how to find the frequency of this nonperiodic composite signal?
I think the question includes a contradiction, the frequency serves to explain the periodicity of a signal in the frequency domain. Then in case of non-periodic signals we use the term bandwith that is the term that indeed that book used, at the end of the paragraph it says, quoted "The bandwidth needed is 5.5124 MHz".
The signal shown is simple so most likely a combination of a few sine waveforms, the highest frequency I see in there is 8Hz, it repeats evey square and there are 8 squares in one second.
I think the textbook's intention when speaking about analog TV is a bit different to what you try to do.