Hardware implementation of a high-resolution auto-tuned time-frequency signal analyzer over TMS320C6713 DSK using a compact support polynomial kernel

This paper explores the hardware implementation of an embedded time-frequency signal analyzer using the Polynomial Cheriet-Belouchrani Distribution (PCBD) with a compact kernel. We implemented this distribution on a Texas Instruments TMS320C6713 Digital Signal Processing Starter Kit (DSK). Compared to other quadratic time-frequency distributions (TFDs), the PCBD requires a low computational cost due to its compact support nature, which reduces the number of points needing calculation. The sole smoothing parameter γ that controls its kernel's bandwidth is an integer, simplifying the unsupervised approach. To ensure that the realized TF analyzer is automatically tuned, an accurate low-complexity performance measure must be employed to achieve optimal concentration, resolution, and cross-term suppression. Failure to do so may result in missing or degraded essential signal characteristics. The Stankovic measure has been identified as the preferred measure among many others for finding the optimal value of the integer γ. We have also been exploring methods to optimize the execution of various algorithms by taking advantage of specific mathematical properties inherent in the compact polynomial kernel and the PCBD. Additionally, we propose a recursive method to minimize the computation cost associated with the discrete PCB kernel. These strategies are designed to enhance efficiency and reduce the required machine cycles. To compare the performances provided, we thoroughly evaluate the numerical complexity of our implemented distribution, both with and without mathematical optimization. The findings obtained demonstrate the effectiveness of using the TMS320C6713 DSK board to design a high-resolution auto-tuned time-frequency signal analyzer. We not only achieved a perfect match with the results obtained from MATLAB, but the optimized approach also reduced runtime by approximately 19 % to 47 % compared to the direct method, depending on the input signal length and the number of loops required to optimize the Stankovic measure. A comparative analysis was also conducted to assess the effectiveness of our approach in relation to other linear and quadratic TF analyzers, including those implemented on field-programmable gate arrays (FPGAs).