Prev: Information Theory - Entropy: h(A U B)
Next: Channel simulation in matlab
From: Vladimir Vassilevsky on 20 Nov 2009 17:49


commengr wrote:

> Hi,
>
> 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?
>
> Also, I don't want to have trial and error (Obviously).

There is no such method for the general case of unrelated functions. You
can only solve it numerically. There are few methods for special simple
cases though, but it is not very interesting.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com


From: commengr on 21 Nov 2009 05:49
>
>
>commengr wrote:
>
>> Hi,
>>
>> 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?
>>
>> Also, I don't want to have trial and error (Obviously).
>
>There is no such method for the general case of unrelated functions. You

>can only solve it numerically. There are few methods for special simple
>cases though, but it is not very interesting.
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>
>

Thanks Vlad, Robert (as always). I wanted to confirm if there was a method
for the task, that I was not aware of therefore took help from you
experts.

I think some people who posted replies did not understand the question.
Any way, its resolved now. Thanks to them for giving their views too.

I must say that the severity of the problem can be judged by the
*solution* Robert suggested. Its good to have Matlab :)

God willing Robert, I'll stay safe.
From: vashkevich on 21 Nov 2009 08:56
>>
>>
>>commengr wrote:
>>
>>> Hi,
>>>
>>> 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?
>>>

When there is no available MatLab
or mathematicians are joking


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 -:)

From: JCH on 21 Nov 2009 10:12

"commengr" <communications_engineer(a)yahoo.com> schrieb im Newsbeitrag
news:xNmdne9c9P8HUpvWnZ2dnUVZ_sSdnZ2d(a)giganews.com...
> Hi,
>
> 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?
>
> Also, I don't want to have trial and error (Obviously).
>


Use Excel or similar!

* http://home.arcor.de/janch/janch/_news/20091121-diagram/

You can do it in minutes.

--
Regards JCH


From: Jerry Avins on 21 Nov 2009 11:35
commengr wrote:
>>
>> commengr wrote:
>>
>>> Hi,
>>>
>>> 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?
>>>
>>> Also, I don't want to have trial and error (Obviously).
>> There is no such method for the general case of unrelated functions. You
>
>> can only solve it numerically. There are few methods for special simple
>> cases though, but it is not very interesting.
>>
>> Vladimir Vassilevsky
>> DSP and Mixed Signal Design Consultant
>> http://www.abvolt.com
>>
>>
>
> Thanks Vlad, Robert (as always). I wanted to confirm if there was a method
> for the task, that I was not aware of therefore took help from you
> experts.
>
> I think some people who posted replies did not understand the question.
> Any way, its resolved now. Thanks to them for giving their views too.
>
> I must say that the severity of the problem can be judged by the
> *solution* Robert suggested. Its good to have Matlab :)
>
> God willing Robert, I'll stay safe.

I solved one minimum by hand pretty easily. The iteration is no more
difficult than finding square roots with Newton's method. Stoll, I
agree, that's whar root-finder programs are for. My hp-41 calculator
would make short work of it.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
First  |  Prev  |  Next  |  Last
Pages: 1 2 3 4
Prev: Information Theory - Entropy: h(A U B)
Next: Channel simulation in matlab