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Need help finding equation for this graph

Attachment 27165Hi,

I am trying to find the equation used to generate this graph shown in the attachment (any one of the lines).

I suspect it is some type of log function, but I have been away from higher math for many, many years.

Any help would be greatly appreciated.

Thanks,

Flygirl

Attachment 27165

Re: Need help finding equation for this graph

You can probably use fourier series to represent this graph over the different intervals

Re: Need help finding equation for this graph

Quote:

Originally Posted by

**flygirl71** Attachment 27165Hi,

I am trying to find the equation used to generate this graph shown in the attachment (any one of the lines).

I suspect it is some type of log function, but I have been away from higher math for many, many years.

Any help would be greatly appreciated.

Thanks,

Flygirl

Attachment 27165

Hi flygirl71! :)

That looks to be some sort of Bode plot.

For instance a Bode plot of $\displaystyle \frac{s + 10}{s + 1}$ looks like this (link included).

It is typically approximated by a straight-line-plot as you have, with corner points at s=1 (down) and s=10 (back to horizontal).

Re: Need help finding equation for this graph

None of the standard functions, except for the absolute value, has a graph consisting of straight line segments. Such graphs can be produced by piecewise-defined function. The linear function that goes through points $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2,y_2)$ is given by $\displaystyle y(x)=y_1+\frac{y_2-y_1}{x_2-x_2}(x-x_1)$. The top graph goes through (10, -3.2) and (500, -2.3). Therefore, the middle portion of the top graph is given by $\displaystyle g(x)=-3.2+\frac{-2.3-(-3.2)}{490}(x-10)$, and the full top graph is given by

$\displaystyle f(x)=\begin{cases}-3.2 & x\le 10\\g(x) & 10<x<500\\ -2.3 & x\ge500\end{cases}$

Another way to define f is using min and max functions.

$\displaystyle f(x)=\max(-3.2,\min(-2.3,g(x)))$