Radio-frequency pulses are widespread for the control of quantum bits and the execution of operations in quantum computers. The ability to tune key pulse parameters such as time-dependent amplitude, phase, and frequency is essential to achieve maximal gate fidelity and mitigate errors. As systems scale, a larger fraction of the control electronic processing will move closer to the qubits, to enhance integration and minimise latency in operations requiring fast feedback. This will constrain the space available in the memory of the control electronics to load time-resolved pulse parameters at high sampling rates. Cubic spline interpolation is a powerful and widespread technique that divides the pulse into segments of cubic polynomials. We show an optimised implementation of this strategy, using a two-stage curve fitting process and additional symmetry operations to load a high-sampling pulse output on an FPGA. This results in a favourable accuracy versus memory footprint trade-off. By simulating single-qubit population transfer and atom transport on a neutral atom device, we show that we can achieve high fidelities with low memory requirements. This is instrumental for scaling up the number of qubits and gate operations in environments where memory is a limited resource.