Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator -- IV. Wideband analysis

We present a Wideband Tapered Gridded Estimator (TGE), which incorporates baseline migration and variation of the primary beam pattern for neutral hydrogen (H0.5mm I) 21-cm intensity mapping (IM) with large frequency bandwidth radio-interferometric observations. Here we have analysed 394-494 \, MHz $(z = 1.9 - 2.6)$ uGMRT data to estimate the Multi-frequency Angular Power Spectrum (MAPS) C₍Δν) from which we have removed the foregrounds using the polynomial fitting (PF) and Gaussian Process Regression (GPR) methods developed in our earlier work. Using the residual C₍Δν) to estimate the mean squared 21-cm brightness temperature fluctuation Δ²(k), we find that this is consistent with 0 ± 2 σ in several k bins. The resulting 2σ upper limit Δ²(k) < (4.68)² \, mK² at k=0.219\,Mpc⁻¹ is nearly $15$ times tighter than earlier limits obtained from a smaller bandwidth (24.4 \, MHz) of the same data. The 2σ upper limit [Ω_ H0.5mm I b_ H0.5mm I] < 1.01 × 10⁻² is within an order of magnitude of the value expected from independent estimates of the H0.5mm I mass density Ω_ H0.5mm I and the H0.5mm I bias b_ H0.5mm I. The techniques used here can be applied to other telescopes and frequencies, including ~ 150 \, MHz Epoch of Reionization observations.