Please help me understand how EQ filters work

[ojezu]

I had an idea, I tested it theoretically but in practical case it failed.
First an experiment
I took flat target curve,
made three filters: low -600, mid 600-2400 and high 2400-

and with filters I calculated responses from target curve

then I made "trace arithmetic" and first made sum (A+B) of filtered low and high

and than added filtered mid to results and got input target curve.

it gone as expected.

And now I have loudspeaker measurement, measurement after repairing tweeter

with worrying me dip around 2.55 kHz and was interested if I can check if this tweeter or mid-range domain (*).
And with prepared filters I made filtered responses,
something I thought will make simulation of speaker system crossover and help me understand which speaker makes which frequencies.
600 and 2400 Hz are ELAC 58.2 crossovers

added low to high, low frequencies and high frequencies results are like original measurement

but, when I add mid filtered part I don't get what I expect,

Can't get original signal back:

where is my mistake?
What is the result "(low+high) + mid"
Can it be done better?

(*) Answer is "mostly tweeter",
but is this opinion right if subtraction (?) and addition back does not sum to zero?

 

[jtalden]

The polarity of the mid driver needs to be inverted.