This research paper proposes a novel robust high-performance power spectrum estimator, and bispactral power density analyzer that has outstanding capabilities in estimating noisy biomedical signal's power spectrum, and bispectrum. Biomedical signals usually are exposed to several sources of noises such as electrical noise from environmental noise from external sources, electrical equipment, and biological noise from the body. Therefore, accuracy and reliability are the most important feature of these systems in processing non-stationary biomedical signals. The proposed computationally-efficient architecture is based on a radix-8 memory-based 1024-point Blackman-Tuckey method power spectral density (PSD) estimator. The proposed nonparametric estimator uses a novel shared-resource CORDIC-Ⅱ unit to avoid multiplications in FFT computation, as well as filtering operations implemented in folded architectures. In order to merge two FFTs, the module uses bidirectional fractional delay filters to estimate half delay samples. By using modified safe-scaling, valid final output would be achieved, without any averaging operation. The proposed and competing designs are implemented on Artix-7 FPGA which is an ideal option for DSP applications. As final results demonstrate, the hardware has a remarkable capability in operating in short word-lengths which allows high-performance in low-power applications to compute the power spectrum and bicoherence of a vital signal.