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composite signal

How can we calculate the bandwidth of distinct signals like this? I guess the right answer is 90 - 10 = 80 Hz. But I have a hard time understanding why is this calculated in that way. I thought the bandwidth is calculated by the diversity of signals and since there aren't in-between frequencies like 11, 12... in the image there are 5 signals, shouldn't the bandwidth be 5 Hz? What am I missing here?

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  • $\begingroup$ To answer this question, first you need to define "bandwidth". There are many definitions, and each gives a different answer. $\endgroup$
    – MBaz
    Dec 5, 2020 at 17:09
  • $\begingroup$ I only used Herz as bandwidth in my question so I thought it would be clear that I am asking about bandwidth as Herz @MBaz $\endgroup$
    – Abcd
    Dec 5, 2020 at 19:02
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    $\begingroup$ I don’t think the units were in question. The point is that bandwidth could have different definitions based on context. What are you doing with it, or do you have a preferred definition which could be used to answer the question? $\endgroup$
    – Dan Szabo
    Dec 5, 2020 at 19:36
  • $\begingroup$ What @DanSzabo said: bandwidth is always measured in Hz, but there are many ways to measure it. $\endgroup$
    – MBaz
    Dec 5, 2020 at 20:45

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Your intuition is basically correct. I'm sure they want the answer of 80Hz because that is the bandwidth that you would need to carry these 5 waves, but pure sinusoids that aren't modulated at all can not carry any information. If they don't carry any information then they are infinitely narrow. (0Hz rather than 5Hz). You could modulate them individually to higher frequencies and put them very close together with any loss of information.

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