Exploring the evolution of Reionisation using a wavelet transform and
  the light cone effect
  The Cosmic Dawn and Epoch of Reionisation, during which collapsed structures
produce the first ionising photons and proceed to reionise the intergalactic
medium, span a large range in redshift (z~30-6) and time (t_{age} ~
0.1-1.0~Gyr). Exploration of these epochs using the redshifted 21~cm emission
line from neutral hydrogen is currently limited to statistical detection and
estimation metrics (e.g., the power spectrum) due to the weakness of the
signal. Brightness temperature fluctuations in the line-of-sight (LOS)
dimension are probed by observing the emission line at different frequencies,
and their structure is used as a primary discriminant between the cosmological
signal and contaminating foreground extragalactic and Galactic continuum
emission. Evolution of the signal over the observing bandwidth leads to the
`line cone effect' whereby the HI structures at the start and end of the
observing band are not statistically consistent, yielding a biased estimate of
the signal power, and potential reduction in signal detectability. We implement
a wavelet transform to wide bandwidth radio interferometry experiments to probe
the local statistical properties of the signal. We show that use of the wavelet
transform yields estimates with improved estimation performance, compared with
the standard Fourier Transform over a fixed bandwidth. With the suite of
current and future large bandwidth reionisation experiments, such as with the
300~MHz instantaneous bandwidth of the Square Kilometre Array, a transform that
retains local information will be important.
