Finite precision arithmetic in Polyphase Filterbank implementations

Abstract

The MeerKAT is the most sensitive radio telescope in its class, and it is important that systematic effects do not limit the dynamic range of the instrument, preventing this sensitivity from being harnessed for deep integrations. During commissioning, spurious artefacts were noted in the MeerKAT passband and the root cause was attributed to systematic errors in the digital signal path. Finite precision arithmetic used by the Polyphase Filterbank (PFB) was one of the main factors contributing to the spurious responses, together with bugs in the firmware. This thesis describes a software PFB simulator that was built to mimic the MeerKAT PFB and allow investigation into the origin and mitigation of the effects seen on the telescope. This simulator was used to investigate the effects in signal integrity of various rounding techniques, overflow strategies and dual polarisation processing in the PFB. Using the simulator to investigate a number of different signal levels, bit-width and algorithmic scenarios, it gave insight into how the periodic dips occurring in the MeerKAT passband were the result of the implementation using an inappropriate rounding strategy. It further indicated how to select the best strategy for preventing overflow while maintaining high quantization effciency in the FFT. This practice of simulating the design behaviour in the PFB independently of the tools used to design the DSP firmware, is a step towards an end-to-end simulation of the MeerKAT system (or any radio telescope using nite precision digital signal processing systems). This would be useful for design, diagnostics, signal analysis and prototyping of the overall instrument.