# adding bode plots together?

I am trying to understand the bode plot result I have obtained.

The blue, green, and red plots are $a$, $b$, and $a+b$ respectively.

What I'm having a hard time understanding is how a+b is formed. Looking at the magnitude of $a$, it is in the range of $500 dB$ or $$10^{25}$$. Whereas, looking at $b$, it is a negative dB gain, so a number of small magnitude. Although I do expect to see the gain of $a+b$ to be lower than that of $a$, I can't explain why the drop is so significant.

Am I missing something fundamentally important here? or is this fishy to anyone else?

If it makes any difference, I directly got this plots in matlab using

bode(a,b,a+b)


TIA

• Looks odd to me. The blue phase numbers are a bit odd too? What exactly are $a$ and $b$? – copper.hat Jun 12 '12 at 7:26
• I recommend asking the moderators to migrate this to dsp.SE which is a far better fit to the topic than math.SE – Dilip Sarwate Jun 12 '12 at 11:05
• @copper.hat a and b are extremely higher order transfer functions (in the range of 1000th degree) and have complex coefficients. I'm not sure if it would be useful posting the entire thing here. As for the phase, I agree that it looks strange, but the addition of the magnitude is very troublesome to me. – suzu Jun 12 '12 at 17:06
• Can you directly evaluate the transfer functions ($a, b, a+b$) at DC and see what that gives? What are $a$, etc?, LTI systems, arrays of numbers, ...? – copper.hat Jun 12 '12 at 18:09
• Regarding (b): Yes, I would suggest generating the frequency response yourself, then plot the various quantities (ie, don't use bode). The fact that the phase response is 4880° at low frequency would be a flag for me. – copper.hat Jun 13 '12 at 17:17