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 \sim 30 - 6 ) and time ( t _ { age } \sim 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 .