Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Sign In with Facebook Sign In with Google Sign In with OpenID

Categories

We have migrated to a new platform! Please note that you will need to reset your password to log in (your credentials are still in-tact though). Please contact lee@programmersheaven.com if you have questions.
Welcome to the new platform of Programmer's Heaven! We apologize for the inconvenience caused, if you visited us from a broken link of the previous version. The main reason to move to a new platform is to provide more effective and collaborative experience to you all. Please feel free to experience the new platform and use its exciting features. Contact us for any issue that you need to get clarified. We are more than happy to help you.

is this possible ?

ShadovvShadovv Posts: 31Member
Does anybody know if this is possible.

Equation as follows.

aSin(20degrees) + bSin(40degrees) + cSin(60degrees) = answer

If the anwser was given in decimal form, is it possible to derive what 'a', 'b', and 'c' are ?, since we already know what the phases are for each.
I recall something about frequency division multiplexing using fast fourier transforms or something like that. But can't quite wrap my head around it.
If there was one signal say 'aSin(20degrees)', then it's simply,
- multiplying the signal with a reference signal that's in phase with signal 'a' with unity amplitude, in this case Sin(20degrees).
- take the average of each resulting product
- double the average, and you have the answer to 'a'.

But what about if it's more then one signal ?
like the one mentioned above,
aSin(20degrees) + bSrin(40degrees) + .....etc


thanks in advance.

Comments

  • DrMartenDrMarten Posts: 748Member
    [b][red]This message was edited by DrMarten at 2005-4-7 20:20:47[/red][/b][hr]
    : Does anybody know if this is possible.
    :
    : Equation as follows.
    :
    : aSin(20degrees) + bSin(40degrees) + cSin(60degrees) = answer
    :
    : If the anwser was given in decimal form, is it possible to derive what 'a', 'b', and 'c' are ?, since we already know what the phases are for each.
    : I recall something about frequency division multiplexing using fast fourier transforms or something like that. But can't quite wrap my head around it.
    : If there was one signal say 'aSin(20degrees)', then it's simply,
    : - multiplying the signal with a reference signal that's in phase with signal 'a' with unity amplitude, in this case Sin(20degrees).
    : - take the average of each resulting product
    : - double the average, and you have the answer to 'a'.
    :
    : But what about if it's more then one signal ?
    : like the one mentioned above,
    : aSin(20degrees) + bSrin(40degrees) + .....etc
    :
    :
    : thanks in advance.
    :


    From a maths point of view you could end up with more than one solution as even if a,b and c here are WHOLE numbers then it is like saying:->

    (2*40) + (3*50) + (4*60)= 80+150+240=470

    From the 470 here you could derive a few numbers like:->

    4+6+460 and again with

    400+50+20 etc

    giving lots of results.

    You could eliminate some results using
    SIMULTANEOUS EQUATIONS methods maybe in a loop?

    Like the following

    1) a+b=12
    2) a+b+c=12
    3) a+b+c+d=12
    4) a+b+c+d+e=12

    Find one term by adding up the rest and solving via addition+subtraction.

    I.E.

    In 1) above If a=5 then b=12-5=7

    In 2) above add the b+c to get a) if you know the answer.

    In 3) above add the b,c&d to get a) if you know the answer

    In 4) add b,c,d,e to get a) if you know the answer.


    If you can create a simultaneous pair of equations from your results then you can produce what a,b,c etc are?

    E.G. To take your problem:-

    aSin(20degrees) + bSin(40degrees) + cSin(60degrees) = answer

    If a=2 b=3 c=4 then answer=6.076504731

    If a became 3 the 2nd and 3rd term would total a higher value

    But if the answer remains the same then b or/and c are reduced.

    Like saying:->

    1) 2a+3b+4c=d
    2) 3a+b+c=d

    Muliply 1) through by -1 giving:-> -2a+ -3b+ -4c = -d

    -2a+ -3b+ -4c = -d
    +3a+ b +c = d

    Adding gives:->

    a -2b - 3c = 0 so a=2b+3c

    You could use the simultaneous equtions idea maybe to get the other results or graphing analysis to see where straight line equations intersect?

    Like
    2a+3b=12 where a=3,b=2 or a=2,b=8/3 Plot a againt b
    3x+2y=12 Plot x againt y

    Where ever the lines cross solves a simultaneous equation.
    If this works for straight lines it would work for SIN or COS wave diagrams I guess. Would help you to eliminate some of the values maybe?

    Just an idea though if it is of any use?

    You would need a clever routine to deal with an ever increasing number of terms or "waveforms" though.

    Plus simple or complex wavforms when overlapped cross at multiple points so there is more than one solution to your problem I guess.

    Hope this helps. :-)



  • jerubaaljerubaal Posts: 19Member
    In order for the "Simultaneous equation method" to work, you need a number of equations equal to your results. For example, if you have 3 variables, you need 3 equations. Look for an online math resource, and read up on systems of equations, and also look at systems of equations using matrices.
    1337 d00d

Sign In or Register to comment.