) -Fc (1)
where {Fc/Fs} means the integer part of Fc/Fs.
Using that Eq. (1), Pavel's Fi (in kHz) is:
Fi = 192(1 + 0) -144 = 48
which is what he said.
So now here's my question: At the risk of lookin'
like (as Fred Sanford would say) a big dummy,
is there a way to solve the above Eq. (1) for Fs
in terms of Fc and Fi?
For some reason (maybe Alzheimers) I can't
figure out how to handle that {Fc/Fs} operation
in algebra.
Thanks,
[-Rick-]
Reply by Rick Lyons●January 30, 20042004-01-30
On 29 Jan 2004 11:33:44 -0800, pawel.kluczynski@comhem.se (Pawel)
wrote:
>r.lyons@REMOVE.ieee.org (Rick Lyons) wrote in message news:<40190b23.59185953@news.west.earthlink.net>...
>>
>> Hi,
>> here are the frequency ranges (in kHz)
>> within which you can have your Fs sample rate:
>>
>> Fs_ranges =
>>
>> 150.0000 -to- 276.0000
>> 100.0000 -to- 138.0000
>> 75.0000 -to- 92.0000
>> 60.0000 -to- 69.0000
>> 50.0000 -to- 55.2000
>> 42.8571 -to- 46.0000
>> 37.5000 -to- 39.4286
>> 33.3333 -to- 34.5000
>> 30.0000 -to- 30.6667
>> 27.2727 -to- 27.6000
>> 25.0000 -to- 25.0909
>>
>> Zak is right, 48 kHz won't work.
>>
>> Good luck,
>> [-Rick-]
>
>Hello,
>Thanks for the answers!
>I did not say I wanted to sample at 48 kHz. I said I have a 144 KHz
>analog signal that I want to alias to 48 kHz by sampling at Fs=192kHz.
>Therefore I was looking for an audio 192 kHz ADC for the application.
>The problem is that they ones I could find have too small analog
>passband so the udersampling trick would not work.
>
>Regards,
>
>Pawel
Hi,
Oh shoot, I misread your first post.
Sorry.
[-Rick-]