FRB 121102 is the only known repeating fast radio burst source .
Here we analyze a wide-frequency-range ( 1 - 8 GHz ) sample of high-signal-to-noise , coherently dedispersed bursts detected using the Arecibo and Green Bank telescopes .
These bursts reveal complex time-frequency structures that include sub-bursts with finite bandwidths .
The frequency-dependent burst structure complicates the determination of a dispersion measure ( DM ) ; we argue that it is appropriate to use a DM metric that maximizes frequency-averaged pulse structure , as opposed to peak signal-to-noise , and find { DM } = 560.57 \pm 0.07 pc cm ^ { -3 } at MJD 57644 .
After correcting for dispersive delay , we find that the sub-bursts have characteristic frequencies that typically drift lower at later times in the total burst envelope .
In the 1.1 - 1.7 GHz band , the \sim 0.5 - 1 -ms sub-bursts have typical bandwidths ranging from 100 - 400 MHz , and a characteristic drift rate of \sim 200 MHz/ms towards lower frequencies .
At higher radio frequencies , the sub-burst bandwidths and drift rate are larger , on average .
While these features could be intrinsic to the burst emission mechanism , they could also be imparted by propagation effects in the medium local to the source .
Comparison of the burst DMs with previous values in the literature suggests an increase of \Delta { DM } \sim 1 - 3 pc cm ^ { -3 } in 4 years , though this could be a stochastic variation as opposed to a secular trend .
This implies changes in the local medium or an additional source of frequency-dependent delay .
Overall , the results are consistent with previously proposed scenarios in which FRB 121102 is embedded in a dense nebula .