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In radio astronomy obtaining a high dynamic range in synthesis imaging of wide fields requires a correction for time and directiondependent effects. Applying direction-dependent correction can be done by either partitioning the image in facets and applying a direction-independent correction per facet, or by including the correction in the gridding kernel (AW-projection). An advantage of AW-projection over faceting is that the effectively applied beam is a sinc interpolation of the sampled beam, where the correction applied in the faceting approach is a discontinuous piece wise constant beam. However, AW-projection quickly becomes prohibitively expensive when the corrections vary over short time scales. This occurs for example when ionospheric effects are included in the correction. The cost of the frequent recomputation of the oversampled convolution kernels then dominates the total cost of gridding. Image domain gridding is a new approach that avoids the costly step of computing oversampled convolution kernels. Instead lowresolution images are made directly for small groups of visibilities which are then transformed and added to the large uv grid. The computations have a simple, highly parallel structure that maps very well onto massively parallel hardware such as graphical processing units (GPUs). Despite being more expensive in pure computation count, the throughput is comparable to classical Wprojection. The accuracy is close to classical gridding with a continuous convolution kernel. Compared to gridding methods that use a sampled convolution function, the new method is more accurate. Hence the new method is at least as fast and accurate as classical W-projection, while allowing for the correction for quickly varying direction-dependent effects.

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Context. Experiments that try to observe the 21-cm redshifted signals from the Epoch of Reionization using interferometric lowfrequency instruments have stringent requirements on the processing accuracy. Aims. We analyse the accuracy of radio interferometric gridding of visibilities with the aim to quantify the power spectrum bias caused by gridding, ultimately to determine the suitability of different imaging algorithms and gridding settings for 21-cm power spectrum analysis. Methods. We simulate realistic Low-Frequency Array (LOFAR) data, and construct power spectra with convolutional gridding and w-stacking, w-projection, image domain gridding and without w-correction. These are compared against directly Fourier transformed data. The influence of oversampling, kernel size, w-quantization, kernel windowing function and image padding are quantified. The gridding excess power is measured with a foreground subtraction strategy, for which foregrounds have been subtracted using Gaussian progress regression, as well as with a foreground avoidance strategy. Results. Constructing a power spectrum that has a bias significantly lower compared to the expected EoR signals is possible with the tested methods, but requires a kernel oversampling factor of at least 4000 and, when using w-correction, at least 500 w-quantization levels. These values are higher than typical values used for imaging, but are computationally feasible. The kernel size and padding factor parameters are less crucial. Among the tested methods, image domain gridding shows the highest accuracy with the lowest imaging time.Conclusions. LOFAR 21-cm power spectrum results are not affected by gridding. Image domain gridding is overall the most suitable algorithm for 21-cm Epoch of Reionization power spectrum experiments, including for future Square Kilometre Array (SKA) EoR analyses. Nevertheless, convolutional gridding with tuned parameters results in sufficient accuracy for interferometric 21-cm Epoch of Reionization experiments. This holds also for w-stacking for wide-field imaging. The w-projection algorithm is less suitable because of the kernel oversampling requirements, and a faceting approach is unsuitable due to the resulting spatial discontinuities.

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We present and implement the concept of the Fourier-domain dedispersion (FDD) algorithm, a brute-force incoherent dedispersion algorithm. This algorithm corrects the frequency-dependent dispersion delays in the arrival time of radio emission from sources such as radio pulsars and fast radio bursts. Where traditional time-domain dedispersion algorithms correct time delays using time shifts, the FDD algorithm performs these shifts by applying phase rotations to the Fourier-transformed time-series data. Incoherent dedispersion to many trial dispersion measures (DMs) is compute-, memory-bandwidth-, and input-output-intensive, and dedispersion algorithms have been implemented on graphics processing units (GPUs) to achieve high computational performance. However, timedomain dedispersion algorithms have low arithmetic intensity and are therefore often memory-bandwidth-limited. The FDD algorithm avoids this limitation and is compute-limited, providing a path to exploit the potential of current and upcoming generations of GPUs. We implement the FDD algorithm as an extension of the dedisp time-domain dedispersion software. We compare the performance and energy-to-completion of the FDD implementation using an NVIDIA Titan RTX GPU against both the standard version and an optimized version of dedisp. The optimized implementation already provides a factor of 1.5 to 2 speedup at only 66% of the energy utilization compared to the original algorithm. We find that the FDD algorithm outperforms the optimized time-domain dedispersion algorithm by another 20% in performance and 5% in energy-to-completion when a large number of DMs ( 512) are required. The FDD algorithm provides additional performance improvements for fast-Fourier-transform-based periodicity surveys of radio pulsars, as the Fourier transform back to the time domain can be omitted. We expect that this computational performance gain will further improve in the future since the Fourier-domain dedispersion algorithm better matches the trends in technological advancements of GPU development.

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