  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 Nan\c{c}ay Radio Telescope with the Nan\c{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.
