In recent years, instrumentation enabling pulsar observations with unprecedentedly high fractional bandwidth has been under development which can be used to substantially improve the precision of pulsar timing experiments. The traditional template-matching method used to calculate pulse times-of-arrival (ToAs), may not function effectively on these broadband data due to a variety of effects such as diffractive scintillation in the interstellar medium, profile variation as a function of frequency, dispersion measure (DM) evolution and so forth. In this paper, we describe the channelised Discrete Fourier Transform method that can greatly mitigate the influence of the aforementioned effects when measuring ToAs from broadband timing data. The method is tested on simulated data, and its potential in improving timing precision is shown. We further apply the method to PSR J1909$-$3744 data collected at the Nanc{c}ay Radio Telescope with the Nanc{c}ay Ultimate Pulsar Processing Instrument. We demonstrate a removal of systematics due to the scintillation effect as well as improvement on ToA measurement uncertainties. Our method also determines temporal variations in dispersion measure, which are consistent with multi-channel timing approaches used earlier.
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