Efficient Partial Recomputation-Based Fault Detection Approaches for Z-transform

The Z-transform is a fundamental and strong tool being widely utilized in signal processing and various other applications such as communications and networking. By analyzing the Z-transform of a signal, one can extract critical information about its stability, causality, frequency response, energy and power, and overall behavior of the signal. However, errors caused either by environmental changes or malicious injections in large-scale integration (VLSI) implementations can critically compromise the integrity and reliability of its output. Failure to detect such faults may result in unpredictable, erroneous, and misleading function analyses. Therefore, the ability to detect soft errors and faults before accepting the results is of paramount importance. In this article, we propose an efficient fault detection method that combines algorithmic-level checks with partial recomputation to identify both transient and permanent faults with a high error coverage rate across various injection scenarios. The AMD/Xilinx field-programmable gate array (FPGA) implementation of our design demonstrated only a modest increase in time and area overhead. To the best of our knowledge, fault detection for the Z-transform function has not been previously studied.