Cool graphs using the sgn(x) function!!!

bobbym · 2012-02-21 02:46:49

Hi anonimnystefy;

That is not correct. It is defined for 0.
Sign[0] = 0.

Here is how it is defined in Wikipedia.

http://en.wikipedia.org/wiki/Sign_function

anonimnystefy · 2012-02-21 08:46:05

hi bobbym

really.oh well.we can take it one the same interval just excluding the zeors of the functions.so for the last function which has three parts we would look at it just over the R\{-1,1}

benice · 2012-02-21 09:06:54

anonimnystefy wrote:

found it:The function

Hi anonimnystefy;

It's a nice expression!

Here is another expression: y = 0.5 sgn(x) (1 + sgn(abs(x) - 1)).

anonimnystefy · 2012-02-21 09:38:00

hi benice

thank you!

now i just need to find the general formula.

benice · 2012-02-21 10:21:48

anonimnystefy wrote:

hi benice
thank you!
now i just need to find the general formula.

y = 0.5 (a sgn(x + 1) + b sgn(x - 1))

Last edited by benice (2012-02-21 11:00:20)

anonimnystefy · 2012-02-22 09:11:23

hi benice

thanks for that formula as well.but i wanted the formula which will give the three lines at hights of a,b and c,respectively.

if you find anything let me now.once again,thank you for the formulas.

anonimnystefy · 2012-02-22 09:25:33

hi benice

i think i found one,but i don't know if it works for all heights and distances:

where a,b and c are the heights i mentioned and d and e are the distances of the breakings in the interval or in other words, d and e are the points where the sgn(x) function breaks according to our 'definition'.

benice · 2012-02-22 14:06:53

anonimnystefy wrote:

hi benice
i think i found one,but i don't know if it works for all heights and distances:
where a,b and c are the heights i mentioned and d and e are the distances of the breakings in the interval or in other words, d and e are the points where the sgn(x) function breaks according to our 'definition'.

Assume d < e.

x<d
=> y = 0.5[(a+c) + (b-a)(-1) + (c-b)(-1)] = 0.5[a+c-b+a-c+b] = a

d<x<e
=> y = 0.5[(a+c) + (b-a)(1) + (c-b)(-1)] = 0.5[a+c+b-a-c+b] = b

x>e
=> y = 0.5[(a+c) + (b-a)(1) + (c-b)(1)] = 0.5[a+c+b-a+c-b] = c

Last edited by benice (2012-02-22 14:09:21)

benice · 2012-02-22 14:32:47

Hi anonimnystefy;

You can use the sgn function to generate curves with dashed line:

x = sgn(cos(32t)) cos(t)
y = sgn(sin(32t)) sin(t)

x = sgn(cos(512t)) [cos(t) + sin(2t)]
y = sgn(sin(512t)) [sin(t) - sin(2t)]

x = sgn(cos(nt)) f(t)
y = sgn(sin(nt)) g(t)

Last edited by benice (2012-02-22 14:35:57)

anonimnystefy · 2012-02-24 06:25:54

hi benice

now those are some nice graphs.thanks for sharing that.

just wondering,you wrote there three formulas,and there are two graphs.which formula is for which graph?

John E. Franklin · 2012-02-25 02:29:01

what is this "sgn" function? Can you provide a definition of it.

bobbym · 2012-02-25 08:11:07

Hi John;

A few examples will do the trick:

sign(0) = 0

sign(+5) = 1

sign(+.3) = 1

sign(-2) = -1

sign(-200.34) = -1

anonimnystefy · 2012-02-25 10:21:09

hi JEF

it's called the sign function.and as its name says,it gives us the "sign" of the number.for positive numbers it returns 1, for negative -1 and for 0 it returns zero.

benice · 2012-02-25 16:41:33

anonimnystefy wrote:

just wondering,you wrote there three formulas ....

The third one is a general formula.

anonimnystefy · 2012-02-25 21:13:01

Hi benice

I don't know why I didn't notice it.

Are f(t) and g(t) random functions?

benice · 2012-02-26 10:06:25

anonimnystefy wrote:

Are f(t) and g(t) random functions?

f and g are arbitrary deterministic (non-random) functions.

anonimnystefy · 2012-02-26 12:02:29

Deterministic?

John E. Franklin · 2012-02-26 12:29:39

thanks for the examples (bobby) and definition (anom).

anonimnystefy · 2012-02-26 12:31:54

You're welcome!

bobbym · 2012-02-26 14:15:12

Hi John E. Franklin;

Your favorite programming language might have that command built in.

anonimnystefy · 2012-02-27 01:44:48

Hi bobbym

And that is?

benice · 2012-02-27 02:18:55

Hi anonimnystefy;

Here is a more general formula:
f(x) = 0.5 {f1(x) + f3(x) + sgn(x-a)[f2(x) - f1(x)] + sgn(x-b)[f3(x) - f2(x)]}

anonimnystefy wrote:

Deterministic?

http://en.wikipedia.org/wiki/Deterministic_system

bobbym · 2012-02-27 03:45:10

Hi anonimnystefy;

And that is?

Sometimes Sgn, Signum or Sign.

While python and C++ do not, mathematica, maple, delphi, Maxima and VB do.

afridinazneen · 2012-03-20 18:03:18

I have gotten some good information here.

bobbym · 2012-03-20 18:11:26

Hi;

Welcome to the forum!

Math Is Fun Forum

#51 2012-02-21 02:46:49

Re: Cool graphs using the sgn(x) function!!!

#52 2012-02-21 08:46:05

Re: Cool graphs using the sgn(x) function!!!

#53 2012-02-21 09:06:54

Re: Cool graphs using the sgn(x) function!!!

#54 2012-02-21 09:38:00

Re: Cool graphs using the sgn(x) function!!!

#55 2012-02-21 10:21:48

Re: Cool graphs using the sgn(x) function!!!

#56 2012-02-22 09:11:23

Re: Cool graphs using the sgn(x) function!!!

#57 2012-02-22 09:25:33

Re: Cool graphs using the sgn(x) function!!!

#58 2012-02-22 14:06:53

Re: Cool graphs using the sgn(x) function!!!

#59 2012-02-22 14:32:47

Re: Cool graphs using the sgn(x) function!!!

#60 2012-02-24 06:25:54

Re: Cool graphs using the sgn(x) function!!!

#61 2012-02-25 02:29:01

Re: Cool graphs using the sgn(x) function!!!

#62 2012-02-25 08:11:07

Re: Cool graphs using the sgn(x) function!!!

#63 2012-02-25 10:21:09

Re: Cool graphs using the sgn(x) function!!!

#64 2012-02-25 16:41:33

Re: Cool graphs using the sgn(x) function!!!

#65 2012-02-25 21:13:01

Re: Cool graphs using the sgn(x) function!!!

#66 2012-02-26 10:06:25

Re: Cool graphs using the sgn(x) function!!!

#67 2012-02-26 12:02:29

Re: Cool graphs using the sgn(x) function!!!

#68 2012-02-26 12:29:39

Re: Cool graphs using the sgn(x) function!!!

#69 2012-02-26 12:31:54

Re: Cool graphs using the sgn(x) function!!!

#70 2012-02-26 14:15:12

Re: Cool graphs using the sgn(x) function!!!

#71 2012-02-27 01:44:48

Re: Cool graphs using the sgn(x) function!!!

#72 2012-02-27 02:18:55

Re: Cool graphs using the sgn(x) function!!!

#73 2012-02-27 03:45:10

Re: Cool graphs using the sgn(x) function!!!

#74 2012-03-20 18:03:18

Re: Cool graphs using the sgn(x) function!!!

#75 2012-03-20 18:11:26

Re: Cool graphs using the sgn(x) function!!!

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