Kind of Simple but its bugging me?

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Bugzy

Joined: 19 Apr 2007
Posts: 16

24 May 2007 15:17 Kind of Simple but its bugging me?

What will be the derivative of sat(y) function where lets say y=-2x1-3x2-5x3.
or in general what will be the derivative of a saturation function.

Thanx in advance.

v_c

Joined: 11 Oct 2005
Posts: 468
Helped: 84

24 May 2007 22:14 Re: Kind of Simple but its bugging me?

Is the saturation function you are described given by
$3$sat(x) = x, \,\,\, -1 \le x \le 1$
$3$sat(x) = 1, \,\,\, x > 1$
$3$sat(x) = -1, \,\,\, x < -1$

If this is true, then the derivative would be zero in the regions >1 and <-1
and 1 in regions between -1 and 1. For your case I am guessing that
derivative of $3$sat(-2x_1-3x_2-5x_3)$ would be 0 if $3$-2x_1-3x_2-5x_3 > 1$ and $3$-2x_1-3x_2-5x_3 < -1$ .

I am not sure about the region $3$-1 \le (-2x_1-3x_2-5x_3) \le 1$ , perhaps all the partial derivatives with respect to $3$x_1, x_2, x_3$ in this region should equal 1.

Best regards,
v_c