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

bode

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

Jav_Rock
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  • Looks odd to me. The blue phase numbers are a bit odd too? What exactly are $a$ and $b$? –  Jun 12 '12 at 07:26
  • 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. –  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, ...? –  Jun 12 '12 at 18:09
  • @copper.hat do you mean to do get a value at 0 Hz? In that case, i expect that a and b to be zero, as it will be a coefficient multiplied by zero (although I will have to verify this later tonight). For your second question, I can't say for sure that the system is LTI, but essentially it is transfer functions multiplied and then summed. –  Jun 12 '12 at 19:03
  • Sorry, I didn't really mean DC. I was wondering what the values of $a,b,a+b$ were (as elements of $\mathbb{C}$) at a low frequency, say $10^{-6}$ Hz. Just to see if it matches up with expectations. –  Jun 12 '12 at 19:50
  • @copper.hat at $10^{-4}$, I have for $a$: 484 dB/4880 degrees $b$: -114 dB/-180 degrees and $a+b$: -60.6 dB/-271 degrees. At first glance it doesn't appear to add up, but I think there is something to do with the complex numbers here that I might be missing. –  Jun 13 '12 at 04:43
  • as an addendum, what I tried to do is write $a$ and $b$ as complex numbers (evaluated at $f = 10^-4$) to see if I could get $a+b$. I got $a = -1.484710^{24}-i5.4010^{23}$ and $b=-210^-6$. According to this, $b$ should be negligible, so the magnitude of $a+b = 20log(1.57910^{24})$ and the phase is -160 degrees. This is kind of what I expected to get, but certainly does not match with my plot. –  Jun 13 '12 at 05:34
  • Yes, something strange indeed. Can you generate the response at an array of frequencies and plot the results yourself? –  Jun 13 '12 at 07:10
  • Two points (a) we prefer not to have cross-posts. I'm inclined to agree with @Dilip that this question belongs much better on DSP. The reason is that the answer to this question is more likely having to do with "incorrect" use of MatLab than having to do with "Mathematics" (since it is already established that the "result" from the signal addition is nonsense). Which leads to (b) How exactly are you representing your systems a and b in MatLab? Are you sure the operator a+b on those objects behave as you expected? –  Jun 13 '12 at 07:49
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    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. –  Jun 13 '12 at 17:17

1 Answers1

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This question is old, but for the benefit of the next person stumbling across it: You have to multiply transfer functions in order to "add" them in the bode plot.

jcsjcs
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