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From: Jerry Avins on 20 Nov 2009 13:46
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).
>
> Thanks.
>
> Ps. Not a HW prob

Find the value(s) of t (or pi*t) that makes the derivative go to zero.
Use that value in the original equation. That will provide a small set
of values to choose from. Alternatively, graph x(t) to get some insight
into which values to use.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
From: Jerry Avins on 20 Nov 2009 13:50
commengr wrote:
>> On Fri, 20 Nov 2009 11:33:36 -0600
>> "commengr" <communications_engineer(a)yahoo.com> wrote:
>>
>>>> On 11/20/2009 10:19 AM, 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).
>>>>>
>>>>> Thanks.
>>>>>
>>>>> Ps. Not a HW prob
>>>> Find the solutions for which the derivative is zero?
>>>>
>>>> --
>>>> Eric Jacobsen
>>>> Minister of Algorithms
>>>> Abineau Communications
>>>> http://www.abineau.com
>>>>
>>> I had also thought of using that approach, however, I'm having
>>> trigonometric functions. How is the derivative gonna be zero? Please
>>> explain?
>> Well, d(sin x)/dx = cos x, d(cos x)/dx = -sin x, and for general
>> functions f(x) and g(x), d(f(x) + g(x))/dx = df(x)/dx + dg(x)/dx. The
>> rest is left as an example for the student.
>>
>> See, and the teacher didn't think I was paying any attention in high
>> school calculus.
>>
>> --
>> Rob Gaddi, Highland Technology
>> Email address is currently out of order
>>
>
> Your school calculus is real good. However, it does not help here.
>
> I assume you are pointing that some terms might cancel... correct me if
> I'm not following you... any way, since the trigonometric components have
> different frequencies, they won't cancel each other out.

They *will* cancel at certain values of t. Why do you think not?

> Let me elaborate, I want to *find* the max and min value of this composite
> signal so that I can decide on the limits of the input voltage to a
> quantizer. I don't want to 'put' external limits just yet.
>
> Perhaps I need a reply from Robert B. J, Vlad etc
>
> If anyone else can help, I'd welcome that too

Averybody who responded helped. Preconceived ideas prevented you from
hearing them.

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
From: Eric Jacobsen on 20 Nov 2009 15:15
On 11/20/2009 10:53 AM, commengr wrote:
>> On Fri, 20 Nov 2009 11:33:36 -0600
>> "commengr"<communications_engineer(a)yahoo.com> wrote:
>>
>>>> On 11/20/2009 10:19 AM, 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).
>>>>>
>>>>> Thanks.
>>>>>
>>>>> Ps. Not a HW prob
>>>> Find the solutions for which the derivative is zero?
>>>>
>>>> --
>>>> Eric Jacobsen
>>>> Minister of Algorithms
>>>> Abineau Communications
>>>> http://www.abineau.com
>>>>
>>> I had also thought of using that approach, however, I'm having
>>> trigonometric functions. How is the derivative gonna be zero? Please
>>> explain?
>> Well, d(sin x)/dx = cos x, d(cos x)/dx = -sin x, and for general
>> functions f(x) and g(x), d(f(x) + g(x))/dx = df(x)/dx + dg(x)/dx. The
>> rest is left as an example for the student.
>>
>> See, and the teacher didn't think I was paying any attention in high
>> school calculus.
>>
>> --
>> Rob Gaddi, Highland Technology
>> Email address is currently out of order
>>
>
> Your school calculus is real good. However, it does not help here.
>
> I assume you are pointing that some terms might cancel... correct me if
> I'm not following you... any way, since the trigonometric components have
> different frequencies, they won't cancel each other out.
>
> Let me elaborate, I want to *find* the max and min value of this composite
> signal so that I can decide on the limits of the input voltage to a
> quantizer. I don't want to 'put' external limits just yet.
>
> Perhaps I need a reply from Robert B. J, Vlad etc
>
> If anyone else can help, I'd welcome that too

You already said in your first post that you can find the min and max
using Matlab, and then said you want to do it without software. Now you
say you want to *find* the max and min for sizing the input to a quantizer.

I don't know why the matlab result that you already said you can find
wouldn't work for that task.

If you really do want to do it "without software" I don't know why the
methods already explained wouldn't work.

At the moment it seems to me that you either haven't explained clearly
what you want, you don't know what you want, or you don't understand the
suggestions you've been given.

Perhaps you can clarify further.
--
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com
From: robert bristow-johnson on 20 Nov 2009 15:55
On Nov 20, 12:53 pm, "commengr" <communications_engin...(a)yahoo.com>
wrote:
>
>
> Let me elaborate, I want to *find* the max and min value of this composite
> signal so that I can decide on the limits of the input voltage to a
> quantizer. I don't want to 'put' external limits just yet.
>
> Perhaps I need a reply from Robert B. J, Vlad etc
>
> If anyone else can help, I'd welcome that too

well, my Pakistani friend, if the Fourier series has completely
general phases like your example:

> >> >> x(t) = sin(10*pi*t) + 2*cos(7*pi*t) + 3*sin(3*pi*t)

then, for an analytical solution, i think you're basically screwed.
there's little you can do other than drop your pants and bend over.

now, if they were *all* cosines, you could do it. that's because the
derivatives are all sines and they go to zero together when pi*t is an
integer. but, just because the derivatives go to zero somewhere,
doesn't guarantee it's the max or min, it might be only a local max or
min and each would have to be tested.

i remember there was a paper done a decade ago for the IEEE Mohonk
conference about using test signals that contained known frequency
components but had a low crest factor (the ratio of peak to r.m.s.)
and, essentially, one had to sorta randomize the phases of each
sinusoidal component to hope to get a decently low crest factor.

i'm still concerned for your safety over there. each time i hear the
news from the region, it's not encouraging.

r b-j
From: Michael Plante on 20 Nov 2009 17:39
>>On Fri, 20 Nov 2009 11:33:36 -0600
>>"commengr" <communications_engineer(a)yahoo.com> wrote:
>>
>>> >On 11/20/2009 10:19 AM, 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).
>>> >>
>>> >> Thanks.
>>> >>
>>> >> Ps. Not a HW prob
>>> >
>>> >Find the solutions for which the derivative is zero?
>>> >
>>> >--
>>> >Eric Jacobsen
>>> >Minister of Algorithms
>>> >Abineau Communications
>>> >http://www.abineau.com
>>> >
>>>
>>> I had also thought of using that approach, however, I'm having
>>> trigonometric functions. How is the derivative gonna be zero? Please
>>> explain?
>>
>>Well, d(sin x)/dx = cos x, d(cos x)/dx = -sin x, and for general
>>functions f(x) and g(x), d(f(x) + g(x))/dx = df(x)/dx + dg(x)/dx. The
>>rest is left as an example for the student.
>>
>>See, and the teacher didn't think I was paying any attention in high
>>school calculus.
>>
>>--
>>Rob Gaddi, Highland Technology
>>Email address is currently out of order
>>
>
>Your school calculus is real good. However, it does not help here.
>
>I assume you are pointing that some terms might cancel... correct me if
>I'm not following you... any way, since the trigonometric components
have
>different frequencies, they won't cancel each other out.
>
>Let me elaborate, I want to *find* the max and min value of this
composite
>signal so that I can decide on the limits of the input voltage to a
>quantizer. I don't want to 'put' external limits just yet.

Is there a reason you can't just take a conservative estimate, and assume
the worst: sum the factors in front? Or, to put the question differently,
what is the worst-case number of bits you'd lose by doing that? If it's
not too bad, you might be spending more effort in this area than
necessary.


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