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Tim Wescott wrote:
> mnentwig wrote:
...
> > If so, the cycle length is simply fs/ft. If ft is an irrational number, it
> > will "never" complete a whole cycle.
..
>
> Where machine precision comes in is that if the _effective_ fs/ft isn't
> a rational number _after_ you've taken rounding into account, then your
> oscillator won't repeat on exact cycle boundaries.

Rounding fs/ft to machine precision will always make it a rational
number. Irrational numbers cannot be represented in any floating-point
format system that I know of.

Regards,
Andor

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Andor wrote:
> Tim Wescott wrote:
> ...
>> So your matrix is
>>
>>     [ 0  -1 ]
>> A = [       ]
>>     [ 1   0 ]
>>
>> this has eigenvalues of 1, -1, ...
> 
> Almost. Rotating those values by pi/2 gives the true eigenvalues :-).
> 
> Regards,
> Andor
> 
@#$%!

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html

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On Tue, 21 Aug 2007 09:13:49 -0700, Andor wrote:

> Tim Wescott wrote:
>> mnentwig wrote:
> ...
>> > If so, the cycle length is simply fs/ft. If ft is an irrational number, it
>> > will "never" complete a whole cycle.
> ..
>>
>> Where machine precision comes in is that if the _effective_ fs/ft isn't
>> a rational number _after_ you've taken rounding into account, then your
>> oscillator won't repeat on exact cycle boundaries.
> 
> Rounding fs/ft to machine precision will always make it a rational
> number. Irrational numbers cannot be represented in any floating-point
> format system that I know of.
> 
> Regards,
> Andor

The effective angular rotation is the arc tangent of the achievable gains,
which are, as you point out, rational ratios.  The arc tangent of a
rational number is not, however, in general, rational.

-- 
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

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On Tue, 21 Aug 2007 10:37:11 -0500, murthy_nssr wrote:

>>mnentwig wrote:
>>> Hello,
>>> 
>>>> Yi[n] = Yi[n-1]*cos(x)-Yq[n-1]*sin(x)
>>>> Yq[n] = Yi[n-1]*sin(x)+Yq[n-1]*cos(x)
>>> 
>>>> x = 2*pi*ft/fs, fs=8000 and ft=2000
>>>> oscillator is completing one period for n=226
>>> 
>>> Isn't that a simple rotating phasor? With the given numbers, 
>>> x = 2*pi*2000/8000=pi/2
>>> 
>>> Therefore I would expect a full cycle every four samples.
>>
>>I would too -- and this may not be the best way to implement a 
>>quadrature oscillator if _all_ you want is output at fs/2.
>>> 
>>> If so, the cycle length is simply fs/ft. If ft is an irrational number,
> 
> it
>>> will "never" complete a whole cycle.
>>> 
>>> I haven't simulated or read the reference. But I've got a feeling that
>>> machine precision could have an impact, since sin/cos(x) appear to the
> 
> nth
>>> power after n samples.
>>> 
>>Where machine precision comes in is that if the _effective_ fs/ft isn't 
>>a rational number _after_ you've taken rounding into account, then your 
>>oscillator won't repeat on exact cycle boundaries.  Worse, depending on 
>>your rounding the oscillations could either build, remain steady, or die
> 
> 
>>off -- you really want them to remain steady, or you want them to have a
> 
> 
>>slight tendency to build that you counteract with a nonlinearity to keep
> 
> 
>>the amplitude constant without much harmonic generation.
>>
>>There must be literature on how to make this happen; I just know that 
>>you need to watch out for it.
>>
>>-- 
>>
>>Tim Wescott
>>Wescott Design Services
>>http://www.wescottdesign.com
>>
>>Do you need to implement control loops in software?
>>"Applied Control Theory for Embedded Systems" gives you just what it
> 
> says.
>>See details at http://www.wescottdesign.com/actfes/actfes.html
> 
> 
> Information is available on the amplitude variations of this oscillator in
> 
> the same reference I mentioned. I am using the AGC method suggested the
> 
> paper by Turner.
> 
> So, isn't there a way i can use this oscillator and capture a cycle of it
> 
> for my I/Q reference?
> 
> If this is not a good way to implement a quadrature oscillator till fs/2,
> 
> can you please suggest something else which stands for my problem.
> 
> Thanks in advance.
> Murthy.

Yes, you could do that, but why?  If you just want to capture a vector of
I and Q values, why not just make up a sine table of the correct length and
play it back?

-- 
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

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On Tue, 21 Aug 2007 09:43:37 -0500, Tim Wescott <t...@seemywebsite.com>
wrote:

  (snipped)
>
>Were I doing this task, I'd control the amplitude of my oscillator output.
>I'd probably read Clay's paper, then either shamelessly copy what he's
>done, or use his thoughts as a springboard for my own implementation --
>but I'd do it.
>
>-- 
>Tim Wescott

Hi,
  Yep.   And, of course, giving full acknowledgement 
to Mr. Clay Turner

[-Rick-]

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>>mnentwig wrote:
>>> Hello,
>>> 
>>>> Yi[n] = Yi[n-1]*cos(x)-Yq[n-1]*sin(x)
>>>> Yq[n] = Yi[n-1]*sin(x)+Yq[n-1]*cos(x)
>>> 

>Thanks in advance.
>Murthy.
>

Rotation of pi/2 is that simple: 

Yi[n] = -Yq[n-1]
Yq[n] =  Yi[n-1]


>>It is a rotating phasor. With the given numbers
>>x = 1.57080, where pi=3.1415926,
>>Hence sin(x)=0.02741
>>cos(x)=0.999624

Yes, sin(pi/2)=0.02741, but only if you interpret the pi/2 as degrees. You
should doublecheck the radiant/degrees settings of your pocket calculator

Cheers
Detlef

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>> So, isn't there a way i can use this oscillator and capture a cycle of
it
for my I/Q reference?

Wait a minute... 
Is it only about generating the LO waveform, for use in a wavetable
lookup?
That's straightforward, I put the equations here:

http://www.elisanet.fi/mnentwig/webroot/IQ_LO/


-Markus

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