Nevena Radovic

Hardware implementation of a system for highly nonstationary two-dimensional FM signals estimation based on the sliding matrix function

Optimal filter for highly nonstationary two-dimensional (2D) FM signals estimation is developed in this paper. The developed system uses a space-varying approach in real-time analysis of 2D nonstationary signals, related to the space/spatial-frequency (S/SF) domain tool based on the 2D cross-terms-free Wigner distribution. The system is based on the correspondence of the filters region of support (FRS) to the local frequency (LF) of the filtered signal. By implementing the LF estimation, the system performs filtering of nonsationary 2D signals. The estimation has been implemented by the sliding matrix operation, which presents the central part of the developed design. The developed filter permits multiple FRS detection in the observed 2D signal point. In this way it enables a very efficient real-time filtering of nonstationary monocomponent and multicomponent FM signals, highly concentrated in the S/SF space and exposed to the high white noise. The design is proven through the verification of the sliding matrix operation. It is also tested by the simulation on the multicomponent highly nonstationary noisy signal filtering.

Pipelined design of a system for highly nonstationary FM signals estimation

Pipelined signal adaptive hardware implementation of an optimal time-frequency (TF) filter has been designed. It is based on the real-time results of TF analysis and on the TF analysis-based instantaneous frequency (IF) estimation. The implemented pipelining technique allows the filter to overlap in execution unconditional steps performimg in neighboring TF instants and, therefore, to significantly enhance time performance. The improvement corresponding to the one clock cycle by a TF point is achieved, which means that the improvement by a TF point can reach even 50% in some TF points. The design is tested on multicomponent signals.).

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

Real-time implementation of the optimal filter for highly nonstationary two-dimensional (2D) signal estimation is designed. It is based on the real-time results of 2D nonstationary signal analysis, on the correspondence of the filters region of support (FRS) to the signals local frequency (LF) and on the real-time LF estimation, implemented by the sliding matrix operation. Multiple FRS detection in the observed 2D signal point is provided by the proposed system, enabling very efficient real-time estimation of nonstationary monocomponent and multicomponent frequency-modulated (FM) noisy signals. The design is proven through the verification of the sliding matrix operation, that represents central part of the designed filter. As well, it is tested by estimation of the nonstationary monocomponent and multicomponent FM signals exposed to the high white noise.

Real-time design of a space/spatial-frequency optimal filter for highly nonstationary two-dimensional signal estimation

Two-dimensional (2D) optimal filter for highly nonstationary 2D signal estimation is developed. It is based on the real-time results of space/spatial-frequency (S/SF) analysis, on the correspondence of filters region of support (FRS) to the signals local frequency (LF) and on the real-time LF estimation algorithm, also proposed in this paper. The filter permits multiple FRS detection in the observed 2D signal point, enabling very efficient filtering (in real-time) of nonstationary monocomponent and multicomponent FM signals, highly concentrated in the S/SF space and exposed to the high white noise influence. The filter is verified on various mono- and multicomponent 2D test signals.

Local frequency estimation-based space/spatial-frequency optimal filter developed in the RTL design methodology versus the corresponding GPU-based implementations

Processing of nonstationary one-dimensional and two-dimensional (2D) signals are usually performed by using high numerically consuming time-frequency and space/spatial-frequency (S/SF) tools, respectively. Being numerically quite complex, these solutions require significant time for calculation and then are usually unsuitable for real-time analysis, but also their application is severely restricted in practice. Hardware implementations, when possible, can overcome these problems. Besides, numerical complexity greatly increases in the 2D signals case, so that demands for hardware implementations of systems for processing of these signals, including their filtering, are more emphasized. However, chip dimensions are significantly enlarged in this case, as well as the power consumption and cost, while the processing speed is seriously reduced. Therefore, having in mind technology limitations in hardware realizations, these systems usually cannot be implemented. To overcome these problems, the register transfer level (RTL) design methodology-based and signal adaptive development of the S/SF filter, suitable for realtime and on-a-chip implementation, has been designed in [1]. However, to significantly suppress time requirements of the space/spatial-frequency-based systems, the graphic processing units (GPUs)-based implementation of these systems can be considered as the possible solution. In this paper, the RTL design methodology-based solution from [1] is compared with the corresponding GPUs-based solutions.

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

Possibility of the pipelining technique application in a local frequency estimation-based system for nonstationary two-dimensional (2D) FM signals estimation, initially observed in [1], [2], but completely developed, implemented (in FPGA), and adapted (extended to the highly nonstationary signals case) in [3], is considered here. The applied technique allows the implemented filter to overlape in execution unconditional steps performing in neighboring space/spatial-frequency (S/SF) instants and, therefore, to significantly improve execution time. In this way, the improvement in execution time coresponding to the one clock cycle (CLK) by an S/SF point is achieved, which means that the improvement by an S/SF point can reach 50% in a great part of S/SF space. The achieved improvement in execution time by an S\SF point is presented on the example of the multicomponent nonstationary noisy signal filering.

Signal adaptive hardware implementation of a smart system for time-frequency signal analysis

This paper outlines the development of an efficient multi-cycle, signal adaptive hardware design of a system for time-frequency (TF) signal analysis, suitable for real-time implementation on an integrated chip. The proposed design allows the implemented system to take variable number of clock (CLK) cycles (the only necessary ones regarding the high auto-terms quality) in different TF points within the execution. In this way, the proposed design optimizes execution time of the implemented system, producing a pure cross-terms-free Wigner distribution (WD) signal representation. Additionally, the proposed multi-cycle design optimizes both critical design performances, related to the complexity of the hardware, and the CLK cycle time. The design has been verified by a field-programmable gate array (FPGA) circuit design, suitable of performing processing of nonstationary signals in real-time.

Improved design of a space/spatial-frequency filter

The improved space/spatial-frequency (S/SF) system for highly nonstationary two-dimensional (2D) FM signal estimation is considered here. The improvement is achieved by the pipelining technique application in the optimal nonstationary filter implementation based on the 2D cross-terms-free Wigner distribution (2D CTFWD) hardware design and on the 2D CTFWD-related local frequency (LF) estimation in a noisy environment. The applied technique allows the implemented filter to overlape in execution unconditional steps performimg in neighboring S/SF points. In this way, the improvement (in execution time) coresponding to the one clock cycle by a S/SF point is achieved, which means that the improvement by a S/SF point can reach even 50% in a great part of S/SF space.

A pipelined time-frequency filter implementation

Multiple-clock-cycle pipelined signal adaptive design of an optimal nonstationary filtering system has been considered here. It is based on the real-time results of time-frequency (TF) analysis and on the TF analysis-based instantaneous frequency (IF) estimation. The pipelining technique allows the implemented filter to overlap in execution unconditional steps performing in neighboring TF instants and, consequently, to significantly improve the execution time. In this way, the improvement in execution time corresponding to the one clock cycle by a TF point is achieved, which means that the improvement by a TF point can reach even 50% in a great part of TF plane. The design and its improvement are tested on the multicomponent signals.