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From: commengr on 21 Nov 2009 11:57
>>
>F= x(t) = sin(10*pi*t) + 2*cos(7*pi*t) + 3*sin(3*pi*t)
>
>Derivative f' = 0 =>
>10cos(10*x) – 14sin(7*x)+9cos(3*x) = 0, x = pi*t
>
>Let's leave frequencies with prime number (3x=10x-7x)
>
>10cos(10x)-14sin(7x)+9cos(10x)cos(7x) + 9sin(10x)sin(7x)
>or
>cos(10x)(10+9cos(7x)) + sin(7x)(9sin(10x) – 14) = 0
>
>y = 10x
>
>Take Taylor series near y = 2pi*k,
>the order of decomposition <= 2 =>
>
>(1-0.5y^2)(10+9(1-(7/10)^2*y^2)) + (7/10)(9*y-14) = 0 =>
>(y^2) (-5 - 9*7*7/200 + 7*9/10) – y * (7*14/10) + 19 = 0 =>
>
>0.905y^2 + 9,8y – 10 = 0
>y1 = (-9.8 + 12.83)/1.81, y2 – not use
>
>x = (1,674 + 2Pi*k)/10
>
>After selection k and check min max
>We get result
>
>max if k = 4 x=pi*t ~ 2,68 (f ~ 5,95)
>min if k = 9 x=pi*t ~ 5,83 (f ~3,95 )
>
>Not strong, but after check int Matlab You see, that accuracy is not so
>rude.
>
>Nevertheless numerical is better -:)
>


Thanks vashkevich, for sharing this useful information. Perhaps this is
the method Vlad was referring to "There are few methods for special simple

cases though, but it is not very interesting"

@ JCH

>> I can find the max and min values using Matlab, however, is there a
>> method to find it without using a software? Simply using a pen and
>> paper? ----------------------
-------

Use Excel or similar!

?
??


From: Andreas Huennebeck on 23 Nov 2009 03:07
commengr wrote:

> Can some expert tell me the simplest method to find the max and min value
> of a composite signal. For eg. if it is given as,
>
> x(t) = sin(10*pi*t) + 2*cos(7*pi*t) + 3*sin(3*pi*t)
>
> I can find the max and min values using Matlab, however, is there a method
> to find it without using a software? Simply using a pen and paper?

-6 <=limit <= +6, knowing that limits of sin(x) and cos(x) are +/-1.

bye
Andreas
--
Andreas H�nnebeck | email: acmh(a)gmx.de
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From: Eric Jacobsen on 23 Nov 2009 10:38
On 11/23/2009 1:07 AM, Andreas Huennebeck wrote:
> commengr wrote:
>
>> Can some expert tell me the simplest method to find the max and min value
>> of a composite signal. For eg. if it is given as,
>>
>> x(t) = sin(10*pi*t) + 2*cos(7*pi*t) + 3*sin(3*pi*t)
>>
>> I can find the max and min values using Matlab, however, is there a method
>> to find it without using a software? Simply using a pen and paper?
>
> -6<=limit<= +6, knowing that limits of sin(x) and cos(x) are +/-1.
>
> bye
> Andreas

I had been going to suggest that as well but the constraints on the
accuracy weren't disclosed. When it was revealed that this was for
sizing a quantizer the next question would then be how much headroom
could be allocated to the potential error in this sort of quick estimate.

That sort of quick limit analysis would be general for any or random
arguments in the functions. Even given the nature of the relative
frequencies for this case it's a reasonable place to start if the
constraints allow it.

--
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com
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