Drawing Mathematical Blank This A.M.

[snip]

-(1-Decimal) or equivalently Decimal-1

So the result is a _sawtooth_.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

"Integer.Decimal" is always a positive number.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

[snip]

There is INT and IF, but IF is useful only where it's not useful ;-)

I just came up with this while having a mac-n-cheese lunch with my

3-year-old grand-daughter:

(Integer.Decimal) - Round(Integer.Decimal)

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

I need it valid for 0 1G ;-)

...Jim Thompson

-- | James E.Thompson, P.E. | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona Voice:(480)460-2350 | | | E-mail Address at Website Fax:(480)460-2142 | Brass Rat | |

| 1962 | I love to cook with wine. Sometimes I even put it in the food.

Do you mean this, or do you mean -(Decimal-1), which would be a continuous inverted-V-shaped function?

If the latter, then maybe something like

0.5 - sqrt((x-0.5)^2)

Best regards, Spehro Pefhany

--
"it's the network..."                          "The Journey is the reward"
speff@interlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com

Does it have to be valid (and is it defined) as above for x < 0 and x > 1 as well?

Best regards, Spehro Pefhany

--
"it's the network..."                          "The Journey is the reward"
speff@interlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com

FRACT(X + 0.5) -0.5

is valid/differentiable for -0.5 < x < 1.5

....not good enough?

Best regards, Spehro Pefhany

--
"it's the network..."                          "The Journey is the reward"
speff@interlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com

....

Looks like you might have a sign function to work with.

So I look at you having two different behaviors, one on each side of 1/2 and think of using the sign function to tease these apart.

I'm assuming that SGN is your sign function and is +1 when the argument is positive and -1 when it is negative. So if I'm right

(SGN(x-1/2)+1)/2 will be +1 for x > 1/2 and 0 elsewhere

-(SGN(x-1/2)-1)/2 will be +1 for x < 1/2 and 0 elsewhere

Now you want a line y=x-1 for x > 1/2 and you want a line y=x for x < 1/2.

Assemble all the bits

(SGN(x-1/2)+1)/2*(x-1)-(SGN(x-1/2)-1)/2*x

Then throw it at Derive (free 30 day trial at

and do a plot of the result to make sure it does what I wanted, discover I had swapped a + and - initially, corrected above. And, then just for grins I tap the Simplify button to ask it if it knows of a simpler form. It responds with (actually Derive uses SIGN, not SGN):

x-1/2-SGN(2*x-1)/2

hummm... which with a few moments thought seems to be

x-1/2-SGN(x-1/2)/2

which I throw back at Derive just to make sure my brain cells haven't completely failed, and all three plots are the same sawtooth.

If I think about the final version for a moment I realize it is a line with the same slope as the one you desire, positioned midway between the two lines you wanted, and they are using SGN to either add or subtract 1/2 to give the desired vertical offset. Cute, I didn't think of that one.

I hope this helps. If you need more fiddling with this let me know and I'll try to think up some alternative solutions.

"Jim Thompson" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com...

Hello Jim, I will express it in a general form.

IF (number-INT(number) > 0.5 THEN result = -( INT(number) + 1 - number ) ELSE result = number - INT(number)

I assume there is an INT-function and an IF-function in PSPICE.

Best Regards, Helmut

"Jim Thompson" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com...

Hello Jim, this is mostly the same, but your wish was:

goal yours

10.499 -> 0.49 0.499 10.500 -> 0.500 -0.500 10.501 -> -0.499 -0.499

Ok, I assume you can live with a small change of your requirement.

Decimal when Decimal is < 0.5

-(1-Decimal) when Decimal is >= 0.5

Best Regards, Helmut

On Fri, 04 Mar 2005 12:04:51 -0700, Jim Thompson wroth:

I would suggest using a PIC.

Jim "Foggy in the evening" Meyer

Try thinking of it as an analogue opamp problem, with a Vin and a Vout.

Offset Vin by -0.5, full wave rectify it, correct for the offset.

Vout = 0.5 - ABS(Vin - 0.5).

Vin Vout

0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0

--
Tony Williams.

That might be the answer, BUT with NEARLY ideal diodes.

My expression, N - Round(N), works by itself, but the sharp discontinuities cause insurmountable convergence issues.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

Nah- it is fundamentally a discontinuous function and that rules out linear analog computation. Going back to the less obvious algebra where a simple guess will not suffice yields the following argument: View in a fixed-width font such as Courier.

F(X)=0.5-FRACT(0.5-X)

+0.5| /x /x /x | / | / | / | ^ | / / / | | / | / | / | |/ / / F(X) 0------------1------------2-----------3---> X | / / / | | | / | / | / ^ | / / / | | / | / | / -0.5| o/ o/ o/

x==LIM F(Y)=F(X) i.e. F(X) "left" continuous Y->X(-)

o== right limit discontinuity

F(X)= (X-0.5) MOD (0,1] -0.5 , modulo a half-open interval

FRACT(Y)= Y MOD [0,1) and 1-FRACT(-Y)=Y MOD (0,1]

Then F(X)= 1-FRACT(0.5-X)-0.5= 0.5- FRACT(0.5-X)

CHECK: EACH INTEGER n>=0, FRACT (-(n+0.5))=0.5 AND 0.5-0.5=0

EACH INTEGER n+y 0

So?

The real issue turns out to be differentiability.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

LTSpice has FLOOR built in and it is faster than using TAN to get there.

--
--
kensmith@rahul.net   forging knowledge

It seems that all those functions are going to have differentiability problems.

If you have do have access to the functions used to define those then

-ATAN(K*(X-1/2))/PI+X-1/2

seems to approximate what you want and is a smooth function, where K is a positive constant, the larger you make it the closer you are to a sawtooth but the larger the negative spike the derivative will have. K perhaps somewhere between 10 and 40 might serve your purposes.

Or, if you have hyperbolic tangent, or can build it from e^x, then

-TANH(K*(X-1/2))/2+X-1/2

also seems to approximate what you want and is a smooth function.

And, if I understood your earlier comment, that you wanted your function to linearly increase for increasing x, then either of these satisfy that, unlike x-ROUND(x) that is a sawtooth repeating over and over and not increasing beyond x=1.

Sawtooth _repeating_ IS what I want.

But I do have TANH available.

Thanks for the pointer.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

Aha! Sweet! Thanks! Nice and smooth! Now I'll try closing the loop :-)

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.