Real-time implementation of the optimal two-dimensional filter for highly nonstationary frequency-modulated signal estimation

Possibility of the pipelining technique application in a space/spatial-frequency filter implementation based on the local frequency estimation

“…An optimal nonstationary 2D filter (1), based on the 2D CTFWD implementation from [17] and on the real-time 2D CTFWD-based LF estimation (3), implemented through the sliding matrix operation, has been initially considered in [1], [2], and completely developed, implemented, and extended for the highly nonstationary signals case in [3]. To help the filter to improve the execution time/processing speed, possibility of the pipelining technique application in the implementation [1]- [3] will be considered here.…”

“…By each STFTLoad/CTFWDStore cycle, they are stored into the FRS detection module, implemented to estimate FRS ( , ) H L n k , to provide movement through the CTFWD samples, and to implement real-time procedure for LF estimation, which follows definition (3), as described in detail in [1]- [3]. This procedure, initially observed in [1], [2] and improved in [3], tests an LF existence in an FF point (k 1 ,k 2 ), k 1 ,k 2 =-N/2+1,..., N/2 for the observed signal point (n 1 ,n 2 ) by grouping frequency-only-dependent 2D CTFWDs, symmetrically distributed around (k 1 ,k 2 ), …”

“…It follows the same implementation principles as the 2D CTFWD design from [17] and the non-pipelined filter design from [1]- [3]. Therefore, it retains desirable characteristics of the signal adaptive MCI designs from [1]- [3], [17], regarding calculation and implementation complexity, as well as the execution time. Besides, by applying the pipelining technique, the proposed design additionally improves S/SF filtering execution time (approximately for 20-35%, depending on the estimated signal shape), overcoming the corresponding S/SFDbased filters regarding almost all critical design performances.…”

“…Besides, GPUs only provide high performance for quite parallel problems such are the non-adaptive LF estimation and S/SF filtering solutions, [11], [14], [21], [22]. However, nonadaptive solutions suffer from the emphasized interference effects (cross-terms), [11], [22], and cannot achieve as high LF estimation/filtering quality, [4], [5], [11], [12], as the signal adaptive-based solution considered in [1], [2] and completely developed in [3].…”

“…An optimal, local frequency (LF) estimation-based filter, suitable for real-time and on-a-chip implementation and initially considered in [1], [2], has been completely developed based on the register transfer level (RTL) design methodology and implemented in the standard FPGA devise in [3]. In this paper we consider the possibility of the pipelining technique application in the optimal LF estimation-based filter implementation from [1]- [3], but also possibility to extend the pipelined 1D optimal filter from [9] to the 2D FM signals case.…”